U.S. DEPARTMENT OF

EDUCATION OFFICE OF

EDUCATIONAL RESEARCH

AND IMPROVEMENT

NATIONAL CENTER FOR EDUCATION STATISTICS

Findings from the National

Assessment of Educational Progress

Findings from the National

Assessment of Educational Progress

NAEP 1996

MATHEMATICS

State Report for

Guam
What is The Nation’s Report Card?

THE NATION’S REPORT CARD, the National Assessment of Educational Progress (NAEP), is the only nationally representative and

continuing assessment of what America’s students know and can do in various subject areas. Since 1969, assessments have been conducted

periodically in reading, mathematics, science, writing, history/geography, and other fields. By making objective information on student

performance available to policymakers at the national, state, and local levels, NAEP is an integral part of our nation’s evaluation of the condition

and progress of education. Only information related to academic achievement is collected under this program. NAEP guarantees the privacy of

individual students and their families.

NAEP is a congressionally mandated project of the National Center for Education Statistics, the U.S. Department of Education. The

Commissioner of Education Statistics is responsible, by law, for carrying out the NAEP project through competitive awards to qualified

organizations. NAEP reports directly to the Commissioner, who is also responsible for providing continuing reviews, including validation studies

and solicitation of public comment, on NAEP’s conduct and usefulness.

In 1988, Congress established the National Assessment Governing Board (NAGB) to formulate policy guidelines for NAEP. The Board is

responsible for selecting the subject areas to be assessed from among those included in the National Education Goals; for setting appropriate

student performance levels; for developing assessment objectives and test specifications through a national consensus approach; for designing the

assessment methodology; for developing guidelines for reporting and disseminating NAEP results; for developing standards and procedures for

interstate, regional, and national comparisons; for determining the appropriateness of test items and ensuring they are free from bias; and for

taking actions to improve the form and use of the National Assessment.

The National Assessment Governing Board

Honorable William T. Randall, Chair

Former Commissioner of Education

State of Colorado

Denver, Colorado

Mary R. Blanton, Vice Chair

Attorney

Salisbury, North Carolina

Patsy Cavazos

Principal

W.G. Love Accelerated Elementary School

Houston, Texas

Catherine A. Davidson

Secondary Education Director

Central Kitsap School District

Silverdale, Washington

Edward Donley

Former Chairman

Air Products & Chemicals, Inc.

Allentown, Pennsylvania

Honorable James Edgar

Member Designate

Governor of Illinois

Springfield, Illinois

James E. Ellingson

Fourth-Grade Classroom Teacher

Probstfield Elementary School

Moorhead, Minnesota

Thomas H. Fisher

Director, Student Assessment Services

Florida Department of Education

Tallahassee, Florida

Michael J. Guerra

Executive Director

Secondary Schools Department

National Catholic Educational Association

Washington, DC

Edward H. Haertel

Professor of Education

Stanford University

Stanford, California

Jan B. Loveless

District Communications Specialist

Midland Public Schools

Midland, Michigan

Marilyn McConachie

Former School Board Member

Glenbrook High Schools

Glenview, Illinois

William J. Moloney

Superintendent of Schools

Calvert County Public Schools

Prince Frederick, Maryland

Honorable Annette Morgan

Former Member

Missouri House of Representatives

Jefferson City, Missouri

Mark D. Musick

President

Southern Regional Education Board

Atlanta, Georgia

Mitsugi Nakashima

First Vice-Chairperson

Hawaii State Board of Education

Honolulu, Hawaii

Michael T. Nettles

Professor of Education & Public Policy

University of Michigan

Ann Arbor, Michigan

and Director

Frederick D. Patterson Research Institute

United Negro College Fund

Honorable Norma Paulus

Superintendent of Public Instruction

Oregon State Department of Education

Salem, Oregon

Honorable Roy Romer

Governor of Colorado

Denver, Colorado

Honorable Edgar D. Ross

Judge

Territorial Court of the Virgin Islands

Christiansted, St. Croix

U.S. Virgin Islands

Fannie L. Simmons

Mathematics Coordinator

District 5 of Lexington/Richland County

Ballentine, South Carolina

Adam Urbanski

President

Rochester Teachers Association

Rochester, New York

Deborah Voltz

Assistant Professor

Department of Special Education

University of Louisville

Louisville, Kentucky

Marilyn A. Whirry

Twelfth-Grade English Teacher

Mira Costa High School

Manhattan Beach, California

Dennie Palmer Wolf

Senior Research Associate

Harvard Graduate School of Education

Cambridge, Massachusetts

Ramon C. Cortines (Ex-Officio)

Acting Assistant Secretary

Office of Educational Research

and Improvement

U.S. Department of Education

Washington, DC

Roy Truby

Executive Director, NAGB

Washington, DC
1$7,21$/&(17(5)25('8&$7,2167$7,67,&6

NAEP 1996 MATHEMATICS STATE REPORT

for

GUAM

Clyde M. Reese

Laura Jerry

Nada Ballator

In collaboration with

Peggy Carr, Jeff Haberstroh

Paul Koehler, Phillip Leung

Mary Lindquist, and John Mazzeo

June 1997

U.S. Department of Education

Office of Educational Research and Improvement

Prepared by Educational Testing Service under a cooperative

agreement with the National Center for Education Statistics.
U.S. Department of Education

Richard W. Riley

Secretary

Office of Educational Research and Improvement

Ramon C. Cortines

Acting Assistant Secretary

National Center for Education Statistics

Pascal D. Forgione, Jr.

Commissioner

Education Assessment Group

Gary W. Phillips

Associate Commissioner

June 1997

SUGGESTED CITATION

Reese, C.M., Jerry, L., and Ballator, N.

NAEP 1996 Mathematics State Report for Guam,

Washington, DC: National Center for Education Statistics, 1997.

FOR MORE INFORMATION

Contact:

Arnold A. Goldstein

202-219-1741

For ordering information on this report, write:

National Library of Education

Office of Educational Research and Improvement

U.S. Department of Education

555 New Jersey Avenue, NW

Washington, D.C. 20208-5641

or call 1-800-424-1616 (in the Washington, DC, metropolitan area call 202-219-1651).

This report also is available on the World Wide Web: http://www.ed.gov/NCES/naep

The work upon which this publication is based was performed for the National Center for Education Statistics,

Office of Educational Research and Improvement, by Educational Testing Service.

Educational Testing Service is an equal opportunity, affirmative action employer.

Educational Testing Service, ETS, and the ETS logo are registered trademarks of Educational Testing Service.
Table of Contents

HIGHLIGHTS ..........................................................................................................1

INTRODUCTION .................................................................................................11

What Was Assessed? ....................................................................................11

Who Was Assessed? .....................................................................................13

Reporting NAEP Mathematics Results ........................................................20

Interpreting NAEP Results ...........................................................................22

How Is This Report Organized? ..................................................................23

PART ONE The Mathematics Scale Score Results for Fourth- and

Eighth-Grade Students ...........................................................................................25

CHAPTER 1 Students’ Mathematics Scale Score Results ..................................27

Comparisons Between Guam and Other Participating Jurisdictions ..........31

Performance on the NAEP Mathematics Content Strands .........................37

CHAPTER 2 Mathematics Scale Score Results by Subpopulations ...................41

 Gender ...........................................................................................................42

 Race/Ethnicity ...............................................................................................45

Students’ Reports of Parents’ Highest Education Level .............................49

Title I Participation .......................................................................................53

Free/Reduced-Price Lunch Program Eligibility ...........................................55

Type of School .............................................................................................57

PART TWO The Mathematics Achievement Level Results for

Fourth- and Eighth-Grade Students ....................................................................61

CHAPTER 3 Students’ Mathematics Achievement Level Results ......................65

Description of NAEP Mathematics Achievement Levels ...........................65

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS i
CHAPTER 4 Mathematics Achievement Level Results by Subpopulations ......73

 Gender ...........................................................................................................74

 Race/Ethnicity ...............................................................................................76

Students’ Reports of Parents’ Highest Education Level .............................79

Title I Participation .......................................................................................83

Free/Reduced-Price Lunch Program Eligibility ...........................................84

Type of School .............................................................................................86

PART THREE Finding a Context for Understanding Students’

Mathematics Performance in Public Schools ....................................................89

CHAPTER 5 School Characteristics Related to Mathematics Instruction ..........91

Emphasis on Mathematics in the School .....................................................91

Resource Availability to Teachers ...............................................................93

In-School Teacher Preparation Time ...........................................................98

Parents as Classroom Aides .......................................................................100

Student Absenteeism ..................................................................................102

CHAPTER 6 Classroom Practices Related to Mathematics Instruction ...........105

NCTM Standards ........................................................................................106

Course-Taking Patterns ..............................................................................110

Instructional Emphasis ...............................................................................114

Communicating Mathematical Ideas ..........................................................118

Collaboration in Small Groups ..................................................................122

Mathematics Homework .............................................................................124

Calculator and Computer Use in the Mathematics Classroom .................129

CHAPTER 7 Influences Beyond School That Facilitate Learning

Mathematics ...................................................................................................141

Discussing Studies at Home .......................................................................141

Literacy Materials in the Home .................................................................144

Television Viewing Habits .........................................................................147

Parental Support .........................................................................................150

Student Mobility .........................................................................................152

Students’ Views About Mathematics .........................................................154

ii THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
APPENDIX A Reporting NAEP 1996 Mathematics Results for

Guam ......................................................................................................................161

APPENDIX B The NAEP 1996 Mathematics Assessment ........................179

APPENDIX C Technical Appendix: The Design, Implementation,

and Analysis of the 1996 State Assessment Program in Mathematics ......183

APPENDIX D Setting the Achievement Levels ..........................................197

APPENDIX E Teacher Preparation ................................................................201

APPENDIX F Discussion of the Grade 8 Asian/Pacific Islander

Sample ....................................................................................................................211

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS iii
iv THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

 HIGHLIGHTS

Monitoring the performance of students in subjects such as mathematics is a

key concern of the citizens, policy makers, and educators concerned with educational

reform efforts. The 1996 National Assessment of Educational Progress (NAEP) in

mathematics (as well as the two previous NAEP assessments in mathematics in 1990

and 1992) assessed the current level of mathematical achievement as a mechanism for

informing education reform. This report contains results for public school students only

for those years in which Guam participated and for which minimum participation rate

guidelines were met. Results are also presented for nonpublic school students at grades

4 and 8 for the 1996 state mathematics assessment.

What Is NAEP?

The National Assessment of Educational Progress (NAEP) is the only nationally

representative and continuing assessment of what students in the United States know and

can do in various academic subjects. NAEP is authorized by Congress and directed by

the National Center for Education Statistics of the U.S. Department of Education. The

National Assessment Governing Board (NAGB), an independent body, provides policy

guidance for NAEP.

Since its inception in 1969, NAEP’s mission has been to collect, analyze, and

produce valid and reliable information about the academic performance of students in

the United States in various learning areas. In 1990, the mission of NAEP was expanded

to provide state-by-state results on academic achievement. Participation in the

state-by-state NAEP is voluntary and has grown from 40 states and territories in 1990

to 48 in 1996.

NAEP has also become a valuable tool in tracking progress towards the National

Education Goals. The subjects assessed by NAEP are those highlighted at the 1989

Education Summit and later legislation.1 The NAEP 1996 assessment in mathematics

marks the third time the subject has been assessed with the new framework in the 1990s,

enabling policy makers and educators to track mathematics achievement since the release

of the National Council of Teachers of Mathematics (NCTM) Curriculum and

Evaluation Standards for School Mathematics2 in 1989.

1

 Executive Office of the President. National Goals for Education. (Washington, DC: Government Printing Office, 1990);

Goals 2000: Educate America Act, Pub. L. No. 103-227 (1994).

2

 National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. (Reston,

VA: NCTM, 1989).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 1
Guam

NAEP 1996 Mathematics Assessment

The NAEP mathematics assessment has been in constant evolution since its

inception in 1973. Major changes took place in the 1990s to complement the

Curriculum and Evaluation Standards for School Mathematics, that was published by the

National Council of Teachers of Mathematics (NCTM) in 1989. The NAEP 1990

mathematics assessment saw the inclusion of short constructed-response questions —

questions that asked students to provide the answer they calculated for a numerical

problem or to write a sentence or two describing the solution to a problem. Also added

in 1990 were a number of questions on which students could use calculators, protractors,

or rulers.

In 1992 the assessment included an increased number of short

constructed-response questions and, for the first time, contained extended

constructed-response questions. Extended constructed-response questions required

students to produce both a solution and a short paragraph describing the solution or its

interpretation in the context of the task. As such, these questions served as indicators

of students’ growth in the areas of reasoning, communication, and problem solving —

important processes receiving heavy emphasis in the NCTM Standards.

In 1996 the NAEP mathematics assessment continued to be revised, most notably

by continuing to increase the use of constructed-response questions. In 1990, students

spent about 30 percent of testing time on constructed-response questions. By 1992, this

percentage had increased to 35 percent, and in 1996 it exceeded 50 percent of the time

spent by students on the assessment.

The 1996 assessment maintained the same five content strands used for the 1990

and 1992 assessments — Number Sense, Properties, and Operations; Measurement;

Geometry and Spatial Sense; Data Analysis, Statistics, and Probability; and Algebra and

Functions. Two of these strands, Number Sense, Properties, and Operations and

Geometry and Spatial Sense, were revised to reflect the NCTM Standards’ emphases

on developing and assessing students’ abilities to make sense of both number/operation

and spatial settings.

The changes made to the NAEP 1996 mathematics assessment refined and

sharpened the assessment to reflect more adequately recent curricular emphases and

objectives; to include what teachers, mathematicians, and measurement experts think

should be in the assessment; and to maintain the connection with the 1990 and 1992

assessments to permit the measurement of trends in student performance since 1990.

Tables H.1 and H.2 show the distribution of mathematics scores and the

percentage of students at or above the Basic, Proficient, and Advanced achievement

levels for fourth- and eighth-grade students attending public schools in Guam in 1996.

2 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE H.1 — GRADES 4 AND 8

Distribution of Mathematics Scale Scores for Public School

Students

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

Grade 4

 Guam 188 ( 1.3) 145 ( 2.9) 166 ( 2.1) 189 ( 0.8) 212 ( 1.8) 231 ( 2.0)

 Nation 222 ( 1.0) 180 ( 1.5) 201 ( 1.3) 224 ( 1.3) 244 ( 1.0) 261 ( 1.0)

Grade 8

 Guam 239 ( 1.7) 187 ( 2.1) 213 ( 5.4) 240 ( 2.3) 267 ( 2.4) 290 ( 3.8)

 Nation 271 ( 1.2) 222 ( 2.0) 247 ( 1.2) 272 ( 1.1) 296 ( 1.4) 316 ( 2.0)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

TABLE H.2 — GRADES 4 AND 8

Percentage of Public School Students Attaining Mathematics

Achievement Levels

Advanced At or Above

Proficient

At or Above

Basic Below Basic

Grade 4

 Guam 0 (****) 3 ( 0.5) 23 ( 1.4) 77 ( 1.4)

 Nation 2 ( 0.3) 20 ( 1.0) 62 ( 1.4) 38 ( 1.4)

Grade 8

 Guam 0 ( ) 6 ( 0.8) 29 ( 1.6) 71 ( 1.6)

 Nation 4 ( 0.6) 23 ( 1.2) 61 ( 1.3) 39 ( 1.3)

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). ** ** Standard

error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 3
Guam

Major Findings for Guam

• The average mathematics scale score for fourth graders in Guam was

188.3 This average was lower than that for the nation (222).

• In terms of achievement levels established for the NAEP mathematics

assessment, 3 percent of the fourth-grade students in Guam performed

at or above the Proficient level.4 This percentage was smaller than that

of students nationwide (20 percent).

• From 1992 to 1996 in grade 4, there was a decrease in the average scale

score of students in Guam; however, there was an increase in that of

students across the nation.

• The average mathematics scale score for eighth graders in Guam was

239. This average was lower than that for the nation (271).

• In terms of achievement levels, 6 percent of the eighth-grade students

in Guam performed at or above the Proficient level. This percentage

was smaller than that of students nationwide (23 percent).

• From 1992 to 1996 for eighth graders, the average scale score of

students in Guam did not change significantly while that of students

across the nation increased somewhat.

• The average scale score for eighth graders in Guam in 1996 (239) was

higher than that in 1990 (232).

3

 The NAEP mathematics scale ranges from 0 to 500.

4

 The Proficient achievement level represents solid academic performance for each grade assessed. Students reaching this

level have demonstrated competency over challenging subject matter, including subject-matter knowledge, application

of such knowledge to real-world situations, and analytical skills appropriate to the subject matter.

4 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Major Findings for Student Subpopulations

The preceding section provided a global view of the mathematics performance of

fourth- and eighth-grade students in Guam. It is also important to examine the average

performance of subgroups within these populations. Typically, NAEP presents results

for demographic subgroups defined by gender, race/ethnicity, and parental education.

In addition, in 1996 NAEP collected information on student participation in Title I

programs and eligibility for the free/reduced-price lunch component of the National

School Lunch Program (NSLP).

The 1996 state assessment in mathematics also continued a component first

introduced with the NAEP 1994 state assessment in reading — assessment of a

representative sample of nonpublic school students.

The reader is cautioned against using NAEP results to make simple or causal

inferences related to subgroup membership. Differences among groups of students are

almost certainly associated with a broad range of socioeconomic and educational factors

not discussed in NAEP reports and possibly not addressed by the NAEP assessment

program.

Results for 1996 related to gender and race/ethnicity are highlighted below. A

comparison of public and nonpublic school results is also presented. More complete

results for the various demographic subgroups examined by the NAEP mathematics

assessment can be found in Chapters 2 and 4 of this report, the NAEP 1996 Mathematics

State Report for Guam.

• The average mathematics scale score of fourth-grade males did not differ

significantly from that of females in both Guam and the nation.

• The average mathematics scale score of eighth-grade males was lower

than that of females in Guam; nationwide, however, the performance

of males did not differ significantly from that of females.

• At the fourth grade, White students in Guam had an average

mathematics scale score that was higher than that of Hispanic students

but was not significantly different from that of Asian/Pacific Islander

students.

• At the eighth grade, Hispanic students in Guam had an average

mathematics scale score that was lower than that of Asian/Pacific

Islander students.

• In Guam, the average scale score of public school fourth graders (188)

was lower than that of nonpublic school students (219).

• In Guam, the average scale score of public school eighth graders (239)

was lower than that of nonpublic school students (275).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 5
Guam

Finding a Context for Understanding Students’ Mathematics

Performance in Public Schools

The mathematics performance of students in Guam may be better understood when

viewed in the context of the environment in which the students are learning. This

educational environment is largely determined by school characteristics, by

characteristics of mathematics instruction in the school, by home support for academics

and other home influences, and by the students’ own views about mathematics.

Information about this environment is gathered by means of the questionnaires

completed by principals and teachers as well as questions answered by students as part

of the assessment.

Because NAEP is administered to a sample of students that is representative of the

fourth- and eighth-grade student populations in the schools of Guam, NAEP results

provide a view of the educational practices in Guam which may be useful for improving

instruction and setting policy. However, despite the richness of context provided by the

NAEP results, it is very important to note that NAEP data cannot establish a

cause-and-effect relationship between educational environment and student scores on the

NAEP mathematics assessment.

The following results are for public school students.

School Characteristics Related to Student Performance5

• The percentage of fourth-grade students in Guam attending public

schools that reported that mathematics was a priority (94 percent) was

greater than the national percentage (76 percent).

• The percentage of Guam eighth graders in public schools that reported

that mathematics was a priority (76 percent) was not significantly

different from that of students nationwide (74 percent).

• The percentage of fourth graders attending public schools in Guam that

reported that absenteeism was a moderate to serious problem

(29 percent) was greater than that of fourth graders across the nation

(13 percent). The percentage of students in Guam public schools

reporting that absenteeism was a moderate to serious problem increased

somewhat from 1992 (27 percent) to 1996 (29 percent).

• The percentage of eighth graders attending public schools in Guam that

reported absenteeism was a moderate to serious problem (66 percent)

was greater than that of eighth-grade students nationwide (25 percent).

There was an increase from 1992 (34 percent) to 1996 (66 percent) in

the percentage of eighth graders attending schools that reported that

absenteeism was a moderate to serious problem.

5

 More detailed results related to school characteristics can be found in Chapter 5 of this report, the NAEP 1996

Mathematics State Report for Guam.

6 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Classroom Practices6

• A small percentage of the fourth-grade students in Guam (1 percent)

had mathematics teachers who reported being very knowledgeable about

the NCTM Standards. This percentage was smaller than the percentage

whose teachers reported having little or no knowledge of the Standards

(63 percent).

• None of the eighth-grade students in Guam (0 percent) had mathematics

teachers who reported being very knowledgeable about the NCTM

Standards.

• In eighth grade, about one third of the students reported taking

eighth-grade mathematics (32 percent), compared to 42 percent taking

prealgebra and 21 percent taking algebra. The percentage of students

taking algebra did not differ significantly from that for the nation

(24 percent).

• About one third of the eighth-grade students expected to take prealgebra

(11 percent) or algebra (24 percent) in the ninth grade. Another

18 percent anticipated taking a geometry class.

• The percentage of fourth graders in Guam whose teachers reported

spending four hours a week or more on mathematics instruction

(56 percent) was smaller than the percentage for the nation

(69 percent). The percentage for Guam in 1996 was smaller than the

percentage in 1992 (71 percent).

• The percentage of eighth graders in Guam whose teachers reported

spending four hours a week or more on mathematics instruction

(68 percent) was greater than the percentage for the nation (34 percent).

The percentage for Guam in 1996 was greater than the percentage in

1992 (28 percent).

• Teachers of 32 percent of the fourth-grade students reported that they

addressed the development of reasoning and analytical ability a lot. In

contrast, 22 percent had teachers who reported spending little or no time

addressing this topic.

• Teachers of 55 percent of the eighth-grade students reported that they

addressed the development of reasoning and analytical ability a lot. A

small percentage of the students (2 percent) had teachers who reported

spending little or no time addressing this topic.

6

 More detailed results related to classroom practices can be found in Chapter 6 of this report, the NAEP 1996

Mathematics State Report for Guam.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 7
Guam

• According to their teachers, 9 percent of the fourth graders in Guam

were asked to write about solving a mathematics problem and

37 percent were asked to discuss solutions with other students almost

every day. By comparison, 32 percent were asked to write about and

8 percent were asked to discuss mathematics solutions never or hardly

ever.

• According to their teachers, 3 percent of the eighth grade students in

Guam were asked to write about solving a mathematics problem and

83 percent were asked to discuss solutions with other students almost

every day. By comparison, 22 percent were asked to write about and

0 percent were asked to discuss mathematics solutions never or hardly

ever.

• According to their teachers, 1 percent of the fourth graders in Guam

were not assigned any mathematics homework each day. In addition,

about three quarters of the students were assigned 15 minutes

(21 percent) or 30 minutes (58 percent) of homework each day.

• According to their teachers, 6 percent of the eighth graders in Guam

were not assigned any mathematics homework each day. In addition,

less than half of the students were assigned 30 minutes (23 percent) or

45 minutes (14 percent) of homework each day.

• More than half of the fourth graders in Guam reported that there was

no computer at home (62 percent) and another 20 percent reported

never or hardly ever using their home computer to do homework. Less

than one fifth of the students reported using a computer at home for

homework almost every day (7 percent) or once or twice a week

(7 percent).

• Less than half of the eighth-grade students reported that there was no

computer at home (47 percent) and another 17 percent reported never

or hardly ever using their home computer to do homework. About one

quarter of the students reported using a computer at home for homework

almost every day (9 percent) or once or twice a week (14 percent).

• Less than one fifth of the fourth graders in Guam had teachers who

reported that students used a calculator in mathematics class almost

every day (1 percent) or once or twice a week (15 percent). More than

half of the students never or hardly ever used a calculator (64 percent).

• About three quarters of the eighth graders had teachers who reported that

students used a calculator in mathematics class almost every day

(57 percent) or once or twice a week (18 percent). Less than one fifth

of the students never or hardly ever used a calculator (14 percent).

8 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Influences Beyond School That Facilitate Learning Mathematics7

• Less than half of the fourth graders (46 percent) said they discussed

their schoolwork at home almost every day. This percentage was larger

than the percentage who said they never or hardly ever had such

discussions (22 percent).

• In Guam, about one third of the eighth-grade students (32 percent) said

they discussed their schoolwork at home almost every day. This

percentage was larger than the percentage who said they never or hardly

ever had such discussions (24 percent).

• The percentage of fourth graders in Guam who reported watching six

or more hours of television a day (16 percent) was smaller than the

percentage for the nation (20 percent).

• The percentage of eighth graders in Guam who reported watching six

or more hours of television a day (17 percent) was not significantly

different from the percentage for the nation (14 percent).

• Overall, all of the fourth-grade students attended schools where

principals characterized parental support as very positive (48 percent)

or somewhat positive (52 percent).

• Overall, more than half of the eighth-grade students attended schools

where principals characterized parental support as very positive

(0 percent) or somewhat positive (58 percent).

7

 More detailed results related to influences beyond the school can be found in Chapter 7 of this report, the NAEP 1996

Mathematics State Report for Guam.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 9
Guam

10 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

 INTRODUCTION

Improving education is often seen as an important first step as the United States

maps out a strategy to remain competitive in an ever-increasing global economy.

Mathematics and science education continued to receive considerable attention at the

1996 Governor’s Summit in Palisades, New Jersey, where the President and the

governors reaffirmed the need to strengthen our schools and to strive for world-class

standards.

Monitoring the performance of students in subjects such as mathematics is a key

concern of the state and national policy makers and educators who direct educational

reform efforts. The 1996 National Assessment of Educational Progress (NAEP) in

mathematics is a key source of information on what the nation’s students can do and

how mathematics achievement has progressed during the 1990s.

What Was Assessed?

The NAEP assessment measures a mathematics domain containing five

mathematics strands (number sense, properties, and operations; measurement; geometry

and spatial sense; data analysis, statistics, and probability; and algebra and functions).

Questions involving content from one or more of the strands are also categorized

according to the domains of mathematical abilities and mathematical power. The first

of these, mathematical abilities, describes the nature of the knowledge or processes

involved in successfully handling the task presented by the question. It may reflect

conceptual understanding, procedural knowledge, or a combination of both in problem

solving. The second domain, mathematical power, reflects processes stressed as major

goals of the mathematical curriculum. Mathematical power refers to the students’ ability

to reason, to communicate, and to make connections of concepts and skills across

mathematical strands, or from mathematics to other curricular areas.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 11
Guam

The mathematics framework for the NAEP 1996 assessment is a revision of that

used in the 1990 and 1992 assessments. Changes were made to the earlier framework

in light of the NCTM Standards and changes taking place in school mathematics

programs. The previous NAEP mathematics framework was refined and sharpened so

that the 1996 assessment would: (1) more adequately reflect recent curricular emphases

and objects and yet (2) maintain a connection with the 1990 and 1992 assessments to

measure trends in student performance. Prior to the 1996 assessment, investigations

were conducted to ensure that results from the assessment could be reported on the

existing NAEP mathematics scale. The conclusion drawn from these investigations was

that results from the 1990, 1992, and 1996 assessments could be reported on a common

scale and trends in mathematics performance since 1990 examined. Appendix B briefly

highlights selected changes in the current NAEP mathematics framework.

The conception of mathematical power as reasoning, connections, and

communication has played an increasingly important role in measuring student

achievement. In 1990, the NAEP assessment included short constructed-response

questions as a way to begin addressing mathematical communication. In 1992, the

extended constructed-response questions included on the assessment required students

not only to communicate their ideas but also to demonstrate the reasoning they used to

solve problems. The 1996 assessment continued to emphasize mathematical power by

including constructed-response questions focusing on reasoning and communication and

by requiring students to connect their learning across mathematical content strands.

These connections were addressed within individual questions reaching across content

strands and by families of questions contained within a single content strand.

In real life, few mathematical situations can be clearly classified as belonging to

one content strand or another, and few situations require only one fact of mathematics

thinking. Therefore, many of the questions are classified in a number of ways. In

addition to being classified by all applicable content strands, each question was classified

by its assessment of applicable mathematical abilities (procedural knowledge, conceptual

understanding, and problem solving) and mathematical powers (reasoning,

communication, and connections). The content strands, mathematical abilities, and

mathematical power combine to form the framework for the NAEP assessment. (A brief

description of the five content strands is presented in Appendix B.)

12 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

The framework continued the shift from multiple-choice questions to questions

that required students to construct responses. In 1996, more than 50 percent of student

assessment time was devoted to constructed-response questions. Two types of

constructed-response questions were included — (1) short constructed-response

questions that required students to provide answers to computation problems or to

describe solutions in one or two sentences, and (2) extended constructed-response

questions that required students to provide longer responses when answering the

questions.

Who Was Assessed?

Fourth- and Eighth-Grade School and Student Characteristics

Tables I.1A and I.1B provide profiles of the demographic characteristics of the

fourth- and eighth-grade students in Guam and the nation. These profiles are based on

data collected from the students and schools participating in the 1992 and 1996 state and

national mathematics assessments at grade 4 and the 1990, 1992, and 1996 state and

national mathematics assessments at grade 8. This report contains results for public

school students only for those years in which Guam participated and for which minimum

participation rate guidelines were met. Results are also presented for nonpublic school

students at grades 4 and 8 for the 1996 state mathematics assessment. As described in

Appendix A, the state data and the national data are drawn from separate samples.

In 1996, approximately 84 percent of fourth graders in Guam attended public

schools, with the remaining students attending nonpublic schools (including Catholic and

other private schools). At eighth grade, 80 percent of students in Guam attended public

schools. For the nation, 89 percent of students at both grades 4 and 8 attended public

schools in 1996.

To ensure comparability across jurisdictions, NCES has established guidelines for

school and student participation rates. Appendix A highlights these guidelines, and

jurisdictions failing to meet these guidelines are noted in tables and figures in NAEP

reports containing state-by-state results. For jurisdictions failing to meet the initial

school participation rate of 70 percent, results are not reported.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 13
Guam

TABLE I.1A — GRADE 4

Profile of Students in Guam and the Nation

Demographic Subgroups

1992 1996

Public Public Nonpublic Combined

Percentage

RACE/ETHNICITY

Guam White 12 ( 0.7) 8 ( 0.8)< 19 ( 2.9) 10 ( 0.8) 

Black 4 ( 0.4) 4 ( 0.5) 2 ( 1.0) 3 ( 0.5) 

Hispanic 20 ( 0.8) 22 ( 1.3) 13 ( 2.0) 21 ( 1.2) 

Asian/Pacific Islander 62 ( 1.0) 64 ( 1.4) 61 ( 3.4) 64 ( 1.2) 

American Indian 2 ( 0.4) 2 ( 0.3) 1 ( 0.5) 2 ( 0.3) 

Nation White 69 ( 0.4) 66 ( 0.6)< 80 ( 4.0) 68 ( 0.4) 

Black 17 ( 0.4) 15 ( 0.4) 8 ( 3.1) 15 ( 0.2) 

Hispanic 10 ( 0.2) 14 ( 0.4)> 7 ( 1.1) 13 ( 0.4) 

Asian/Pacific Islander 3 ( 0.3) 3 ( 0.2) 3 ( 0.8) 3 ( 0.2) 

American Indian 2 ( 0.2) 2 ( 0.2) 1 ( 0.3) 2 ( 0.2) 

PARENTS’ EDUCATION

Guam Did not finish high school 6 ( 0.6) 5 ( 0.7) 3 ( 1.1) 4 ( 0.6) 

Graduated from high school 13 ( 0.8) 14 ( 1.0) 9 ( 1.3) 13 ( 0.8) 

Some education after high school 6 ( 0.5) 5 ( 0.6) 4 ( 1.3) 5 ( 0.6) 

Graduated from college 31 ( 0.9) 36 ( 1.4)> 49 ( 2.5) 38 ( 1.3) 

I don't know 44 ( 1.0) 40 ( 1.5) 34 ( 2.0) 39 ( 1.3) 

Nation Did not finish high school 4 ( 0.3) 4 ( 0.4) 1 ( 0.3) 4 ( 0.3) 

Graduated from high school 13 ( 0.6) 13 ( 0.7) 8 ( 0.9) 13 ( 0.6) 

Some education after high school 7 ( 0.4) 7 ( 0.4) 7 ( 1.0) 7 ( 0.4) 

Graduated from college 40 ( 1.1) 38 ( 1.2) 58 ( 2.6) 40 ( 1.1) 

I don't know 36 ( 0.8) 37 ( 1.0) 27 ( 1.9) 36 ( 1.0) 

GENDER

Guam Male 52 ( 1.2) 52 ( 1.3) 47 ( 3.3) 51 ( 1.1) 

Female 48 ( 1.2) 48 ( 1.3) 53 ( 3.3) 49 ( 1.1) 

Nation Male 50 ( 0.7) 51 ( 0.7) 51 ( 2.0) 51 ( 0.7) 

Female 50 ( 0.7) 49 ( 0.7) 49 ( 2.0) 49 ( 0.7) 

TITLE I

Guam Participated --- (--.-) 1 ( 0.5) 0 ( ) 1 ( 0.4) 

Did not participate --- (--.-) 99 ( 0.5) 100 (** **) 99 ( 0.4) 

Nation Participated --- (--.-) 24 ( 1.5) 5 ( 1.9) 22 ( 1.4) 

Did not participate --- (--.-) 76 ( 1.5) 95 ( 1.9) 78 ( 1.4) 

FREE/REDUCED-PRICE LUNCH

Guam Eligible --- (--.-) 35 ( 1.4) 4 ( 1.1) 31 ( 1.2) 

Not eligible --- (--.-) 59 ( 1.4) 91 ( 1.4) 64 ( 1.2) 

Information not available --- (--.-) 6 ( 0.3) 5 ( 0.9) 6 ( 0.3) 

Nation Eligible --- (--.-) 34 ( 1.6) 7 ( 1.8) 31 ( 1.4) 

Not eligible --- (--.-) 52 ( 2.5) 54 ( 6.8) 53 ( 2.5) 

Information not available --- (--.-) 13 ( 3.1) 39 ( 6.8) 16 ( 3.0) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level. The percentages for Race/Ethnicity may not add to 100 percent because some

students categorized themselves as “Other.” --- Title I and Free/Reduced-Price Lunch results are not available for the 1992

assessment.   Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

14 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE I.1B — GRADE 8

Profile of Students in Guam and the Nation

Demographic Subgroups

1990 1992 1996

Public Public Public Nonpublic Combined

Percentage

RACE/ETHNICITY

Guam White 7 ( 0.7) 5 ( 0.5) 4 ( 0.5)« 9 ( 2.6) 5 ( 0.7) 

Black 1 ( 0.4) 1 ( 0.3) 1 ( 0.4) 1 (** **) 1 ( 0.3) 

Hispanic 19 ( 1.0) 15 ( 0.9)« 17 ( 1.4) 7 ( 1.8) 15 ( 1.3) 

Asian/Pacific Islander 72 ( 1.2) 76 ( 1.1)» 76 ( 1.4) 75 ( 2.8) 76 ( 1.4) 

American Indian 1 ( 0.2) 1 ( 0.1) 0 ( 0.2) 0 ( ) 0 ( 0.2) 

Nation White 70 ( 0.5) 69 ( 0.4) 68 ( 0.5)« 80 ( 3.4) 69 ( 0.2) 

Black 16 ( 0.3) 16 ( 0.2) 15 ( 0.4)< 7 ( 2.5) 14 ( 0.2) 

Hispanic 10 ( 0.4) 10 ( 0.3) 13 ( 0.3)»> 9 ( 2.0) 12 ( 0.1) 

Asian/Pacific Islander 2 ( 0.5) 2 ( 0.2) 3 ( 0.3) 3 ( 0.7) 3 ( 0.2) 

American Indian 2 ( 0.7) 1 ( 0.2) 1 ( 0.3) 1 ( 0.3) 1 ( 0.2) 

PARENTS’ EDUCATION

Guam Did not finish high school 10 ( 0.7) 10 ( 0.9) 8 ( 0.9) 1 (** **) 7 ( 0.8) 

Graduated from high school 30 ( 1.2) 27 ( 1.1) 30 ( 1.5) 11 ( 2.8) 26 ( 1.3) 

Some education after HS 11 ( 0.8) 13 ( 0.7) 14 ( 1.3) 16 ( 2.1) 15 ( 1.2) 

Graduated from college 27 ( 1.1) 28 ( 1.2) 27 ( 1.3) 57 ( 2.3) 33 ( 1.2) 

I don't know 22 ( 1.3) 22 ( 1.2) 20 ( 1.3) 15 ( 3.3) 19 ( 1.3) 

Nation Did not finish high school 10 ( 0.8) 8 ( 0.6) 8 ( 0.5) 2 ( 0.4) 7 ( 0.4) 

Graduated from high school 25 ( 1.2) 25 ( 0.8) 23 ( 0.8) 13 ( 1.5) 22 ( 0.8) 

Some education after HS 17 ( 0.9) 18 ( 0.6) 19 ( 0.8) 16 ( 0.9) 19 ( 0.7) 

Graduated from college 39 ( 1.9) 40 ( 1.4) 40 ( 1.4) 61 ( 2.7) 42 ( 1.3) 

I don't know 9 ( 0.7) 9 ( 0.5) 11 ( 0.6) 9 ( 1.6) 11 ( 0.6) 

GENDER

Guam Male 51 ( 1.2) 52 ( 1.2) 53 ( 1.4) 53 ( 2.4) 53 ( 1.3) 

Female 49 ( 1.2) 48 ( 1.2) 47 ( 1.4) 47 ( 2.4) 47 ( 1.3) 

Nation Male 51 ( 1.1) 52 ( 0.6) 52 ( 0.9) 53 ( 2.1) 52 ( 0.8) 

Female 49 ( 1.1) 48 ( 0.6) 48 ( 0.9) 47 ( 2.1) 48 ( 0.8) 

TITLE I

Guam Participated --- (--.-) --- (--.-) 0 ( ) 0 (** **) 0 ( )

Did not participate --- (--.-) --- (--.-) 100 (** **) 100 ( ) 100 (** **) 

Nation Participated --- (--.-) --- (--.-) 13 ( 1.8) 2 ( 1.2) 12 ( 1.6) 

Did not participate --- (--.-) --- (--.-) 87 ( 1.8) 98 ( 1.2) 88 ( 1.6) 

FREE/REDUCED-PRICE LUNCH

Guam Eligible --- (--.-) --- (--.-) 17 ( 1.3) 2 ( 0.7) 14 ( 1.0) 

Not eligible --- (--.-) --- (--.-) 82 ( 1.4) 78 ( 1.5) 81 ( 1.1) 

Information not available --- (--.-) --- (--.-) 1 ( 0.3) 20 ( 1.2) 5 ( 0.4) 

Nation Eligible --- (--.-) --- (--.-) 30 ( 1.6) 4 ( 1.5) 27 ( 1.4) 

Not eligible --- (--.-) --- (--.-) 56 ( 2.6) 53 ( 7.5) 55 ( 2.4) 

Information not available --- (--.-) --- (--.-) 14 ( 3.1) 43 ( 7.6) 17 ( 2.9) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

» («) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1990

at about the 95 percent confidence level. If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. The percentages for

Race/Ethnicity may not add to 100 percent because some students categorized themselves as “Other.” --- Title I and

Free/Reduced-Price Lunch results are not available for the NAEP 1990 and 1992 mathematics assessments.

**** Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 15
Guam

Schools and Students Assessed

Tables I.2A and I.2B summarize participation data for schools and students

sampled in Guam for the 1996 state assessment program in mathematics and previous

NAEP state assessments in mathematics.8

In Guam, 22 public schools and 9 nonpublic schools participated in the 1996

fourth-grade mathematics assessment. These numbers include participating substitute

schools that were selected to replace some of the nonparticipating schools from the

original sample. The weighted school participation rates after substitution in 1996 were

100 percent for public schools and 78 percent for nonpublic schools, which means that

the fourth-grade students in this sample were directly representative of 100 percent and

78 percent of all the fourth-grade public and nonpublic school students, respectively, in

Guam.

At the eighth grade, 6 public schools and 8 nonpublic schools in Guam

participated in the 1996 mathematics assessment. These numbers include participating

substitute schools that were selected to replace some of the nonparticipating schools

from the original sample. The weighted school participation rates after substitution in

1996 were 100 percent for public schools and 76 percent for nonpublic schools, which

means that the eighth-grade students in this sample were directly representative of

100 percent and 76 percent of all the eighth-grade public and nonpublic school students,

respectively, in Guam.

In each school, a random sample of students was selected to participate in the

assessment. In 1996, on the basis of sample estimates, 9 percent of the fourth-grade

public school population and 3 percent of the nonpublic school population were

classified as students with limited English proficiency (LEP). At the eighth grade,

3 percent of the public school population and 1 percent of the nonpublic school

population were classified as students with limited English proficiency. At the fourth

grade, 7 percent of the students in public schools and 0 percent of the students in

nonpublic schools had an Individualized Education Plan (IEP), and at the eighth grade,

6 percent of students in public schools and 0 percent of students in nonpublic schools

had an IEP. An IEP is a plan written for a student who has been determined to be

eligible for special education. The IEP typically sets forth goals and objectives for the

student and describes a program of activities and/or related services necessary to achieve

the goals and objectives.

8

 For a detailed discussion of the NCES guidelines for sample participation, see Appendix A of this report or the

Technical Report of the NAEP 1996 State Assessment Program in Mathematics. (Washington, DC: National Center for

Education Statistics, 1997).

16 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Schools were permitted to exclude certain students from the assessment, provided

that the following criteria were met. To be excluded, a student had to be categorized

as LEP or had to have an IEP or equivalent and (in either case) be judged incapable of

participating in the assessment. The intent was to assess all selected students; therefore,

all selected students who were capable of participating in the assessment should have

been assessed. However, schools were allowed to exclude those students who, in the

judgment of school staff, could not meaningfully participate. The NAEP guidelines for

exclusion are intended to assure uniformity of exclusion criteria from school to school.

Note that some students classified as LEP and some students having an IEP were

deemed eligible to participate and not excluded from the assessment. The students in

Guam who were excluded from the assessment because they were categorized as LEP

or had an IEP represented 13 percent of the public school population and 2 percent of

the nonpublic school population in grade 4 and 4 percent of the public school

population and 0 percent of the nonpublic school population in grade 8.

In Guam 1,431 public school and 317 nonpublic school fourth-grade students were

assessed in 1996. The weighted student participation rates were 94 percent for public

schools and 94 percent for nonpublic schools. This means that the sample of

fourth-grade students who took part in the assessment was directly representative of

94 percent of the eligible public school student population and 94 percent of the eligible

nonpublic school student population in participating schools in Guam (that is, all

students from the population represented by the participating schools, minus those

students excluded from the assessment). The overall weighted response rates (school

rate times student rate) were 94 percent and 74 percent for public and nonpublic

schools, respectively. This means that the sample of students who participated in the

assessment was directly representative of 94 percent of the eligible fourth-grade public

school population and 74 percent of the eligible fourth-grade nonpublic school

population in Guam.

In Guam 928 public school and 202 nonpublic school eighth-grade students were

assessed in 1996. The weighted student participation rates were 86 percent for public

schools and 95 percent for nonpublic schools. This means that the sample of

eighth-grade students who took part in the assessment was directly representative of

86 percent of the eligible public school student population and 95 percent of the eligible

nonpublic school student population in participating schools in Guam (that is, all

students from the population represented by the participating schools, minus those

students excluded from the assessment). The overall weighted response rates (school

rate times student rate) were 86 percent and 72 percent for public and nonpublic

schools, respectively. This means that the sample of students who participated in the

assessment was directly representative of 86 percent of the eligible eighth-grade public

school population and 72 percent of the eligible eighth-grade nonpublic school

population in Guam.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 17
Guam

TABLE I.2A — GRADE 4

Profile of the Population Assessed in Guam

1992 1996

Public Public Nonpublic

SCHOOL PARTICIPATION

Weighted school participation rate before substitution 94% 100% 78% 

Weighted school participation rate after substitution 94% 100% 78% 

Number of schools originally sampled 21 22 14 

Number of schools not eligible 0 0 1 

Number of schools in original sample participating 20 22 9 

Number of substitute schools provided 0 0 0 

Number of substitute schools participating 0 0 0 

Total number of participating schools 20 22 9 

STUDENT PARTICIPATION

Weighted student participation rate after makeups 95% 94% 94% 

Number of students selected to participate in the

 assessment 2,262 1,691 346

Number of students withdrawn from the assessment 91 67 6 

Percentage of students who were of Limited English

Proficiency 7% 9% 3% 

Percentage of students excluded from the assessment

due to Limited English Proficiency 3% 7% 2% 

Percentage of students who had an Individualized

Education Plan 6% 7% 0% 

Percentage of students excluded from the assessment

due to Individualized Education Plan status 4% 6% 0% 

Number of students to be assessed 2,038 1,520 336 

Number of students assessed 1,933 1,431 317 

Overall weighted response rate 89% 94% 74% 

Guam failed to meet one or more established participation guidelines in 1996. See Appendix A for details. In 1992 the

nonparticipating schools included a class of schools with similar characteristics, which together accounted for more than

five percent of the state’s total weighted sample of public schools. See the Technical Report of the NAEP 1992 Trial State

Assessment in Mathematics. In 1992 the Trial State Assessment was based on all eligible schools. There was no sampling

of schools.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

18 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE I.2B — GRADE 8

Profile of the Population Assessed in Guam

1990 1992 1996

Public Public Public Nonpublic

SCHOOL PARTICIPATION

Weighted school participation rate before substitution 100% 100% 100% 76% 

Weighted school participation rate after substitution 100% 100% 100% 76% 

Number of schools originally sampled 7 6 6 11 

Number of schools not eligible 1 0 0 0 

Number of schools in original sample participating 6 6 6 8 

Number of substitute schools provided 0 0 0 0 

Number of substitute schools participating 0 0 0 0 

Total number of participating schools 6 6 6 8 

STUDENT PARTICIPATION

Weighted student participation rate after makeups 93% 90% 86% 95% 

Number of students selected to participate in the

 assessment 1,872 1,790 1,136 213

Number of students withdrawn from the assessment 58 51 36 1 

Percentage of students who were of Limited English

Proficiency 2% 2% 3% 1% 

Percentage of students excluded from the assessment

due to Limited English Proficiency 1% 1% 2% 0% 

Percentage of students who had an Individualized

Education Plan 5% 5% 6% 0% 

Percentage of students excluded from the assessment

due to Individualized Education Plan status 4% 3% 2% 0% 

Number of students to be assessed 1,739 1,667 1,076 212 

Number of students assessed 1,617 1,496 928 202 

Overall weighted response rate 93% 90% 86% 72% 

Guam failed to meet one or more established participation guidelines in 1996. See Appendix A for details. In 1990 and

1992, the Trial State Assessment was based on all eligible schools. There was no sampling of schools.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 19
Guam

In accordance with standard practice in survey research, the results presented in

this report were based on calculations that incorporate adjustments for the

nonparticipating schools and students. Hence, the final results derived from the sample

provide estimates of the mathematics performance for the full population of eligible

fourth- and eighth-grade students in Guam. However, in instances where

nonparticipation rates are large, these nonparticipation adjustments may not adequately

compensate for the missing sample schools and students.

In order to guard against potential nonparticipation bias in published results, the

National Center for Education Statistics (NCES) has established minimum participation

levels as a condition for the publication of 1996 state assessment program results. NCES

also established additional guidelines addressing four ways in which nonparticipation

bias could be introduced into a jurisdiction’s published results (see Appendix A). In

1996 Guam met minimum participation levels for both public and nonpublic schools at

grades 4 and 8. Hence, results for both types of schools are included in this report.

Guam met all other established NCES participation guidelines for public schools at

grades 4 and 8 but failed to meet one or more of these guidelines for nonpublic schools

at grades 4 and 8. The weighted participation rates for the initial samples of nonpublic

schools at grades 4 and 8 were below 85 percent and the weighted school participation

rates after substitution were below 90 percent (see Appendix A).

In the analysis of student data and reporting of results, nonresponse weighting

adjustments have been made at both the school and student level, with the aim of making

the sample of participating students as representative as possible of the entire eligible

fourth- and eighth-grade population. For details of the nonresponse weighting

adjustment procedures, see the Technical Report of the NAEP 1996 State Assessment

Program in Mathematics.

Reporting NAEP Mathematics Results

The NAEP 1996 state assessment program in mathematics provides a wealth of

information on the mathematical abilities and skills of the fourth- and eighth-grade

students in participating jurisdictions. To maximize usefulness to policy makers,

educators, parents, and other interested parties, the NAEP results are presented both as

average scale scores on the NAEP mathematics scale and in terms of the percentage of

students attaining NAEP mathematics achievement levels. Thus, NAEP results not only

provide information about what students know and can do, but also indicate whether

their achievement meets expectations of what students should know and should be able

to do. Furthermore, the descriptions of skills and abilities expected of students at each

achievement level help make the reporting of assessment results more meaningful.

20 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

The Mathematics Scale

Students’ responses to the NAEP 1996 mathematics assessment were analyzed to

determine the percentage of students responding correctly to each multiple-choice

question and the percentage of students responding in each of several score categories

for constructed-response questions. Item response theory (IRT) methods were used to

produce across-grade scales that summarized results for each of the five mathematics

content strands discussed earlier. Each of the content-strand scales, which range from

0 to 500, was linked to its corresponding scale from 1990 and 1992 through IRT

equating.

An overall composite scale was developed by weighting the separate

content-strand scales based on the relative importance to each content strand in the

NAEP mathematics framework. The resulting scale, which was also linked to the 1990

and 1992 mathematics composite scales, is the reporting metric used in Parts One and

Three to present results. (Details of the scaling procedures are presented in

Appendix C of this report, in the NAEP 1996 Technical Report, and in the Technical

Report of the NAEP 1996 State Assessment Program in Mathematics.)

Mathematics Achievement Levels

Results for the NAEP 1996 assessment in mathematics are also reported using the

mathematics achievement levels that were authorized by the NAEP legislation and

adopted by the National Assessment Governing Board. The achievement levels are

based on collective judgments about what students should know and be able to do

relative to the body of content reflected in the NAEP mathematics assessment. Three

levels were defined for each grade — Basic, Proficient, and Advanced. The levels were

defined by a broadly representative panel of teachers, education specialists, and members

of the general public.

For reporting purposes, the achievement levels for each grade are placed on the

NAEP mathematics scale. Figure 1 presents the policy definitions of the achievement

levels, while Chapter 3 contains specific descriptions for the levels at each grade.

Figure 1. Policy Definitions of NAEP Achievement Levels

Basic This level denotes partial mastery of

prerequisite knowledge and skills that are

fundamental for proficient work at each grade.

Proficient This level represents solid academic performance

for each grade assessed. Students reaching

this level have demonstrated competency over

challenging subject matter, including subjectmatter knowledge, application of such knowledge

to real-world situations, and analytical skills

appropriate to the subject matter.

Advanced This level signifies superior performance.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 21
Guam

It should be noted that setting achievement levels is a relatively new process for

NAEP, and it is still in transition. Some evaluations have concluded that the percentage

of students at certain levels may be underestimated.9 On the other hand, critiques of

those evaluations have asserted that the weight of the empirical evidence does not

support such conclusions.10 A further review is currently being conducted by the

National Academy of Sciences.

The student achievement levels in this report have been developed carefully and

responsibly, and the procedures used have been refined and revised as new technologies

have become available. Upon review of the available information, the Commissioner

of Education Statistics has judged that the achievement levels are in a developmental

status. However, the Commissioner and the Governing Board also believe that the

achievement levels are useful and valuable for reporting on the educational achievement

of students in the United States. Part Two presents results reported in terms of the

mathematics achievement levels.

Interpreting NAEP Results

This report describes mathematics performance for fourth and eighth graders and

compares the results for various groups of students within these populations — for

example, those who have certain demographic characteristics or who responded to a

specific background question in a particular way. The report examines the results for

individual demographic groups and for individual background questions. It does not

include an analysis of the relationships among combinations of these subpopulations or

background questions.

Because the percentages of students in these subpopulations and their average

mathematics scale scores are based on samples — rather than on the entire population

of fourth and eighth graders in a jurisdiction — the numbers reported are necessarily

estimates. As such, they are subject to a measure of uncertainty, reflected in the

standard error of the estimate. When the percentages or average scale scores of certain

groups are compared, it is essential to take the standard error into account, rather than

to rely solely on observed similarities or differences. Therefore, the comparisons

discussed in this report are based on statistical tests that consider both the magnitude

of the difference between the means or percentages and the standard errors of those

statistics.

9

 General Accounting Office. Educational Achievement Standards: NAGB’s Approach Yields Misleading

Interpretations. (Washington, DC: General Accounting Office, 1993); National Academy of Education. Setting

Performance Standards for Student Achievement. A Report of the National Academy of Education Panel on the

Evaluation of the NAEP Trial State Assessment: An Evaluation of the 1992 Achievement Levels. (Stanford, CA:

National Academy of Education, 1993).

10 Cizek, G. Reactions to the National Academy of Education report. (Washington, DC: National Assessment Governing

Board, 1993); Kane, M. Comments on the NAE Evaluation of the NAGB Achievement Levels. (Washington, DC: National

Assessment Governing Board, 1993); NAEP Reading Revisited: An Evaluation of the 1992 Achievement Levels

Descriptions. (American College Testing, Washington, DC: National Assessment Governing Board, 1993); Technical

Report on Setting Achievement Levels on the 1992 National Assessment of Educational Progress in Mathematics,

Reading, and Writing. (American College Testing, Washington, DC: National Assessment Governing Board, 1993).

22 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

The statistical tests determine whether the evidence — based on the data from the

groups in the sample — is strong enough to conclude that the averages or percentages

are really different for those groups in the population. If the evidence is strong (i.e., the

difference is statistically significant), the report describes the group averages or

percentages as being different (e.g., one group performed higher than or lower than

another group) — regardless of whether the sample averages or sample percentages

appear to be about the same or not. If the evidence is not sufficiently strong (i.e., the

difference is not statistically significant), the averages or percentages are described as

being not significantly different — again, regardless of whether the sample averages or

sample percentages appear to be about the same or widely discrepant. The reader is

cautioned to rely on the results of the statistical tests — rather than on the apparent

magnitude of the difference between sample averages or percentages — to determine

whether those sample differences are likely to represent actual differences between the

groups in the population. The statistical tests are discussed in greater detail in

Appendix A.

In addition, some of the percentages reported in the text of the report are given

quantitative descriptions (e.g., relatively few, about half, almost all, etc.). The

descriptive phrases used and the rules used to select them are also described in

Appendix A.

How Is This Report Organized?

The NAEP 1996 Mathematics State Report for Guam is a computer-generated

report that describes the mathematics performance of fourth- and eighth-grade students

in Guam and the nation. A separate report describes additional fourth- and eighth-grade

mathematics assessment results for the nation and the states, as well as the national

results for grade 12.11 The State Report consists of five sections:

• An Introduction provides background information about what was

assessed, who was sampled, and how the results are reported.

• Part One shows the distribution of mathematics scale score results for

fourth- and eighth-grade students in Guam and the nation.

• Part Two presents mathematics achievement level results for fourth- and

eighth-grade students in Guam and the nation.

11 Reese, C.M., K.E. Miller, J. Mazzeo, and J.A. Dossey. NAEP 1996 Mathematics Report Card. (Washington, DC:

National Center for Education Statistics, 1997).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 23
Guam

• Part Three relates fourth- and eighth-grade public school students’

mathematics scale scores to contextual information about school

characteristics, instruction, and home support for mathematics in Guam

and the nation.

• Several Appendices are presented to support the results discussed in the

report:

Appendix A Reporting NAEP 1996 Mathematics

Results for Guam

Appendix B NAEP 1996 Mathematics Assessment

 Appendix C Technical Appendix

Appendix D Setting the Achievement Levels

 Appendix E Teacher Preparation

Appendix F Discussion of the Grade 8

Asian/Pacific Islander Sample

24 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

 PART ONE

The Mathematics Scale Score Results for

Fourth- and Eighth-Grade Students

The following chapters describe the average mathematics scale scores of fourthand eighth-grade students in Guam. As described in the Introduction, the NAEP

mathematics scale is a composite of the five content strands that comprise the assessment

and ranges from 0 to 500. The performance of both fourth- and eighth-grade students

is reported on this one scale.

This part of the report contains two chapters. Chapter 1 compares the overall

mathematics performance of public school students in Guam to the nation. Chapter 2

summarizes mathematics performance for subgroups of public school students defined

by gender, race/ethnicity, parental education, participation in Title I programs and

services, and eligibility for the free/reduced-price lunch component of the National

School Lunch Program. The second chapter also provides the combined results for

public and nonpublic school students, as well as the results for only nonpublic school

students.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 25
Guam

26 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

CHAPTER 1

Students’ Mathematics Scale Score Results

The delivery of education to the millions of school-age students in our country is

primarily a function of the states. Therefore, monitoring the performance of students in

subjects such as mathematics is a key concern of those policy makers directing

educational reform at the state level. Monitoring the mathematics performance of

students is also a concern at the national level.

The need to assess the current level of mathematical ability as a mechanism for

informing education reform efforts is highlighted by the current National Assessment

of Educational Progress (NAEP) in mathematics (as well as the two previous NAEP

assessments in mathematics in 1990 and 1992) and the Third International Mathematics

and Science Study (TIMSS) conducted in 1994 and 1995 with support from the U.S.

Department of Education.12

The mathematics community has taken a lead in communicating the importance

of mathematics in today’s society. With the release of the National Council of Teachers

of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics

in 1989, mathematics educators have accepted the challenges set forth by the national

and state policy makers.13 Based on drafts of the NCTM Standards, NAEP developed

the 1990 and 1992 mathematics assessments.14 The framework and specifications for

the NAEP 1996 mathematics assessment was refined to better reflect the NCTM

Standards.

15 Results from the 1996 assessment can be compared to those from the 1990

and 1992 assessments, regardless of the refinement of the framework.

12 The Third International Mathematics and Science Study was conducted in 1994 in the southern hemisphere and in 1995

in the northern hemisphere.

13 National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. (Reston,

VA: NCTM, 1989).

14 National Assessment of Educational Progress (NAEP). Mathematics Objectives: 1990 Assessment. (Princeton, NJ:

Educational Testing Service, 1988).

15 National Assessment Governing Board. Mathematics Framework for the 1996 National Assessment of Educational

Progress. (Washington, DC: National Assessment Governing Board, 1994).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 27
Guam

The NAEP 1996 state mathematics assessment at grades 4 and 8 continues the

state-level NAEP component begun in 1990 with the NAEP Trial State Assessment

(TSA) in mathematics at grade 8, which was followed by the 1992 TSA in mathematics

at grades 4 and 8.16 The current assessment is also the largest with 48 participating

jurisdictions.17 The following results from the NAEP 1996 state mathematics

assessment represent a current picture of the mathematics performance of fourth- and

eighth-grade students in Guam and the nation.

Table 1.1A shows the distribution of mathematics scale scores for fourth-grade

students attending public schools in Guam and the nation. Results are presented for the

1992 and 1996 assessments and comparisons between the two years are indicated.18

The 1992 and 1996 mathematics assessments examined the performance of two

independent samples of fourth-grade students (i.e., cross-sectional performance). NAEP

does not measure the growth of a group of students (i.e., longitudinal performance), but

rather collects data for the same grade levels at different points in time. Table 1.1B

presents similar results for eighth-grade students.

16 Based on positive evaluations of the 1990, 1992, and 1994 TSAs, the “Trial” designation has been removed from the

1996 state-level NAEP assessment.

17 Jurisdictions refers to states, territories, the District of Columbia, and Department of Defense Education Activities

schools.

18 Mathematics was not assessed at grade 4 in 1990.

28 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

1996, Public School Students, Grade 4

The average mathematics scale score in Guam was 188. This average

was lower than that for the nation (222).19

1992 vs. 1996, Public School Students, Grade 4

From 1992 to 1996, there was a decrease in the average scale score of

students in Guam; however, there was an increase in that of students

across the nation.

TABLE 1.1A — GRADE 4

Distribution of Mathematics Scale Scores for Public School

Students

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

1992

 Guam 193 ( 0.8) 150 ( 1.4) 170 ( 1.2) 193 ( 1.1) 215 ( 1.3) 236 ( 1.7)

 Nation 219 ( 0.8) 176 ( 1.1) 197 ( 0.9) 220 ( 1.0) 241 ( 1.1) 259 ( 0.9)

1996

 Guam 188 ( 1.3)< 145 ( 2.9) 166 ( 2.1) 189 ( 0.8)< 212 ( 1.8) 231 ( 2.0)

 Nation 222 ( 1.0)> 180 ( 1.5) 201 ( 1.3) 224 ( 1.3) 244 ( 1.0) 261 ( 1.0)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

19 Differences reported as significant are statistically different at the 95 percent confidence level. This means that with

95 percent confidence there is a real difference in the average mathematics scale score between the two populations

of interest.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 29
Guam

Table 1.1B shows the distribution of mathematics scale scores for eighth-grade

students attending public schools in Guam and the nation. Results are presented for the

1990, 1992, and 1996 assessments and comparisons among the three years are indicated.

1996, Public School Students, Grade 8

The average mathematics scale score in Guam was 239. This average

was lower than that for the nation (271).

1992 vs. 1996, Public School Students, Grade 8

From 1992 to 1996, the average scale score of students in Guam did not

change significantly while that of students across the nation increased

somewhat.

1990 vs. 1996, Public School Students, Grade 8

The average scale score in Guam in 1996 (239) was higher than that in

1990 (232).

TABLE 1.1B — GRADE 8

Distribution of Mathematics Scale Scores for Public School

Students

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

1990

 Guam 232 ( 0.7) 182 ( 1.7) 205 ( 1.7) 231 ( 1.7) 258 ( 1.9) 282 ( 2.0)

 Nation 262 ( 1.4) 214 ( 1.8) 237 ( 1.7) 263 ( 1.4) 288 ( 1.7) 307 ( 1.9)

1992

 Guam 235 ( 1.0)» 185 ( 1.9) 208 ( 3.3) 234 ( 1.9) 262 ( 1.7) 287 ( 1.8)

 Nation 267 ( 1.0)» 219 ( 1.5) 242 ( 1.4) 268 ( 1.2)» 293 ( 1.5) 314 ( 1.4)»

1996

 Guam 239 ( 1.7)» 187 ( 2.1) 213 ( 5.4) 240 ( 2.3)» 267 ( 2.4)» 290 ( 3.8)

 Nation 271 ( 1.2)»> 222 ( 2.0)» 247 ( 1.2)»> 272 ( 1.1)»> 296 ( 1.4)» 316 ( 2.0)»

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation » («) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1990 at about the 95 percent confidence level. If the notation > (<)

appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992 at

about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

30 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Comparisons Between Guam and Other Participating

Jurisdictions

The maps on the following pages provide a method for making appropriate

comparisons of the average mathematics scale scores for public school students in Guam

with those of other jurisdictions participating in the NAEP 1996 mathematics

assessment. The different shadings of the states on the map show whether or not the

average scale scores of public school students in the other jurisdictions were statistically

different from that of public school students in Guam (“Target State”). States with

horizontal lines have a significantly lower average mathematics scale score than Guam

and states in gray have a significantly higher average scale score. The unshaded states

have average scale scores that did not differ significantly from the average for Guam.

Several states, those with large crosshatching, did not meet minimum participation rate

guidelines established by NCES for the NAEP assessments. A description of the

statistical procedures used to produce the data represented in these maps is contained in

Appendix A.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 31
Guam

32 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS

Guam

34 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS

Guam

36 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Performance on the NAEP Mathematics Content Strands

The framework and specifications that guided the development of the NAEP

mathematics assessments are anchored in broad strands of mathematical content similar

to the content standards in the NCTM Standards. These content strands are

• Number Sense, Properties, and Operations

• Measurement

• Geometry and Spatial Sense

• Data Analysis, Statistics, and Probability

• Algebra and Functions20

Tables 1.2A and 1.2B show the distribution of content strand scale scores for

Guam and the nation. Appendix B describes the five content strands, and

Appendix C contains a more extensive discussion of the scaling procedures used to

develop the five content-strand scales as well as the composite NAEP mathematics scale.

1996, Public School Students, Grade 4

Students in Guam performed lower than students nationwide in all five

of the content strands.

1992 vs. 1996, Public School Students, Grade 4

The performance of students in Guam did not change significantly

between 1992 and 1996 in any of the five content strands.

20 At the fourth-grade level, the Algebra and Functions strand was treated in informal and exploratory ways, often through

the study of patterns.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 37
Guam

TABLE 1.2A — GRADE 4

Distribution of Mathematics Scale Scores for Public School

Students by Content Area

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

Number Sense, Properties,

and Operations

1992

Guam 190 ( 1.1) 141 ( 1.4) 165 ( 1.3) 190 ( 1.3) 215 ( 1.4) 237 ( 1.5)

Nation 216 ( 0.9) 170 ( 1.2) 193 ( 1.2) 217 ( 1.1) 240 ( 0.9) 259 ( 1.1)

1996

Guam 185 ( 2.0) 128 ( 7.1) 158 ( 3.8) 187 ( 2.2) 214 ( 2.0) 237 ( 2.2)

Nation 219 ( 1.1) 174 ( 1.1) 197 ( 0.8) 221 ( 1.1) 243 ( 1.3) 262 ( 1.6)

Measurement

1992

Guam 193 ( 1.1) 146 ( 2.9) 169 ( 2.0) 194 ( 1.3) 218 ( 1.3) 239 ( 2.5)

Nation 223 ( 0.9) 178 ( 1.2) 201 ( 1.3) 225 ( 0.9) 247 ( 1.8) 265 ( 1.0)

1996

Guam 188 ( 2.1) 125 ( 3.1)< 155 ( 3.1)< 190 ( 2.9) 221 ( 3.2) 248 ( 2.9)

Nation 224 ( 1.2) 178 ( 2.3) 201 ( 1.8) 226 ( 1.5) 248 ( 1.3) 266 ( 1.0)

Geometry and Spatial Sense

1992

Guam 203 ( 1.2) 159 ( 2.4) 181 ( 2.2) 203 ( 1.1) 226 ( 1.4) 244 ( 1.8)

Nation 221 ( 0.7) 181 ( 1.6) 201 ( 0.8) 222 ( 1.1) 243 ( 1.2) 260 ( 1.1)

1996

Guam 197 ( 2.4) 140 ( 3.8)< 170 ( 2.7) 201 ( 2.0) 227 ( 2.4) 250 ( 5.6)

Nation 224 ( 0.9) 184 ( 1.1) 205 ( 0.9) 226 ( 1.4) 245 ( 0.8) 261 ( 1.2)

Data Analysis, Statistics,

and Probability

1992

Guam 190 ( 0.9) 142 ( 2.0) 166 ( 1.4) 190 ( 1.0) 215 ( 1.8) 236 ( 2.1)

Nation 219 ( 1.0) 175 ( 1.7) 198 ( 1.2) 221 ( 1.4) 243 ( 1.6) 260 ( 1.6)

1996

Guam 183 ( 4.1) 114 ( 6.0)< 149 ( 5.4) 185 ( 3.4) 220 ( 4.2) 248 ( 4.0)

Nation 223 ( 1.4) 180 ( 1.8) 202 ( 1.6) 225 ( 1.4) 246 ( 1.5) 263 ( 1.1)

Algebra and Functions

1992

Guam 194 ( 1.0) 150 ( 3.5) 171 ( 1.9) 195 ( 0.9) 218 ( 1.2) 239 ( 2.1)

Nation 218 ( 0.9) 173 ( 1.3) 195 ( 0.9) 219 ( 1.4) 241 ( 1.5) 259 ( 1.8)

1996

Guam 194 ( 4.0) 126 ( 5.1)< 161 ( 3.9) 197 ( 4.2) 229 ( 2.8)> 256 ( 5.1)

Nation 226 ( 1.2)> 185 ( 1.8)> 206 ( 1.3)> 227 ( 1.7)> 247 ( 1.5) 264 ( 1.5)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

38 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

1996, Public School Students, Grade 8

Guam students performed lower than students across the nation in all

five of the content strands.

1992 vs. 1996, Public School Students, Grade 8

There was an improvement in the performance of students in Guam from

1992 to 1996 in algebra and functions. There was no significant change

in the performance of students in Guam from 1992 to 1996 in number

sense, properties, and operations; measurement; geometry and spatial

sense; and data analysis, statistics, and probability.

1990 vs. 1996, Public School Students, Grade 8

There was an improvement in the performance of students in Guam from

1990 to 1996 in geometry and spatial sense; data analysis, statistics, and

probability; and algebra and functions. There was no significant change

in the performance of students in Guam from 1990 to 1996 in number

sense, properties, and operations and measurement.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 39
Guam

TABLE 1.2B — GRADE 8

Distribution of Mathematics Scale Scores for Public School

Students by Content Area

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

Number Sense, Properties,

and Operations

1990

Guam 240 ( 0.7) 194 ( 1.4) 215 ( 1.1) 239 ( 1.0) 265 ( 1.2) 288 ( 2.2)

Nation 266 ( 1.3) 220 ( 2.4) 242 ( 2.3) 267 ( 1.2) 291 ( 1.4) 309 ( 1.3)

1992

Guam 241 ( 1.3) 188 ( 1.9) 212 ( 2.1) 241 ( 2.7) 269 ( 1.8) 295 ( 2.2)

Nation 271 ( 0.9)» 225 ( 0.8) 247 ( 1.0) 272 ( 1.4) 296 ( 1.0) 315 ( 1.2)» 

1996

Guam 243 ( 2.6) 179 ( 3.9)« 212 ( 4.2) 246 ( 3.3) 278 ( 5.2) 305 ( 7.1)

Nation 272 ( 1.2)» 225 ( 1.5) 249 ( 1.6) 274 ( 1.6)» 298 ( 1.2)» 317 ( 1.4)» 

Measurement

1990

Guam 229 ( 1.3) 178 ( 2.5) 202 ( 2.0) 228 ( 1.8) 255 ( 1.8) 280 ( 1.1)

Nation 258 ( 1.6) 202 ( 1.9) 230 ( 2.7) 259 ( 2.2) 288 ( 2.2) 312 ( 2.3)

1992

Guam 229 ( 1.6) 168 ( 2.8) 197 ( 2.8) 229 ( 1.9) 261 ( 3.9) 291 ( 2.1)» 

Nation 265 ( 1.3)» 207 ( 1.5) 234 ( 1.6) 266 ( 1.7) 296 ( 1.7) 323 ( 2.8)

1996

Guam 225 ( 6.1) 127 (12.8)« 179 ( 8.1) 228 ( 7.7) 277 ( 4.8)» 316 ( 5.9)»>

Nation 268 ( 1.6)» 206 ( 2.2) 238 ( 1.9) 270 ( 1.8)» 301 ( 2.7)» 328 ( 2.3)» 

Geometry and Spatial Sense

1990

Guam 236 ( 1.1) 189 ( 1.8) 211 ( 1.6) 237 ( 1.5) 262 ( 1.1) 283 ( 2.4)

Nation 259 ( 1.4) 213 ( 2.0) 236 ( 1.7) 260 ( 1.2) 284 ( 1.4) 303 ( 1.9)

1992

Guam 240 ( 1.5) 197 ( 2.3) 217 ( 2.1) 240 ( 1.9) 263 ( 1.9) 284 ( 2.9)

Nation 262 ( 1.0) 217 ( 1.0) 239 ( 1.4) 263 ( 1.0) 287 ( 1.1) 306 ( 1.3)

1996

Guam 245 ( 2.2)» 190 ( 4.9) 219 ( 2.3) 246 ( 4.2) 274 ( 4.3) 299 ( 3.6)» 

Nation 268 ( 1.3)»> 225 ( 1.9)»> 247 ( 1.6)»> 270 ( 1.4)»> 291 ( 1.2)» 310 ( 1.9)

Data Analysis, Statistics,

and Probability

1990

Guam 214 ( 1.2) 144 ( 3.6) 176 ( 2.0) 214 ( 2.0) 251 ( 1.9) 284 ( 2.4)

Nation 262 ( 1.6) 207 ( 3.1) 234 ( 2.0) 264 ( 1.4) 292 ( 1.4) 313 ( 1.6)

1992

Guam 222 ( 1.9)» 164 ( 3.6)» 191 ( 2.9)» 220 ( 2.2) 253 ( 1.9) 283 ( 1.7)

Nation 267 ( 1.1) 213 ( 1.3) 238 ( 1.4) 268 ( 1.6) 297 ( 1.5) 320 ( 1.7)

1996

Guam 222 ( 2.7)» 135 ( 3.3)< 180 ( 7.2) 226 ( 4.4) 269 ( 5.7) 303 ( 7.4)

Nation 270 ( 1.7)» 212 ( 1.8) 243 ( 2.1) 274 ( 1.8)» 301 ( 2.4)» 324 ( 1.8)» 

Algebra and Functions

1990

Guam 230 ( 1.0) 182 ( 2.7) 203 ( 1.6) 229 ( 1.2) 255 ( 1.3) 281 ( 2.2)

Nation 260 ( 1.3) 212 ( 2.6) 235 ( 1.7) 261 ( 1.5) 286 ( 1.6) 308 ( 2.6)

1992

Guam 236 ( 1.1)» 181 ( 1.6) 207 ( 1.8) 236 ( 2.0) 265 ( 1.7)» 292 ( 2.1)» 

Nation 267 ( 1.1)» 219 ( 1.4) 241 ( 1.2) 267 ( 1.1) 292 ( 1.3) 314 ( 2.1)

1996

Guam 247 ( 3.7)»> 186 ( 7.3) 217 ( 6.3) 249 ( 4.6)» 280 ( 3.8)»> 304 ( 3.5)» 

Nation 272 ( 1.2)»> 226 ( 1.9)» 248 ( 1.8)»> 272 ( 1.3)» 297 ( 1.4)» 318 ( 2.1)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation » («) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1990 at about the 95 percent confidence level. If the notation > (<)

appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992 at

about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

40 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

CHAPTER 2

Mathematics Scale Score Results by

Subpopulations

The previous chapter provided a global view of the mathematics performance of

fourth- and eighth-grade students in Guam and the nation. It is also important to

examine the average performance of subgroups since past NAEP assessments in

mathematics, as well as in other academic subjects, have shown substantial differences

among groups defined by gender, racial/ethnic background, parental education, and other

demographic characteristics.21 A key contribution of NAEP to the ongoing

conversations on education reform is its ability to monitor the performance of subgroups

of students in academic achievement.

The NAEP 1996 state assessment in mathematics provides performance

information for subgroups of fourth and eighth graders in Guam and the nation. In

addition to the more typical demographic subgroups defined by gender, race/ethnicity,

and parental education, the 1996 assessment also collected information on student

participation in Title I programs and services and eligibility for the free/reduced-price

lunch component of the National School Lunch Program.

The 1996 state assessment in mathematics also continues a component first

introduced with the NAEP 1994 state assessment in reading — assessment of a

representative sample of nonpublic school students. The 1996 state assessment marks

the first time that NAEP mathematics results for public and nonpublic school students

can be presented and compared at the state level. The comparison of public and

nonpublic school students’ performance does not account for confounding factors such

as student composition, family socioeconomic status, and parental involvement in their

child’s education. The size of the NAEP nonpublic school sample in most jurisdictions

does not allow for such in-depth analyses, and a more complete picture of public and

nonpublic school comparisons may be achieved by supplementing NAEP results with

data from other sources, such as the School and Staffing Survey (SASS) or National

Education Longitudinal Study (NELS).22

21 Campbell, J.R., P.L. Donahue, C.M. Reese, and G.W. Phillips. NAEP 1994 Reading Report Card for the Nation and

the States. (Washington, DC: National Center for Education Statistics, 1996); Beatty, A.S., C.M. Reese, H.R. Persky,

and P. Carr. NAEP 1994 U.S. History Report Card. (Washington, DC: National Center for Education Statistics, 1996);

Persky, H.R., C.M. Reese, C.Y. O'Sullivan, S. Lazer, J. Moore, and S. Shakrani. NAEP 1994 Geography Report Card.

(Washington, DC: National Center for Education Statistics, 1996); Campbell, J.R., C.M. Reese, C. O'Sullivan, and J.A.

Dossey. NAEP 1994 Trends in Academic Progress. (Washington, DC: National Center for Education Statistics, 1996).

22 National Center for Education Statistics. Schools and Staffing in the United States: A Statistical Profile, 1993-94.

(Washington, DC: National Center for Education Statistics, 1996); National Education Longitudinal Study. National

Education Longitudinal Study of 1988: Base Year Student Survey. (Washington, DC: National Center for Education

Statistics, 1995).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 41
Guam

A description of the subgroups and how they are defined is presented in

Appendix A. The reader is cautioned against making simple or causal inferences related

to the performance of various subgroups of students or about the effectiveness of public

and nonpublic schools or Title I programs. Average performance differences between

two groups of students may, in part, be due to socioeconomic or other factors. For

example, differences observed among racial/ethnic subgroups are almost certainly

associated with a broad range of socioeconomic and educational factors not discussed

in this report and possibly not addressed by the NAEP assessment program. Similarly,

differences in performance between students participating in Title I programs and those

who are not does not account for the initial performance level of the students prior to

placement in Title I programs or differences in course content and emphasis between the

two groups.

Gender

Consistent with research findings, NAEP mathematics results have shown little

difference in the performance of male and female fourth and eighth graders.23 As shown

in Table 2.1A, the NAEP 1996 state mathematics assessment results for fourth graders

in Guam are consistent with those general findings.

1996, Public School Students, Grade 4

The average mathematics scale score of males did not differ significantly

from that of females in both Guam and the nation.

1992 vs. 1996, Public School Students, Grade 4

From 1992 to 1996 in Guam, the average scale score of males did not

change significantly while that of females decreased.

23 Frost, L.A., J.S. Hyde, and E. Fennema. “Gender, Mathematics Performance, and Mathematics-Related Attitudes and

Affect: A Meta-analytic Synthesis,” in International Journal of Educational Research, 21, pp. 373-385, 1994; Reese,

C.M., K.E. Miller, J. Mazzeo, and J.A. Dossey. NAEP 1996 Mathematics Report Card. (Washington, DC: National

Center for Education Statistics, 1997).

42 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 2.1A — GRADE 4

Distribution of Mathematics Scale Scores for Public School

Students by Gender

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

Male

1992 Guam 190 ( 1.2) 147 ( 1.8) 167 ( 2.0) 191 ( 2.9) 213 ( 1.7) 234 ( 3.3)

Nation 220 ( 0.9) 175 ( 1.3) 198 ( 0.8) 221 ( 1.4) 243 ( 1.4) 261 ( 1.6)

1996 Guam 187 ( 1.5) 143 ( 3.9) 164 ( 2.3) 188 ( 1.7) 212 ( 2.0) 231 ( 3.8)

Nation 224 ( 1.2)> 181 ( 1.8) 202 ( 2.5) 225 ( 1.3) 246 ( 0.8) 264 ( 1.6)

Female

1992 Guam 195 ( 1.0) 153 ( 2.2) 172 ( 1.7) 196 ( 1.4) 218 ( 1.3) 238 ( 1.8)

Nation 218 ( 1.1) 176 ( 1.2) 197 ( 2.2) 219 ( 1.1) 239 ( 2.2) 257 ( 1.1)

1996 Guam 189 ( 1.8)< 146 ( 5.0) 168 ( 2.3) 190 ( 3.0) 212 ( 1.7)< 231 ( 3.1)

Nation 221 ( 1.1) 180 ( 1.9) 201 ( 1.6) 223 ( 1.3) 242 ( 0.9) 259 ( 1.0)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 43
Guam

Table 2.1B presents results for male and female eighth graders for Guam and the

nation.

1996, Public School Students, Grade 8

The average mathematics scale score of males was lower than that of

females in Guam; nationwide, however, the performance of males did

not differ significantly from that of females.

1992 vs. 1996, Public School Students, Grade 8

From 1992 to 1996 in Guam, the average scale score of both males and

females did not change significantly. The observed gender gap favoring

females for Guam in 1996 was not significantly different from the

similar gap in 1992.

1990 vs. 1996, Public School Students, Grade 8

From 1990 to 1996 in Guam, the average scale score of males did not

change significantly while that of females increased.

TABLE 2.1B — GRADE 8

Distribution of Mathematics Scale Scores for Public School

Students by Gender

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

Male

1990 Guam 232 ( 1.4) 181 ( 3.9) 205 ( 3.4) 231 ( 2.2) 259 ( 2.6) 283 ( 2.8)

Nation 262 ( 1.7) 213 ( 2.6) 237 ( 2.2) 263 ( 1.3) 289 ( 2.1) 310 ( 2.0)

1992 Guam 233 ( 1.5) 181 ( 2.5) 204 ( 2.0) 232 ( 1.4) 262 ( 3.3) 287 ( 3.1)

Nation 266 ( 1.1) 218 ( 1.4) 241 ( 2.0) 267 ( 1.5) 293 ( 1.0) 313 ( 1.9)

1996 Guam 235 ( 2.7) 183 ( 5.1) 209 ( 4.6) 236 ( 3.6) 263 ( 3.7) 288 ( 4.4)

Nation 270 ( 1.5)» 219 ( 3.0) 245 ( 2.0) 272 ( 1.8)» 298 ( 1.7)» 318 ( 1.5)

Female

1990 Guam 231 ( 1.1) 183 ( 3.6) 206 ( 1.9) 231 ( 1.9) 257 ( 1.9) 281 ( 2.8)

Nation 261 ( 1.4) 215 ( 3.5) 237 ( 2.2) 263 ( 1.4) 286 ( 1.4) 304 ( 1.6)

1992 Guam 237 ( 1.5)» 190 ( 6.2) 212 ( 1.6) 236 ( 1.9) 263 ( 2.0) 286 ( 2.0)

Nation 267 ( 1.1)» 220 ( 2.0) 242 ( 1.4) 268 ( 1.3) 292 ( 1.1)» 314 ( 1.6)» 

1996 Guam 242 ( 2.4)» 192 ( 2.7) 216 ( 2.8)» 244 ( 2.2)» 271 ( 4.3)» 291 ( 2.7)

Nation 271 ( 1.2)» 225 ( 1.7) 248 ( 2.2)» 272 ( 1.7)» 295 ( 1.5)» 314 ( 1.3)» 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation » («) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1990 at about the 95 percent confidence level. If the notation > (<)

appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992 at

about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

44 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Race/Ethnicity

As part of the background questions administered with the NAEP 1996

mathematics assessment, students were asked to identify the racial/ethnic subgroup that

best describes them. The five mutually exclusive categories were White, Black,

Hispanic, Asian or Pacific Islander, and American Indian or Alaskan Native.

The national results for eighth-grade Asian/Pacific Islander students are not

included in the main body of this report. A thorough investigation into the quality and

credibility of these results, which included an independent review by the National

Institute of Statistical Sciences, was initiated by NCES. Collateral results from the grade

8 state assessment program in mathematics suggested that the 1996 national results may

substantially underestimate actual achievement of the Asian/Pacific Islander group.

Because of its potential to misinform, NCES decided to omit the national grade 8

Asian/Pacific Islander results from the body of the report and to include them in an

appendix. Appendix F includes 1996 results for this group along with a description of

the findings that led to this decision.

Research over past decades has shown that racial/ethnic differences exist in

mathematics performance, and findings from previous NAEP assessments are consistent

with this body of research.24 However, when interpreting differences in subgroup

performance, confounding factors related to socioeconomic status, home environment,

and educational opportunities available to students need to be considered.25 The

distribution of fourth-grade mathematics scale scores for Guam and the nation are shown

in Table 2.2A for White, Hispanic, and Asian/Pacific Islander students.26

1996, Public School Students, Grade 4

White students in Guam demonstrated an average mathematics scale

score that was higher than that of Hispanic students but was not

significantly different from that of Asian/Pacific Islander students.

1992 vs. 1996, Public School Students, Grade 4

From 1992 to 1996, there was no significant change in the average scale

score of White, Hispanic, or Asian/Pacific Islander students in Guam.

24 Campbell, J.R., C.M. Reese, C. O'Sullivan, and J.A. Dossey. NAEP 1994 Trends in Academic Progress. (Washington,

DC: National Center for Education Statistics, 1996); Reese, C.M., K.E. Miller, J. Mazzeo, and J.A. Dossey. NAEP 1996

Mathematics Report Card. (Washington, DC: National Center for Education Statistics, 1997).

25 McKenzie, F.D. “Educational Strategies for the 1990s,” in The State of Black America 1991. (New York, NY: National

Urban League, Inc., 1991).

26 Results are reported for racial/ethnic subgroups meeting established sample size requirements (see Appendix A).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 45
Guam

TABLE 2.2A — GRADE 4

Distribution of Mathematics Scale Scores for Public School

Students by Race/Ethnicity

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

White

1992 Guam 206 ( 2.0) 157 ( 5.9) 183 ( 3.1) 210 ( 2.1) 232 ( 3.2) 251 ( 7.1)

Nation 227 ( 1.0) 189 ( 1.6) 208 ( 1.2) 229 ( 0.9) 247 ( 1.2) 263 ( 1.2)

1996 Guam 198 ( 5.2) 146 ( 7.4) 170 ( 8.9) 197 ( 3.6) 225 ( 8.6) 250 ( 7.3)

Nation 231 ( 1.1)> 195 ( 1.2) 213 ( 2.0) 232 ( 1.0) 250 ( 0.9) 266 ( 1.0)

Hispanic

1992 Guam 181 ( 2.1) 139 ( 8.4) 158 ( 2.7) 179 ( 2.2) 203 ( 3.3) 225 ( 3.5)

Nation 201 ( 1.5) 163 ( 3.1) 181 ( 1.8) 201 ( 1.4) 221 ( 1.7) 239 ( 2.6)

1996 Guam 176 ( 3.8) 133 ( 9.0) 152 ( 4.7) 176 ( 3.6) 199 ( 3.7) 219 ( 7.0)

Nation 205 ( 2.2) 163 ( 3.7) 184 ( 2.9) 206 ( 2.1) 227 ( 2.1) 244 ( 0.8)

Asian/Pacific Islander

1992 Guam 195 ( 1.1) 153 ( 2.4) 173 ( 2.1) 195 ( 1.0) 216 ( 1.5) 235 ( 3.0)

Nation 233 ( 2.5) 193 ( 5.5) 215 ( 6.1) 234 ( 3.0) 254 ( 5.2) 270 ( 5.1)

1996 Guam 192 ( 1.5) 151 ( 4.2) 172 ( 2.1) 193 ( 1.7) 215 ( 1.3) 233 ( 1.6)

Nation 231 ( 4.6) 192 ( 9.3) 212 ( 6.0) 232 ( 7.3) 248 ( 6.0) 273 ( 8.9)

The NAEP mathematics scale ranges from 0 to 500. Results are reported for racial/ethnic subgroups meeting established

sample size requirements (see Appendix A). The standard errors of the statistics appear in parentheses. It can be said

with about 95 percent confidence that, for each population of interest, the value for the entire population is within ± 2

standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

46 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 2.2B shows the distribution of mathematics scale scores for Hispanic and

Asian/Pacific Islander eighth-grade public school students in Guam and the nation.27

1996, Public School Students, Grade 8

Hispanic students in Guam demonstrated an average mathematics scale

score that was lower than that of Asian/Pacific Islander students.

1992 vs. 1996, Public School Students, Grade 8

From 1992 to 1996, there was an increase in the average scale score of

Asian/Pacific Islander students in Guam. From 1992 to 1996, there was

no significant change in the average scale score of Hispanic students in

Guam.

1990 vs. 1996, Public School Students, Grade 8

From 1990 to 1996, there was an increase in the average scale score of

Asian/Pacific Islander students in Guam. From 1990 to 1996, there was

no significant change in the average scale score of Hispanic students in

Guam.

27 Results are reported for racial/ethnic subgroups meeting established sample size requirements (see Appendix A).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 47
Guam

TABLE 2.2B — GRADE 8

Distribution of Mathematics Scale Scores for Public School

Students by Race/Ethnicity

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

Hispanic

1990 Guam 210 ( 1.9) 168 ( 3.5) 186 ( 4.3) 209 ( 3.5) 231 ( 2.0) 253 ( 2.7)

Nation 242 ( 2.8) 198 ( 2.5) 218 ( 2.9) 243 ( 5.5) 268 ( 2.3) 284 ( 2.3)

1992 Guam 218 ( 2.9) 170 ( 2.1) 189 ( 4.0) 216 ( 7.3) 246 ( 8.3) 272 ( 6.4)

Nation 245 ( 1.3) 203 ( 2.0) 222 ( 2.1) 245 ( 2.1) 269 ( 2.1) 289 ( 1.6)

1996 Guam 218 ( 4.9) 163 (11.0) 189 ( 8.0) 220 ( 4.7) 249 ( 7.3) 271 ( 7.9)

Nation 250 ( 2.1) 202 ( 4.0) 225 ( 2.0) 250 ( 1.8) 275 ( 2.0) 295 ( 2.4)» 

Asian/Pacific Islander

1990 Guam 235 ( 0.9) 188 ( 1.7) 210 ( 1.4) 235 ( 1.4) 260 ( 1.2) 284 ( 2.3)

1992 Guam 237 ( 1.1) 188 ( 2.2) 211 ( 1.8) 236 ( 1.8) 263 ( 2.2) 286 ( 1.9)

1996 Guam 242 ( 2.1)»> 195 ( 7.1) 218 ( 3.1) 243 ( 2.6) 269 ( 2.4)» 291 ( 4.9)

The NAEP mathematics scale ranges from 0 to 500. Results are reported for racial/ethnic subgroups meeting established

sample size requirements (see Appendix A). The standard errors of the statistics appear in parentheses. It can be said

with about 95 percent confidence that, for each population of interest, the value for the entire population is within ± 2

standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation » («) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1990 at about the 95 percent confidence level. If the notation > (<)

appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992 at

about the 95 percent confidence level. ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

48 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Students’ Reports of Parents’ Highest Education Level

Students were asked to indicate the level of education completed by each parent.

Four levels of education were identified: did not finish high school, graduated high

school, some education after high school, and graduated college. A choice of “I don’t

know” was also available. For this analysis the highest education level reported for

either parent was used.

In general, results show that with each increment in reported parental education,

student performance increases significantly. In reviewing these results, it is important

to note that nationally, approximately one third of fourth graders and one tenth of eighth

graders did not know the level of education that either of their parents had completed.

For public school students in Guam, the percentages were 40 percent for fourth graders

and 20 percent for eighth graders. Despite the fact that some research has questioned

the accuracy of student-reported data from similar groups of students,28 past NAEP

assessments in mathematics, as well as other subject areas, have found that

student-reported level of parental education exhibits a consistent positive relationship

with student performance on the assessments.29 Other research has also replicated

NAEP findings.30

Table 2.3A shows the results for fourth-grade public school students who reported

that at least one parent graduated from high school, at least one parent had some

education after high school, at least one parent graduated from college, or that they did

not know their parents’ highest education level.31 The following discussion pertains to

those students who reported knowing the educational level of one or both parents.

1996, Public School Students, Grade 4

The average mathematics scale score of students in Guam who reported

that at least one parent graduated from high school did not differ

significantly from that of students who reported that at least one parent

had some education after high school or at least one parent graduated

from college.

1992 vs. 1996, Public School Students, Grade 4

The average scale score of students in Guam who reported that at least

one parent graduated from high school, at least one parent had some

education after high school, or at least one parent graduated from college

did not change significantly between 1992 and 1996.

28 Looker, E.D. “Accuracy of Proxy Reports of Parental Status Characteristics,” in Sociology of Education, 62(4), pp.

257-276, 1989.

29 Reese, C.M., K.E. Miller, J. Mazzeo, and J.A. Dossey. NAEP 1996 Mathematics Report Card. (Washington, DC:

National Center for Education Statistics, 1997); Campbell, J.R., P.L. Donahue, C.M. Reese, and G.W. Phillips. NAEP

1994 Reading Report Card for the Nation and the States. (Washington, DC: National Center for Education Statistics,

1996); Beatty, A.S., C.M. Reese, H.R. Persky, and P. Carr. NAEP 1994 U.S. History Report Card. (Washington, DC:

National Center for Education Statistics, 1996); Persky, H.R., C.M. Reese, C.Y. O'Sullivan, S. Lazer, J. Moore, and

S. Shakrani. NAEP 1994 Geography Report Card. (Washington, DC: National Center for Education Statistics, 1996).

30 National Education Longitudinal Study. National Education Longitudinal Study of 1988: Base Year Student Survey.

(Washington, DC: National Center for Education Statistics, 1995).

31 Results are reported for parental education subgroups meeting established sample size requirements (see

Appendix A).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 49
Guam

TABLE 2.3A — GRADE 4

Distribution of Mathematics Scale Scores by Public School

Students’ Reports of Parents’ Highest Education Level

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

Graduated from high school

1992 Guam 188 ( 2.8) 147 ( 4.8) 166 ( 4.1) 188 ( 2.6) 210 ( 2.7) 229 ( 3.4)

Nation 214 ( 1.6) 174 ( 3.0) 193 ( 2.8) 216 ( 1.5) 234 ( 1.5) 252 ( 2.7)

1996 Guam 185 ( 4.1) 138 ( 8.9) 160 ( 5.8) 187 ( 3.2) 210 ( 5.0) 231 ( 8.8)

Nation 218 ( 1.7) 178 ( 3.7) 198 ( 1.6) 220 ( 2.1) 240 ( 1.6) 255 ( 2.0)

Some education after HS

1992 Guam 208 ( 3.4) 154 (10.3) 183 ( 4.0) 212 ( 3.2) 234 ( 3.1) 255 ( 3.1)

Nation 224 ( 1.7) 181 ( 1.5) 204 ( 3.8) 228 ( 2.0) 246 ( 2.3) 260 ( 2.6)

1996 Guam 195 ( 5.2) 145 ( 7.6) 169 ( 4.5) 196 (11.3) 222 ( 6.7) 245 ( 6.5)

Nation 232 ( 1.7)> 197 ( 2.8)> 216 ( 6.1) 233 ( 1.1) 250 ( 2.7) 265 ( 3.6)

Graduated from college

1992 Guam 193 ( 1.5) 149 ( 3.9) 170 ( 3.5) 193 ( 1.2) 216 ( 2.7) 237 ( 2.4)

Nation 226 ( 1.1) 181 ( 3.2) 205 ( 1.5) 228 ( 2.1) 248 ( 1.5) 266 ( 2.0)

1996 Guam 189 ( 2.2) 146 ( 4.6) 167 ( 3.8) 190 ( 2.2) 213 ( 1.6) 230 ( 2.4)

Nation 230 ( 1.6) 188 ( 2.9) 210 ( 1.2) 232 ( 2.1) 251 ( 1.4) 268 ( 1.6)

I don’t know

1992 Guam 193 ( 1.2) 151 ( 1.6) 170 ( 1.4) 194 ( 1.7) 215 ( 2.0) 235 ( 3.2)

Nation 213 ( 0.9) 173 ( 1.4) 193 ( 1.0) 214 ( 1.3) 235 ( 1.5) 252 ( 1.6)

1996 Guam 190 ( 1.5) 148 ( 4.7) 168 ( 2.5) 190 ( 3.7) 211 ( 4.4) 232 ( 2.4)

Nation 216 ( 1.5) 175 ( 4.6) 196 ( 2.3) 218 ( 1.3) 238 ( 1.2) 255 ( 2.4)

The NAEP mathematics scale ranges from 0 to 500. Results are reported for parental education subgroups meeting

established sample size requirements (see Appendix A). The standard errors of the statistics appear in parentheses. It

can be said with about 95 percent confidence that, for each population of interest, the value for the entire population is

within ± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error

of the difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school

students was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

50 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 2.3B presents results for eighth-grade students by students’ reports of

highest level of parental education. As with fourth-grade results, discussion focuses on

those students who reported an educational level for one or both parents.

1996, Public School Students, Grade 8

The average mathematics scale score of students in Guam who reported

that neither parent graduated from high school did not differ

significantly from that of students who reported that at least one parent

graduated from high school but was lower than that of students who

reported that at least one parent had some education after high school

or at least one parent graduated from college.

1992 vs. 1996, Public School Students, Grade 8

The average scale score of students in Guam who reported that neither

parent graduated from high school, at least one parent graduated from

high school, at least one parent had some education after high school,

or at least one parent graduated from college did not change significantly

between 1992 and 1996.

1990 vs. 1996, Public School Students, Grade 8

The average scale score of students in Guam who reported that neither

parent graduated from high school, at least one parent graduated from

high school, at least one parent had some education after high school,

or at least one parent graduated from college did not change significantly

between 1990 and 1996.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 51
Guam

TABLE 2.3B — GRADE 8

Distribution of Mathematics Scale Scores by Public School

Students’ Reports of Parents’ Highest Education Level

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

Did not finish high school

1990 Guam 219 ( 2.7) 177 ( 3.8) 193 ( 1.9) 218 ( 2.2) 242 ( 3.7) 264 ( 4.1)

Nation 241 ( 2.0) 204 ( 4.7) 223 ( 1.9) 242 ( 4.0) 261 ( 3.9) 277 ( 3.0)

1992 Guam 224 ( 2.5) 182 ( 2.2) 202 ( 3.0) 223 ( 3.1) 246 ( 4.9) 270 ( 5.5)

Nation 249 ( 1.8)» 209 ( 2.6) 227 ( 1.4) 246 ( 3.5) 271 ( 2.0) 291 ( 2.7)» 

1996 Guam 225 ( 7.3) 170 (61.7) 193 ( 9.8) 227 (13.3) 254 ( 7.3) 275 (10.6)

Nation 254 ( 1.9)» 210 ( 4.2) 231 ( 3.1) 257 ( 1.7)» 278 ( 5.7) 296 ( 5.5)

Graduated from high school

1990 Guam 227 ( 1.6) 179 ( 2.7) 199 ( 2.2) 226 ( 2.2) 251 ( 3.8) 277 ( 4.1)

Nation 255 ( 1.5) 212 ( 3.4) 233 ( 2.2) 255 ( 1.3) 277 ( 3.6) 297 ( 1.5)

1992 Guam 230 ( 1.9) 184 ( 1.6) 206 ( 3.7) 230 ( 2.3) 255 ( 2.5) 276 ( 1.1)

Nation 257 ( 1.3) 213 ( 2.2) 234 ( 1.4) 257 ( 1.6) 281 ( 1.9) 299 ( 1.7)

1996 Guam 232 ( 4.2) 182 ( 6.4) 205 ( 7.3) 232 ( 7.4) 259 ( 5.1) 282 ( 7.7)

Nation 260 ( 1.3)» 215 ( 1.9) 238 ( 1.5) 262 ( 1.9) 284 ( 1.0) 303 ( 2.5)

Some education after HS

1990 Guam 248 ( 2.7) 201 ( 5.9) 225 ( 5.2) 249 ( 2.0) 271 ( 3.8) 295 ( 3.4)

Nation 267 ( 1.6) 222 ( 6.4) 245 ( 1.9) 268 ( 1.9) 289 ( 2.2) 305 ( 1.4)

1992 Guam 245 ( 2.4) 197 ( 6.0) 220 ( 4.4) 245 ( 2.8) 272 ( 4.3) 291 ( 5.7)

Nation 270 ( 1.2) 227 ( 1.7) 249 ( 1.7) 270 ( 3.1) 293 ( 1.1) 314 ( 1.7)» 

1996 Guam 254 ( 3.9) 202 ( 4.2) 229 ( 5.6) 256 (11.8) 281 ( 2.5) 302 ( 4.2)

Nation 279 ( 1.5)»> 239 ( 1.6)> 258 ( 2.6)» 280 ( 2.2)» 300 ( 2.2) 318 ( 3.3)» 

Graduated from college

1990 Guam 243 ( 1.4) 191 ( 4.0) 218 ( 1.2) 243 ( 3.0) 269 ( 1.6) 290 ( 2.0)

Nation 274 ( 1.6) 226 ( 2.4) 252 ( 1.2) 277 ( 1.5) 299 ( 1.8) 318 ( 2.8)

1992 Guam 246 ( 1.9) 189 ( 4.4) 215 ( 4.2) 249 ( 3.9) 277 ( 1.1)» 301 ( 3.9)

Nation 279 ( 1.4) 231 ( 2.1) 255 ( 2.9) 282 ( 1.8) 305 ( 2.4) 324 ( 1.8)

1996 Guam 246 ( 4.2) 195 ( 9.9) 220 ( 4.9) 248 ( 3.5) 275 ( 6.4) 297 ( 4.1)

Nation 281 ( 1.8)» 232 ( 3.2) 258 ( 1.5) 283 ( 1.7) 307 ( 1.9) 326 ( 3.0)

I don’t know

1990 Guam 223 ( 1.8) 179 ( 8.0) 199 ( 2.4) 221 ( 3.0) 245 ( 2.6) 268 ( 3.3)

Nation 240 ( 3.3) 191 ( 6.6) 215 ( 4.2) 240 ( 3.2) 265 ( 4.0) 287 (10.0)

1992 Guam 227 ( 2.0) 180 (10.3) 201 ( 3.2) 226 ( 2.2) 249 ( 3.8) 273 ( 2.5)

Nation 251 ( 1.7)» 208 ( 2.6) 228 ( 3.6) 250 ( 2.5) 275 ( 3.9) 296 ( 3.3)

1996 Guam 234 ( 3.9) 188 (16.6) 211 ( 6.5) 234 ( 5.2) 261 ( 6.4) 281 ( 5.3)

Nation 253 ( 1.7)» 206 ( 4.3) 229 ( 1.7) 253 ( 3.7) 279 ( 2.4) 298 ( 1.9)

The NAEP mathematics scale ranges from 0 to 500. Results are reported for parental education subgroups meeting

established sample size requirements (see Appendix A). The standard errors of the statistics appear in parentheses. It

can be said with about 95 percent confidence that, for each population of interest, the value for the entire population is

within ± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error

of the difference (see Appendix A for details). If the notation » («) appears, it signifies that the value for public school

students was significantly higher (lower) than the value for 1990 at about the 95 percent confidence level. If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

52 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Title I Participation

The Improving America’s Schools Act of 1994 (P.L. 103-382) reauthorized the

Elementary and Secondary Education Act of 1965 (ESEA). Title I Part A of the ESEA

provides local education agencies with financial assistance to meet the educational needs

of children who are failing or most at risk of failing.32 Title I programs are designed

to help disadvantaged students meet challenging academic performance standards.

Through Title I, schools are assisted in improving teaching and learning and in providing

students with opportunities to acquire the knowledge and skills outlined in their state’s

content and performance standards. For high poverty Title I schools, all children in the

school may benefit through participation in schoolwide programs. Title I funding

supports state and local education reform efforts and promotes coordinating of resources

to improve education for all students.

NAEP first collected student-level information on participation in Title I programs

in 1994. Therefore, results comparing the performance of participating and

nonparticipating students are not available for previous NAEP mathematics assessments.

The NAEP program will continue to monitor the performance of Title I program

participants in future assessments. The Title I information collected by NAEP refers to

current participation in Title I services. Students who participated in such services in

the past but do not currently receive services are not identified as Title I participants.

Differences between students who receive Title I services and those who do not should

not be viewed as an evaluation of Title I programs. Typically, Title I services are

intended for students who score poorly on assessments. To properly evaluate Title I

programs, the performance of students participating in such programs must be monitored

over time and their progress must be assessed.33

Table 2.4 presents results for fourth- and eighth-grade students by Title I

participation. (Results for students participating in Title I programs are not reported for

Guam due to the size of the sample.)

1996, Public School Students, Grade 4

The average scale score of Guam students who did not receive Title I

services (189) was lower than the national average (229).

1996, Public School Students, Grade 8

The average scale score of Guam students who did not receive Title I

services (239) was lower than the national average (274).

32 U.S. Department of Education, Office of Elementary and Secondary Compensatory Education Programs. Improving

Basic Programs Operated by Local Education Agencies. (Washington, DC: U.S. Department of Education, 1996).

33 For a study of mathematics performance of Title I students in 1991-1992, see U.S. Department of Education,

PROSPECTS: The Congressionally Mandated Study of Educational Growth and Opportunity, Interim Report:

Language, Minority and Limited English Proficient Students. (Washington, DC: U.S. Department of Education, 1995).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 53
Guam

TABLE 2.4 — GRADES 4 AND 8

Distribution of Mathematics Scale Scores for Public School

Students by Title I Participation

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

GRADE 4

Did not participate

1996 Guam 189 ( 1.3) 145 ( 3.9) 167 ( 2.4) 190 ( 0.9) 212 ( 1.6) 232 ( 2.3)

Nation 229 ( 1.1) 191 ( 1.2) 211 ( 1.3) 231 ( 1.1) 249 ( 1.6) 265 ( 1.2)

GRADE 8

Did not participate

1996 Guam 239 ( 1.7) 187 ( 2.0) 213 ( 4.9) 240 ( 2.4) 267 ( 2.4) 290 ( 3.8)

Nation 274 ( 1.3) 228 ( 3.2) 252 ( 2.4) 276 ( 1.3) 299 ( 1.6) 318 ( 2.1)

The NAEP mathematics scale ranges from 0 to 500. Results are reported for students participating in Title I programs

only if established sample size requirements are met (see Appendix A). The standard errors of the statistics appear in

parentheses. It can be said with about 95 percent confidence that, for each population of interest, the value for the entire

population is within ± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the

standard error of the difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does

not allow accurate determination of the variability of this statistic.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

54 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Free/Reduced-Price Lunch Program Eligibility

The free/reduced-price lunch component of the National School Lunch Program

(NSLP), offered through the U.S. Department of Agriculture (USDA), is designed to

ensure that children near or below the poverty line receive nourishing meals.34

Eligibility for the free/reduced-price lunch program is included as an indicator of

poverty. The program is available to public schools, nonprofit private schools, and

residential child care institutions. Eligibility for free or reduced-price meals is

determined through the USDA’s Income Eligibility Guidelines.

NAEP first collected information on student-level eligibility for the federally

funded NSLP in 1996. Although results cannot be presented for previous NAEP

mathematics assessments, the NAEP program will continue to monitor the performance

of these students in future assessments. Table 2.5 shows the results for fourth and eighth

graders based on their eligibility for this program.

1996, Public School Students, Grade 4

The average mathematics scale score of students in Guam who were

eligible for free or reduced-price lunch (177) was lower than that of

students nationwide (207). The average scale score of Guam students

who were not eligible for free or reduced-price lunch (195) was lower

than the national average (231). The average scale score of Guam

students who were eligible for free or reduced-price lunch was lower

than that of students who were not.

1996, Public School Students, Grade 8

The average mathematics scale score of students in Guam who were

eligible for free or reduced-price lunch (217) was lower than that of

students nationwide (252). The average scale score of Guam students

who were not eligible for this service (243) was lower than the national

average (279). In Guam, the average scale score of students eligible

for free or reduced-price lunch was lower than that of students who were

not eligible for this service.

34 U.S. General Services Administration. Catalog of Federal Domestic Assistance. (Washington, DC: Executive Office

of the President, Office of Management and Budget, 1995).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 55
Guam

TABLE 2.5 — GRADES 4 AND 8

Distribution of Mathematics Scale Scores for Public School

Students by Free/Reduced-Price Lunch Eligibility

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

GRADE 4

Eligible

1996 Guam 177 ( 2.0) 135 ( 3.7) 156 ( 1.7) 178 ( 2.3) 199 ( 1.9) 218 ( 2.1)

Nation 207 ( 2.0) 167 ( 3.6) 185 ( 2.4) 207 ( 2.3) 230 ( 2.0) 246 ( 1.2)

Not eligible

1996 Guam 195 ( 1.8) 153 ( 3.6) 174 ( 2.6) 196 ( 2.4) 218 ( 2.5) 238 ( 3.7)

Nation 231 ( 1.1) 195 ( 1.6) 213 ( 1.6) 231 ( 1.3) 249 ( 1.5) 266 ( 1.6)

Information not available

1996 Guam 186 ( 3.2) 139 ( 9.8) 165 ( 5.0) 190 ( 3.9) 212 ( 7.1) 230 ( 6.5)

Nation 230 ( 4.2)! 190 ( 7.5)! 211 ( 6.3)! 232 ( 4.0)! 252 ( 4.0)! 267 ( 5.4)! 

GRADE 8

Eligible

1996 Guam 217 ( 3.7) 168 (11.5) 193 (15.1) 220 ( 4.3) 243 ( 7.2) 264 ( 5.2)

Nation 252 ( 1.5) 207 ( 2.1) 228 ( 1.7) 252 ( 1.8) 275 ( 2.6) 294 ( 1.7)

Not eligible

1996 Guam 243 ( 1.9) 194 ( 4.3) 218 ( 3.1) 245 ( 1.8) 271 ( 1.8) 293 ( 2.8)

Nation 279 ( 1.5) 235 ( 3.1) 257 ( 1.3) 280 ( 1.6) 303 ( 1.4) 321 ( 2.8)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

56 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Type of School

The NAEP 1996 state assessment marks the first time that nonpublic school

students were assessed in mathematics at the state level. Therefore, separate nonpublic

school results can be reported for Guam. Also, results based on a combined sample of

public and nonpublic school students can be presented. (Trend results are not presented

for nonpublic school students because they were not included in previous state-level

NAEP assessments of mathematics.)

In 1996, approximately 84 percent of fourth graders in Guam attended public

schools, with the remaining students attending nonpublic schools (including Catholic and

other private schools). At eighth grade, 80 percent of students in Guam attended public

schools. For the nation, 89 percent of students at both grades 4 and 8 attended public

schools in 1996.

Previous NAEP mathematics assessments and other survey research on educational

achievement have found significant differences in the performance of students attending

public and nonpublic schools.35 However, the reader is cautioned against using NAEP

results to make simplistic inferences about the relative effectiveness of public and

nonpublic schools. Average performance differences between the two types of schools

may, in part, be related to socioeconomic and sociological factors, such as levels of

parental involvement in their child’s education. To get a clearer picture of the

differences between public and nonpublic schools, more in-depth investigations must

be conducted that are beyond the scope of the NAEP state assessment program.

Table 2.6A shows the distribution of mathematics scale scores for the public,

nonpublic, and combined fourth-grade populations in Guam and the nation.

1996, Nonpublic School Students, Grade 4

The average mathematics scale score of students attending nonpublic

schools in Guam (219) was lower than that of nonpublic school students

across the nation (237).

1996, Public vs. Nonpublic School Students, Grade 4

In Guam, the average scale score of public school students (188) was

lower than that of nonpublic school students (219).

1996, Public and Nonpublic School Students Combined, Grade 4

The average mathematics scale score of public and nonpublic school

students combined in Guam (193) was lower than that of students

nationwide (224).

35 Campbell, J.R., C.M. Reese, C. O'Sullivan, and J.A. Dossey. NAEP 1994 Trends in Academic Progress. (Washington,

DC: National Center for Education Statistics, 1996); National Education Longitudinal Study. National Education

Longitudinal Study of 1988: Base Year Student Survey. (Washington, DC: National Center for Education Statistics,

1995).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 57
Guam

TABLE 2.6A — GRADE 4

Distribution of Mathematics Scale Scores for Students by

Type of School

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

Public

1996 Guam 188 ( 1.3) 145 ( 2.9) 166 ( 2.1) 189 ( 0.8) 212 ( 1.8) 231 ( 2.0)

Nation 222 ( 1.0) 180 ( 1.5) 201 ( 1.3) 224 ( 1.3) 244 ( 1.0) 261 ( 1.0)

Nonpublic

1996 Guam 219 ( 3.3) 176 ( 4.5) 197 ( 6.3) 221 ( 3.9) 242 ( 4.3) 260 ( 2.9)

Nation 237 ( 1.9) 202 ( 5.7) 219 ( 2.6) 238 ( 1.8) 255 ( 1.3) 270 ( 2.4)

Combined

1996 Guam 193 ( 1.2) 148 ( 2.6) 170 ( 1.6) 194 ( 1.1) 218 ( 2.0) 240 ( 3.2)

Nation 224 ( 0.9) 182 ( 1.1) 204 ( 1.3) 226 ( 1.0) 246 ( 0.7) 263 ( 1.0)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

58 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 2.6B shows the distribution of mathematics scale scores for the public,

nonpublic, and combined eighth-grade populations in Guam and the nation.

1996, Nonpublic School Students, Grade 8

In Guam, the average mathematics scale score of students attending

nonpublic schools (275) was lower than that of nonpublic school

students across the nation (284).

1996, Public vs. Nonpublic School Students, Grade 8

The average scale score of public school students in Guam (239) was

lower than that of nonpublic school students (275).

1996, Public and Nonpublic School Students Combined, Grade 8

The average scale score of public and nonpublic school students

combined in Guam (246) was lower than that of students nationwide

(272).

TABLE 2.6B — GRADE 8

Distribution of Mathematics Scale Scores for Students by

Type of School

Average

Scale Score

10th

Percentile

25th

Percentile

50th

Percentile

75th

Percentile

90th

Percentile

Public

1996 Guam 239 ( 1.7) 187 ( 2.1) 213 ( 5.4) 240 ( 2.3) 267 ( 2.4) 290 ( 3.8)

Nation 271 ( 1.2) 222 ( 2.0) 247 ( 1.2) 272 ( 1.1) 296 ( 1.4) 316 ( 2.0)

Nonpublic

1996 Guam 275 ( 1.9) 232 ( 9.9) 251 ( 3.4) 273 ( 3.4) 298 ( 5.4) 323 ( 4.4)

Nation 284 ( 2.4) 242 ( 4.4) 262 ( 4.6) 286 ( 1.8) 307 ( 2.4) 326 ( 3.1)

Combined

1996 Guam 246 ( 1.4) 192 ( 4.4) 219 ( 3.3) 247 ( 1.9) 274 ( 2.2) 298 ( 3.0)

Nation 272 ( 1.1) 224 ( 1.8) 248 ( 1.3) 273 ( 1.0) 298 ( 1.4) 317 ( 1.2)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 59
Guam

60 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

 PART TWO

The Mathematics Achievement Level Results

for Fourth- and Eighth-Grade Students

While providing information about what students can do in mathematics is

essential for understanding the current state of mathematics performance, knowing what

students can do is made even more relevant by also looking at what students should be

able to do. For that reason, the National Assessment Governing Board (NAGB) has

provided NAEP with achievement levels in mathematics that set standards for

performance in mathematics at grades 4, 8, and 12.

This part of the report presents results using the student achievement levels as

authorized by the NAEP legislation and adopted by NAGB.36 The achievement levels

are based on collective judgments, gathered from a broadly representative panel of

teachers, education specialists, and members of the general public, about what students

should know and be able to do relative to a body of content reflected in the NAEP

mathematics frameworks. For reporting purposes, the achievement level cutscores are

placed on the traditional NAEP scale. For each grade, the results divide the scale into

four ranges — Basic, Proficient, Advanced, and the region below Basic.

Initiated in 1990, the levels have been used to report the national and state results

in mathematics in 1990 and 1992, as well as in other subjects such as reading,

U.S. history, and geography. The mathematics achievement levels were developed by

American College Testing (ACT) under contract with NAGB. While setting student

achievement levels on NAEP is relatively new and developing, the achievement levels

are consistent with recent education reform efforts. Some state and local jurisdictions

are also developing standards and reporting their test results using them.37

36 P.L. 103-382. Improving America’s Schools Act of 1994.

37 States such as Kentucky, Maryland, Colorado, Connecticut, and North Carolina all have standard-setting initiatives

resulting in student achievement levels.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 61
Guam

Despite the commitment to standards-based reporting of NAEP results, the

transition is incomplete. There have been some critical reviews and congressionally

mandated evaluations that cast doubt on the interpretability of achievement levels and

also on the applicability of the underlying technical methodology used to develop them.

These studies were conducted by the General Accounting Office (GAO)38 and the

National Academy of Education (NAE).39 Their findings question, for example, the

application of the Angoff method for large-scale assessments like NAEP, given the

significant modifications required to accommodate the complexity of the NAEP item

structure and the multiple cutpoints. They conclude that discretion should be used in

making particular inferences about what students at each level actually know and can

do. In addition, there were concerns that the proportion of students at certain levels,

but particularly at the Advanced levels, may be underestimated.

On the other hand, the Angoff procedure is the most widely documented,

researched, and frequently used method in the standard-setting field. Many well-known

experts support the use of a modified-Angoff method on NAEP. Several critics of the

NAE studies,40 for example, have reaffirmed the integrity of the process employed by

NAGB and have concluded that the weight of the empirical evidence presented does not

support the NAE’s conclusions about achievement levels or the use of the

modified-Angoff process. In addition, the Council of Chief State School Officers’

advisory panel of state assessment directors, fully aware of the NAE’s conclusions,

supported the use of the achievement levels to report NAEP results.41

Taken together, the results of the various studies suggest the need for further

research and development. A standard-setting conference was held in the fall of 1994,

jointly sponsored by NCES and NAGB. The proceedings, which were recently released,

show the variety of approaches which can be used to achieve similar goals and the

general lack of agreement on which approach may constitute the best way.42

38 General Accounting Office. Educational Achievement Standards: NAGB’s Approach Yields Misleading

Interpretations. (Washington, DC: General Accounting Office, 1993).

39 National Academy of Education. Setting Performance Standards for Student Achievement. (Stanford, CA: National

Academy of Education, 1993).

40 American College Testing. Technical Report on Setting Achievement Levels on the 1992 National Assessment of

Educational Progress in Mathematics, Reading, and Writing. (Washington, DC: National Assessment Governing Board,

1993); G. Cizek. Reactions to the National Academy of Education Report. (Washington, DC: National Assessment

Governing Board, 1993); M. Kane. Comments on the NAE Evaluation of the NAGB Achievement Levels. (Washington,

DC: National Assessment Governing Board, 1993).

41 Education Information Advisory Committee of the Council of Chief State School Officers. A Resolution of the

Education Information Advisory Committee. (Alexandria, VA, 1994).

42 National Assessment Governing Board (NAGB) and National Center for Education Statistics (NCES). Joint Conference

on Standard Setting for Large Scale Assessments. (Washington, DC: U.S. Government Printing Office, 1995).

62 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

In summary, the student achievement levels in this report have been developed

carefully and responsibly, and have been subject to refinements and revisions in

procedures as new technologies have become available. However, standards-based

reporting for NAEP data is still in transition. The NAEP legislation states that the

student achievement levels shall be “. . . developed through a national consensus

approach, . . . used on a developmental basis, . . . and updated as appropriate.” It

requires that the developmental status of achievement levels be clearly stated in NAEP

reports. Upon review of the available information, the Commissioner of Education

Statistics has judged that the achievement levels are in a developmental status.

However, the Commissioner and NAGB also believe that the achievement levels are

useful and valuable in reporting on the educational achievement of American students.

Part Two of this report focuses on results of the NAEP 1996 state assessment

program in mathematics in terms of the NAGB achievement levels. Chapter 3 provides

an overview of the achievement level descriptors. In addition, the percentages of public

school students in Guam and the nation who performed at or above each of the

achievement levels are presented. Chapter 4 expands on these results by presenting

achievement level data for subgroups defined by gender, race/ethnicity, parental

education, participation in Title I services and programs, and eligibility for the

free/reduced-price lunch component of the National School Lunch Program. Chapter 4

also presents results for students in nonpublic schools and combined results for both

public and nonpublic school students.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 63
Guam

64 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

CHAPTER 3

Students’ Mathematics Achievement Level

Results

Achievement levels are based on collective judgments, gathered from a broadly

representative panel of teachers, education specialists, and members of the general

public, about what students should know and be able to do relative to the body of content

reflected in the NAEP mathematics framework (see Appendix B for a description of the

framework). These judgments translate into specific points on the NAEP scale that

identify boundaries between levels of achievement — Basic, Proficient, and Advanced

— for each grade. Performance at the Basic level denotes partial mastery of the

knowledge and skills that are fundamental for proficient work. Performance at the

Proficient level, represents solid academic performance. Students reaching this level

demonstrate competency over challenging subject matter. Performance at the Advanced

level signifies superior performance beyond proficient grade-level mastery. In this

report, the percentage of students at or above the three achievement levels, as well as

the percentage of students below Basic, is presented for fourth- and eighth-grade students

in Guam and the nation.

Description of NAEP Mathematics Achievement Levels

The achievement levels for the NAEP mathematics assessments were first set in

1990 and slightly revised following the 1992 mathematics assessment. Appendix D

briefly describes the process of gathering expert judgments about Basic, Proficient, and

Advanced performance — as defined by NAGB policy — on each mathematics question.

The appendix also discusses procedures for combining the various judgments on the

various questions and mapping them onto the NAEP mathematics scale. The result of

the achievement level setting process is a set of scale score cutpoints used to classify

students as Basic, Proficient, or Advanced. (Separate cutpoints are defined for each

grade.) The three mathematics achievement levels for grades 4 and 8 are elaborated on

in Figure 3.1, and examples of questions appropriate at each achievement level are also

provided. It should be noted that constructed-response questions in the assessment occur

at all levels of mathematics achievement.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 65
Guam

GRADE 4

NAEP mathematics content strands: (1) Number Sense, Properties, and Operations; (2) Measurement; (3)

Geometry and Spatial Sense; (4) Data Analysis, Statistics, and Probability; (5) Algebra and Functions.

(Note: At the fourth-grade level, algebra and functions are treated in informal and exploratory ways, often

through the study of patterns.)

Skills are cumulative across levels — from Basic to Proficient to Advanced.

Specifically, fourth graders performing at the Basic level should be able to estimate and use basic facts to

perform simple computations with whole numbers; show some understanding of fractions and decimals; and

solve simple real-world problems in all NAEP content strands. Students at this level should be able to use

— though not always accurately — four-function calculators, rulers, and geometric shapes. Their written

responses are often minimal and presented without supporting information.

Specifically, fourth graders performing at the Proficient level should be able to use whole numbers to

estimate, compute, and determine whether results are reasonable. They should have a conceptual

understanding of fractions and decimals; be able to solve real-world problems in all NAEP content strands;

and use four-function calculators, rulers, and geometric shapes appropriately. Students at the Proficient level

should employ problem-solving strategies such as identifying and using appropriate information. Their

written solutions should be organized and presented both with supporting information and explanations of

how they were achieved.

Specifically, fourth graders performing at the Advanced level should be able to solve complex and

nonroutine real-world problems in all NAEP content strands. They should display mastery in the use of

four-function calculators, rulers, and geometric shapes. These students are expected to draw logical

conclusions and justify answers and solution processes by explaining why, as well as how, they were

achieved. They should go beyond the obvious in their interpretations and be able to communicate their

thoughts clearly and concisely.

FIGURE 3.1

Mathematics Achievement Levels

BASIC

LEVEL

Fourth-grade students performing at the Basic level should show some

evidence of understanding the mathematical concepts and procedures in the

five NAEP content strands. In relation to the NAEP mathematics scale,

Basic-level achievement for fourth grade is defined by scale scores at or

above 214.

PROFICIENT

LEVEL

Fourth-grade students performing at the Proficient level should consistently

apply integrated procedural knowledge and conceptual understanding to

problem solving in the five NAEP content strands. In relation to the NAEP

mathematics scale, Proficient-level achievement for fourth grade is defined

by scale scores at or above 249.

ADVANCED

LEVEL

Fourth-grade students performing at the Advanced level should apply

integrated procedural knowledge and conceptual understanding to complex

and nonroutine real-world problem solving in the five NAEP content strands.

In relation to the NAEP scale, Advanced-level achievement for fourth grade is

defined by scale scores at or above 282.

66 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Grade 4 Basic-Level Example Item

Refer to the rectangle below. (NOTE: Size reduced from original.)

Use your centimeter ruler to make the following measurement to the nearest

centimeter.

What is the length in centimeters of one of the longer sides of the rectangle?

Answer: (8 centimeters)

Grade 4 Proficient-Level Example Item

Carol wanted to estimate the distance from A to D along the path shown on the map below.

She correctly rounded each of the given distances to the nearest mile and then added them.

Which of the following sums could be hers?

A. 4 + 6 + 5 = 15

B. 5 + 6 + 5 = 16

* C. 5 + 6 + 6 = 17

D. 5 + 7 + 6 = 18

Grade 4 Advanced-Level Example Item

If represents the number of newspapers that Lee delivers each day, 

which of the following represents the total number of newspapers that Lee delivers in 5 days?

A. 5 +

*B. 5 x

 C. :5 _

 D. ( +) x 5

FIGURE 3.1 (continued)

Mathematics Achievement Levels

1992 Percent Correct

Nation 50 (1.6)

4.6 miles

6.3 miles

5.7 miles A

B

C

D

1992 Percent Correct

Nation 25 (1.7)

1992 Percent Correct

Nation 48 (1.4)

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 67
Guam

GRADE 8

NAEP mathematics content strands: (1) Number Sense, Properties, and Operations;

(2) Measurement; (3) Geometry and Spatial Sense; (4) Data Analysis, Statistics, and

Probability; (5) Algebra and Functions.

Skills are cumulative across all levels — from Basic to Proficient to Advanced.

Specifically, eighth graders performing at the Basic level should complete problems correctly with the help

of structural prompts such as diagrams, charts, and graphs. They should be able to solve problems in all

NAEP content strands through the appropriate selection and use of strategies and technological tools —

including calculators, computers, and geometric shapes. Students at this level should also be able to use

fundamental algebraic and informal geometric concepts in problem solving.

As they approach the Proficient level, students at the Basic level should be able to determine which of

available data are necessary and sufficient for correct solutions and use them in problem solving. However,

these eighth graders may show limited skill in communicating mathematically.

Specifically, eighth graders performing at the Proficient level should be able to conjecture, defend their

ideas, and give supporting examples. They should understand the connections between fractions, percents,

decimals, and other mathematical topics such as algebra and functions. Students at the Proficient level are

expected to have a thorough understanding of basic level arithmetic operations — an understanding

sufficient for problem solving in practical situations.

Quantity and spatial relationships in problem solving and reasoning should be familiar to them, and they

should be able to convey underlying reasoning skills beyond the level of arithmetic. They should be able

to compare and contrast mathematical ideas and generate their own examples. These students should make

inferences from data and graphs; apply properties of informal geometry; and accurately use the tools of

technology. Students at this level should understand the process of gathering and organizing data and be

able to calculate, evaluate, and communicate results within the domain of statistics and probability.

Specifically, eighth graders performing at the Advanced level should be able to probe examples and

counterexamples in order to shape generalizations from which they can develop models. Eighth graders

performing at this level should use number sense and geometric awareness to consider the reasonableness

of an answer. They are expected to use abstract thinking to create unique problem-solving techniques and

explain the reasoning processes underlying their conclusions.

FIGURE 3.1 (continued)

Mathematics Achievement Levels

BASIC

LEVEL

Eighth-grade students performing at the Basic level should exhibit evidence

of conceptual and procedural understanding in the five NAEP content

strands. This level of performance signifies an understanding of arithmetic

operations — including estimation — on whole numbers, decimals, fractions,

and percents. In relation to the NAEP mathematics scale, Basic-level

achievement for eighth grade is defined by scale scores at or above 262.

PROFICIENT

LEVEL

Eighth-grade students performing at the Proficient level should apply

mathematical concepts and procedures consistently to complex problems in

the five NAEP content strands. In relation to the NAEP mathematics scale,

Proficient-level achievement for eighth grade is defined by scale scores at or

above 299.

ADVANCED

LEVEL

Eighth-grade students at the Advanced level should be able to reach beyond

the recognition, identification, and application of mathematical rules in order

to generalize and synthesize concepts and principles in the five NAEP content

strands. In relation to the NAEP mathematics scale, Advanced-level

achievement for eighth grade is defined by scale scores at or above 333.

68 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Grade 8 Basic-Level Example Item

Which of the following is both a multiple of 3 and a multiple of 7?

 A. 7,007

 B. 8,192

*C. 21,567

 D. 22,287

 E. 40,040

Did you use the calculator on this question?

 Yes No

Grade 8 Proficient-Level Example Item

 80 -

 70 -

Number 60 -

 of 50 -

Sit-ups 40 -

 30 -

 10 15 20 25 30

Age in Years

In the graph above, each dot shows the number of sit-ups and the

corresponding age for one of 13 people. According to this graph, what is the

median number of sit-ups for these 13 people?

 A. 15

 B. 20

 C. 45

* D. 50

 E. 55

Did you use the calculator on this question?

 Yes No

FIGURE 3.1 (continued)

Mathematics Achievement Levels

1992 Percent Correct

Nation 76 (1.3)

• • • • •

•

• • • • • • •

1992 Percent Correct

Nation 23 (1.4)

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 69
Guam

Grade 8 Advanced-Level Example Item

 ..

 ..

 ..

If the pattern shown in the table were continued, what number would appear

in the box at the bottom of column B next to 14?

 A. 19

 B. 21

 C. 23

 D. 25

* E. 29

FIGURE 3.1 (continued)

Mathematics Achievement Levels

A B

2 5

4 9

6 13

8 17

14 ?

1992 Percent Correct

Nation 25 (1.4)

70 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 3.1A indicates the percentage of fourth-grade public school students at or

above each achievement level, as well as the percentage of students below the Basic

level.

1996, Public School Students, Grade 4

In Guam, 3 percent of students performed at or above the Proficient

level. This percentage was smaller than that of students nationwide

(20 percent).

1992 vs. 1996, Public School Students, Grade 4

From 1992 to 1996, there was no significant change in the percentage

of Guam students who attained the Proficient level (5 percent in 1992

and 3 percent in 1996).

TABLE 3.1A — GRADE 4

Percentage of Public School Students Attaining Mathematics

Achievement Levels

Advanced At or Above

Proficient

At or Above

Basic Below Basic

1992

 Guam 0 ( 0.2) 5 ( 0.5) 26 ( 1.4) 74 ( 1.4)

 Nation 2 ( 0.3) 17 ( 1.1) 57 ( 1.2) 43 ( 1.2)

1996

 Guam 0 (****) 3 ( 0.5) 23 ( 1.4) 77 ( 1.4)

 Nation 2 ( 0.3) 20 ( 1.0) 62 ( 1.4)> 38 ( 1.4)<

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level.   Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 71
Guam

Table 3.1B provides the percentage of eighth-grade public school students at or

above each achievement level and the percentage of students below the Basic level.

1996, Public School Students, Grade 8

In Guam, 6 percent of students performed at or above the Proficient

level. This percentage was smaller than that of students nationwide

(23 percent).

1992 vs. 1996, Public School Students, Grade 8

From 1992 to 1996, there was no significant change in the percentage

of Guam students who attained the Proficient level (6 percent in 1992

and 6 percent in 1996).

1990 vs. 1996, Public School Students, Grade 8

From 1990 to 1996, the percentage of students who performed at or

above the Proficient level in Guam did not change significantly

(4 percent in 1990 and 6 percent in 1996).

TABLE 3.1B — GRADE 8

Percentage of Public School Students Attaining Mathematics

Achievement Levels

Advanced At or Above

Proficient

At or Above

Basic Below Basic

1990

 Guam 0 ( 0.2) 4 ( 0.4) 22 ( 1.0) 78 ( 1.0)

 Nation 2 ( 0.4) 15 ( 1.1) 51 ( 1.5) 49 ( 1.5)

1992

 Guam 0 ( 0.1) 6 ( 0.6)» 25 ( 1.4) 75 ( 1.4)

 Nation 3 ( 0.4) 20 ( 1.0)» 56 ( 1.2)» 44 ( 1.2)«

1996

 Guam 0 (** **) 6 ( 0.8) 29 ( 1.6)» 71 ( 1.6)«

 Nation 4 ( 0.6) 23 ( 1.2)» 61 ( 1.3)»> 39 ( 1.3)«<

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

» («) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1990

at about the 95 percent confidence level. If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.   Standard error

estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

72 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

CHAPTER 4

Mathematics Achievement Level Results by

Subpopulations

As discussed in Chapter 2 of this report, NAEP assessments have repeatedly

shown differences in performance for subpopulations of students. This chapter presents

achievement level results for Guam and the nation for subgroups of public school

students defined by gender, race/ethnicity, parental education, participation in Title I

programs, and eligibility for the free/reduced-price lunch component of the National

School Lunch Program. Results for students attending nonpublic schools are also

reported. (A description of the subgroups and how they are defined is presented in

Appendix A.)

As stated in Part One, the reader is cautioned against using NAEP results to make

simple or causal inferences related to subgroup membership or the effectiveness of

public and nonpublic schools or Title I programs.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 73
Guam

Gender

Table 4.1A provides the achievement level results by gender for fourth-grade

public school students.

1996, Public School Students, Grade 4

The percentage of males in Guam who performed at or above the

Proficient level (4 percent) was not significantly different from that of

females (3 percent).

1992 vs. 1996, Public School Students, Grade 4

In Guam from 1992 to 1996, the percentage of both males and females

who attained the Proficient level did not change significantly.

TABLE 4.1A — GRADE 4

Percentage of Public School Students Attaining Mathematics

Achievement Levels by Gender

Advanced At or Above

Proficient

At or Above

Basic Below Basic

Male

1992 Guam 0 ( 0.1) 4 ( 0.7) 24 ( 2.0) 76 ( 2.0)

Nation 2 ( 0.4) 19 ( 1.2) 59 ( 1.3) 41 ( 1.3)

1996 Guam 0 (** **) 4 ( 0.7) 23 ( 2.2) 77 ( 2.2)

Nation 3 ( 0.5) 22 ( 1.2) 63 ( 1.8) 37 ( 1.8)

Female

1992 Guam 0 ( ) 5 ( 0.8) 29 ( 1.6) 71 ( 1.6)

Nation 1 ( 0.3) 16 ( 1.4) 56 ( 1.8) 44 ( 1.8)

1996 Guam 0 (** **) 3 ( 0.8) 23 ( 1.7)< 77 ( 1.7)> 

Nation 1 ( 0.4) 17 ( 1.2) 61 ( 1.7) 39 ( 1.7)

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level.   Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

74 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 4.1B presents achievement level results for male and female eighth graders.

1996, Public School Students, Grade 8

The percentage of males who performed at or above the Proficient level

in Guam (6 percent) was not significantly different from that of females

(6 percent).

1992 vs. 1996, Public School Students, Grade 8

In Guam from 1992 to 1996, the percentage of both males and females

who attained the Proficient level did not change significantly.

1990 vs. 1996, Public School Students, Grade 8

From 1990 to 1996, the percentage of both males and females who

attained the Proficient level did not change significantly.

TABLE 4.1B — GRADE 8

Percentage of Public School Students Attaining Mathematics

Achievement Levels by Gender

Advanced At or Above

Proficient

At or Above

Basic Below Basic

Male

1990 Guam 1 ( 0.3) 4 ( 0.8) 23 ( 1.6) 77 ( 1.6)

Nation 2 ( 0.5) 17 ( 1.5) 51 ( 2.0) 49 ( 2.0)

1992 Guam 0 ( 0.3) 6 ( 1.0) 25 ( 1.5) 75 ( 1.5)

Nation 3 ( 0.5) 20 ( 1.3) 55 ( 1.5) 45 ( 1.5)

1996 Guam 0 (** **) 6 ( 1.3) 26 ( 2.6) 74 ( 2.6)

Nation 4 ( 0.7) 24 ( 1.6)» 60 ( 1.9)» 40 ( 1.9)« 

Female

1990 Guam 0 ( ) 3 ( 0.7) 21 ( 1.4) 79 ( 1.4)

Nation 2 ( 0.5) 14 ( 1.2) 51 ( 1.7) 49 ( 1.7)

1992 Guam 1 ( 0.2) 5 ( 1.0) 26 ( 2.0) 74 ( 2.0)

Nation 3 ( 0.5) 20 ( 1.3)» 56 ( 1.5) 44 ( 1.5)

1996 Guam 1 (** **) 6 ( 1.0) 32 ( 2.7)» 68 ( 2.7)« 

Nation 3 ( 0.6) 21 ( 1.4)» 61 ( 1.5)»> 39 ( 1.5)«<

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

» («) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1990

at about the 95 percent confidence level. If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.   Standard error

estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 75
Guam

Race/Ethnicity

Table 4.2A provides the percentages of fourth-grade public school students at or

above each of the three mathematics achievement levels and also the percentage below

the Basic level for White, Hispanic, and Asian/Pacific Islander students.43

1996, Public School Students, Grade 4

The percentage of White students in Guam who attained the Proficient

level was not significantly different from that of Hispanic or

Asian/Pacific Islander students.

1992 vs. 1996, Public School Students, Grade 4

From 1992 to 1996, there was no significant change in the percentage

of White, Hispanic, or Asian/Pacific Islander students who attained the

Proficient level in Guam.

Table 4.2B provides the percentages of eighth-grade public school students at or

above each of the three mathematics achievement levels and the percentage below the

Basic level for Hispanic and Asian/Pacific Islander students in Guam and the nation.44

1996, Public School Students, Grade 8

The percentage of Hispanic students in Guam who attained the

Proficient level was smaller than that of Asian/Pacific Islander students.

1992 vs. 1996, Public School Students, Grade 8

From 1992 to 1996, there was no significant change in the percentage

of Hispanic or Asian/Pacific Islander students who attained the

Proficient level in Guam.

1990 vs. 1996, Public School Students, Grade 8

From 1990 to 1996, there was no significant change in the percentage

of Asian/Pacific Islander students who attained the Proficient level in

Guam.

43 Results are reported for racial/ethnic subgroups meeting established sample size requirements (see Appendix A).

44 The 1996 national and regional results for eighth-grade Asian/Pacific Islander students are not included in this report.

Following a thorough investigation into the quality and credibility of these results, NCES decided to omit these results

from the body of the report and to include the national results in an appendix. (See Appendix F for further discussion.)

76 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 4.2A — GRADE 4

Percentage of Public School Students Attaining Mathematics

Achievement Levels by Race/Ethnicity

Advanced At or Above

Proficient

At or Above

Basic Below Basic

White

1992 Guam 1 (** **) 11 ( 1.9) 43 ( 3.8) 57 ( 3.8)

Nation 2 ( 0.4) 22 ( 1.5) 69 ( 1.4) 31 ( 1.4)

1996 Guam 1 ( ) 11 ( 4.3) 35 ( 6.2) 65 ( 6.2)

Nation 3 ( 0.5) 26 ( 1.3) 74 ( 1.6) 26 ( 1.6)

Hispanic

1992 Guam 0 (** **) 2 ( 0.9) 16 ( 2.3) 84 ( 2.3)

Nation 0 ( ) 5 ( 1.0) 33 ( 2.3) 67 ( 2.3)

1996 Guam 0 (** **) 1 ( 0.8) 13 ( 4.3) 87 ( 4.3)

Nation 0 ( ) 7 ( 1.0) 40 ( 2.6) 60 ( 2.6)

Asian/Pacific Islander

1992 Guam 0 (** **) 4 ( 0.8) 27 ( 1.7) 73 ( 1.7)

Nation 4 ( 2.0) 30 ( 4.9) 75 ( 3.5) 25 ( 3.5)

1996 Guam 0 ( ) 3 ( 0.7) 26 ( 1.5) 74 ( 1.5)

Nation 5 ( 2.8) 24 ( 6.0) 72 ( 5.5) 28 ( 5.5)

Results are reported for racial/ethnic subgroups meeting established sample size requirements (see Appendix A). The

standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level. ** ** Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 77
Guam

TABLE 4.2B — GRADE 8

Percentage of Public School Students Attaining Mathematics

Achievement Levels by Race/Ethnicity

Advanced At or Above

Proficient

At or Above

Basic Below Basic

Hispanic

1990 Guam 0 ( ) 1 (** **) 6 ( 1.5) 94 ( 1.5)

Nation 0 ( 0.2) 5 ( 1.5) 31 ( 3.2) 69 ( 3.2)

1992 Guam 0 ( ) 3 ( 1.3) 15 ( 2.7) 85 ( 2.7)

Nation 0 ( 0.3) 6 ( 0.8) 32 ( 2.1) 68 ( 2.1)

1996 Guam 0 (** **) 2 ( 1.4) 16 ( 3.0)» 84 ( 3.0)« 

Nation 1 ( ) 8 ( 1.6) 37 ( 2.5) 63 ( 2.5)

Asian/Pacific Islander

1990 Guam 1 ( 0.2) 4 ( 0.6) 23 ( 1.2) 77 ( 1.2)

1992 Guam 1 ( 0.2) 6 ( 0.6) 25 ( 1.5) 75 ( 1.5)

1996 Guam 0 (** **) 6 ( 1.1) 31 ( 2.2)» 69 ( 2.2)« 

Results are reported for racial/ethnic subgroups meeting established sample size requirements (see Appendix A). The

standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

» («) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1990

at about the 95 percent confidence level. If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.   Standard error

estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

78 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Students’ Reports of Parents’ Highest Education Level

Table 4.3A shows the mathematics achievement level results for fourth-grade

public school students who reported that at least one parent graduated from high school,

at least one parent had some education after high school, at least one parent graduated

from college, or that they did not know their parents’ highest education level.45 It should

be noted that 40 percent of fourth graders in Guam reported that they did not know the

education level of either of their parents.

1996, Public School Students, Grade 4

The percentage of Guam students who reported that at least one parent

graduated from high school who attained the Proficient level did not

differ significantly from that of students who reported that at least one

parent had some education after high school or at least one parent

graduated from college.

1992 vs. 1996, Public School Students, Grade 4

The percentage of students in Guam who reported that at least one

parent graduated from high school, at least one parent had some

education after high school, or at least one parent graduated from college

who attained the Proficient level did not change significantly between

1992 and 1996.

45 Results are reported for parental education subgroups meeting established sample size requirements (see

Appendix A).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 79
Guam

TABLE 4.3A — GRADE 4

Percentage of Public School Students Attaining Mathematics

Achievement Levels by Students’ Reports of Parents’ Highest

Education Level

Advanced At or Above

Proficient

At or Above

Basic Below Basic

Graduated from high school

 1992 Guam 0 (** **) 2 ( 1.1) 21 ( 2.8) 79 ( 2.8)

 Nation 0 ( ) 12 ( 1.9) 52 ( 2.9) 48 ( 2.9)

 1996 Guam 0 (** **) 2 ( 1.4) 22 ( 2.8) 78 ( 2.8)

 Nation 1 ( ) 15 ( 2.0) 58 ( 3.0) 42 ( 3.0)

Some education after HS

 1992 Guam 2 (** **) 14 ( 3.3) 46 ( 5.8) 54 ( 5.8)

 Nation 2 ( 0.8) 21 ( 2.5) 67 ( 3.0) 33 ( 3.0)

 1996 Guam 1 ( ) 7 ( 3.3) 33 ( 6.6) 67 ( 6.6)

 Nation 2 ( 1.1) 27 ( 3.1) 76 ( 3.0) 24 ( 3.0)

Graduated from college

 1992 Guam 0 (** **) 5 ( 1.1) 27 ( 1.9) 73 ( 1.9)

 Nation 3 ( 0.6) 25 ( 2.0) 66 ( 1.5) 34 ( 1.5)

 1996 Guam 0 ( ) 3 ( 1.0) 24 ( 1.9) 76 ( 1.9)

 Nation 4 ( 0.7) 27 ( 1.9) 70 ( 1.9) 30 ( 1.9)

I don’t know

 1992 Guam 0 (** **) 4 ( 0.8) 26 ( 2.2) 74 ( 2.2)

 Nation 1 ( 0.3) 12 ( 1.1) 50 ( 1.5) 50 ( 1.5)

 1996 Guam 0 ( ) 4 ( 0.9) 23 ( 2.2) 77 ( 2.2)

 Nation 1 ( 0.4) 14 ( 1.2) 55 ( 2.1) 45 ( 2.1)

Results are reported for parental education subgroups meeting established sample size requirements (see Appendix A).

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level. ** ** Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

80 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 4.3B presents achievement level results for eighth-grade students by

students’ reports of highest level of parental education. It should be noted that

20 percent of eighth graders in Guam reported that they did not know the education

level of either of their parents.

1996, Public School Students, Grade 8

In Guam, the percentage of students who reported that at least one parent

graduated from high school who attained the Proficient level did not

differ significantly from that of students who reported that at least one

parent had some education after high school or at least one parent

graduated from college.

1992 vs. 1996, Public School Students, Grade 8

The percentage of students in Guam who reported that at least one

parent graduated from high school, at least one parent had some

education after high school, or at least one parent graduated from college

who attained the Proficient level did not change significantly between

1992 and 1996.

1990 vs. 1996, Public School Students, Grade 8

The percentage of students in Guam who reported that at least one

parent graduated from high school, at least one parent had some

education after high school, or at least one parent graduated from college

who attained the Proficient level did not change significantly between

1990 and 1996.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 81
Guam

TABLE 4.3B — GRADE 8

Percentage of Public School Students Attaining Mathematics

Achievement Levels by Students’ Reports of Parents’ Highest

Education Level

Advanced At or Above

Proficient

At or Above

Basic Below Basic

Did not finish high school

 1990 Guam 1 ( ) 1 (** **) 11 ( 3.6) 89 ( 3.6)

 Nation 0 ( ) 3 ( 1.1) 24 ( 3.5) 76 ( 3.5)

 1992 Guam 1 (** **) 3 ( 1.6) 14 ( 2.7) 86 ( 2.7)

 Nation 1 ( ) 6 ( 1.7) 34 ( 3.2) 66 ( 3.2)

 1996 Guam 0 (** **) 3 ( ) 18 ( 6.9) 82 ( 6.9)

 Nation 1 (** **) 8 ( 2.1) 44 ( 2.7)» 56 ( 2.7)«

Graduated from high school

 1990 Guam 0 ( ) 3 ( 0.6) 17 ( 1.6) 83 ( 1.6)

 Nation 0 (** **) 8 ( 1.3) 41 ( 2.0) 59 ( 2.0)

 1992 Guam 0 ( ) 3 ( 1.0) 19 ( 2.1) 81 ( 2.1)

 Nation 1 ( 0.4) 10 ( 1.1) 45 ( 2.1) 55 ( 2.1)

 1996 Guam 0 (** **) 4 ( 1.5) 22 ( 3.8) 78 ( 3.8)

 Nation 1 ( 0.5) 12 ( 1.3) 50 ( 2.1)» 50 ( 2.1)«

Some education after HS

 1990 Guam 0 ( ) 7 ( 2.8) 36 ( 4.3) 64 ( 4.3)

 Nation 3 ( 0.9) 15 ( 2.0) 57 ( 2.7) 43 ( 2.7)

 1992 Guam 1 (** **) 6 ( 2.1) 35 ( 4.1) 65 ( 4.1)

 Nation 3 ( 0.7) 20 ( 1.4) 60 ( 1.8) 40 ( 1.8)

 1996 Guam 1 ( ) 11 ( 3.0) 43 ( 5.7) 57 ( 5.7)

 Nation 4 ( 0.8) 26 ( 2.0)» 71 ( 2.1)»> 29 ( 2.1)«<

Graduated from college

 1990 Guam 1 ( 0.5) 6 ( 1.3) 32 ( 2.0) 68 ( 2.0)

 Nation 4 ( 0.8) 25 ( 2.2) 66 ( 2.1) 34 ( 2.1)

 1992 Guam 1 ( 0.4) 11 ( 1.5) 38 ( 2.7) 62 ( 2.7)

 Nation 5 ( 0.8) 31 ( 1.9) 70 ( 1.5) 30 ( 1.5)

 1996 Guam 1 (** **) 8 ( 2.1) 36 ( 3.6) 64 ( 3.6)

 Nation 7 ( 1.2) 34 ( 2.2) 72 ( 1.6) 28 ( 1.6)

I don’t know

 1990 Guam 0 ( ) 2 ( 0.9) 13 ( 1.8) 87 ( 1.8)

 Nation 0 (** **) 5 ( 1.7) 29 ( 3.5) 71 ( 3.5)

 1992 Guam 0 ( ) 3 ( 1.2) 16 ( 2.1) 84 ( 2.1)

 Nation 0 (** **) 9 ( 1.4) 38 ( 2.5) 62 ( 2.5)

 1996 Guam 0 ( ) 3 (** **) 24 ( 3.7) 76 ( 3.7)

 Nation 1 ( 0.3) 10 ( 1.5) 41 ( 2.2) 59 ( 2.2)

Results are reported for parental education subgroups meeting established sample size requirements (see Appendix A).

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

» («) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1990

at about the 95 percent confidence level. If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.   Standard error

estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

82 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Title I Participation

Table 4.4 presents the percentage of fourth and eighth graders at or above each

of the mathematics achievement levels as well as the percentage of students below Basic

by Title I participation. (Results based on participation in Title I programs are not

available for previous state-level mathematics assessments.)

1996, Public School Students, Grade 4

A small percentage of the students who did not receive Title I services

attained the Proficient level (3 percent).

1996, Public School Students, Grade 8

A small percentage of the students who did not receive Title I services

attained the Proficient level (6 percent).

TABLE 4.4 — GRADES 4 AND 8

Percentage of Public School Students Attaining Mathematics

Achievement Levels by Title I Participation

Advanced At or Above

Proficient

At or Above

Basic Below Basic

GRADE 4

Did not participate

1996 Guam 0 (** **) 3 ( 0.6) 23 ( 1.5) 77 ( 1.5)

Nation 3 ( 0.4) 25 ( 1.3) 72 ( 1.6) 28 ( 1.6)

GRADE 8

Did not participate

1996 Guam 0 ( ) 6 ( 0.8) 29 ( 1.6) 71 ( 1.6)

Nation 4 ( 0.7) 25 ( 1.4) 66 ( 1.4) 34 ( 1.4)

Results are reported for students participating in Title I programs only if established sample size requirements are met

(see Appendix A). The standard errors of the statistics appear in parentheses. It can be said with about 95 percent

confidence that, for each population of interest, the value for the entire population is within ± 2 standard errors of the

estimate for the sample. In comparing two estimates, one must use the standard error of the difference (see Appendix

A for details). ** * Sample size is insufficient to permit a reliable estimate. **** Standard error estimates cannot be

accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 83
Guam

Free/Reduced-Price Lunch Program Eligibility

Table 4.5 shows 1996 mathematics achievement level results for fourth and eighth

graders based on their eligibility for the federally funded free/reduced-price lunch

component of the National School Lunch Program. (Similar results are not available for

previous NAEP mathematics assessments.)

1996, Public School Students, Grade 4

The percentage of students in Guam eligible for free or reduced-price

lunch who performed at or above the Proficient level (1 percent) was

smaller than that of students nationwide (8 percent). The percentage

of students in Guam who were not eligible for this service who attained

this level (5 percent) was smaller than the figure for the nation

(25 percent). In Guam, the percentage of students eligible for free or

reduced-price lunch who attained the Proficient level was smaller than

that of students who were not.

1996, Public School Students, Grade 8

The percentage of students in Guam who were not eligible for this

service who attained this level (7 percent) was smaller than the

corresponding national figure (29 percent).

84 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 4.5 — GRADES 4 AND 8

Percentage of Public School Students Attaining Mathematics

Achievement Levels by Free/Reduced-Price Lunch Eligibility

Advanced At or Above

Proficient

At or Above

Basic Below Basic

GRADE 4

Eligible

1996 Guam 0 ( ) 1 ( 0.5) 13 ( 1.8) 87 ( 1.8)

Nation 0 ( 0.3) 8 ( 1.2) 41 ( 2.6) 59 ( 2.6)

Not eligible

1996 Guam 0 (** **) 5 ( 1.0) 29 ( 2.5) 71 ( 2.5)

Nation 3 ( 0.6) 25 ( 1.4) 73 ( 1.8) 27 ( 1.8)

Information not available

1996 Guam 0 ( ) 3 ( 2.0) 24 ( 5.9) 76 ( 5.9)

Nation 3 ( 1.6) 28 ( 5.4) 72 ( 5.6) 28 ( 5.6)

GRADE 8

Eligible

1996 Guam 0 (** **) 1 ( ) 11 ( 2.7) 89 ( 2.7)

Nation 1 ( 0.3) 8 ( 1.1) 39 ( 1.8) 61 ( 1.8)

Not eligible

1996 Guam 1 (** **) 7 ( 1.0) 33 ( 1.8) 67 ( 1.8)

Nation 5 ( 0.9) 29 ( 1.7) 71 ( 1.7) 29 ( 1.7)

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). *** Sample

size is insufficient to permit a reliable estimate.   Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 85
Guam

Type of School

Table 4.6A provides the percentage of fourth-grade students at or above each

achievement level for the public, nonpublic, and combined populations. Trend results

are not presented for the nonpublic and combined populations because the nonpublic

schools were not included in previous NAEP state mathematics assessments.

1996, Nonpublic School Students, Grade 4

The percentage of nonpublic school students who performed at or above

the Proficient level in Guam (19 percent) was smaller than that of

nonpublic school students nationwide (33 percent).

1996, Public vs. Nonpublic School Students, Grade 4

In Guam, the percentage of public school students who attained the

Proficient level (3 percent) was smaller than the corresponding

percentage of nonpublic school students (19 percent).

1996, Public and Nonpublic School Students Combined, Grade 4

In Guam, 6 percent of public and nonpublic school students combined

performed at or above the Proficient level. This percentage was smaller

than that of students across the nation (21 percent).

TABLE 4.6A — GRADE 4

Percentage of Students Attaining Mathematics Achievement

Levels by Type of School

Advanced At or Above

Proficient

At or Above

Basic Below Basic

Public

1996 Guam 0 (** **) 3 ( 0.5) 23 ( 1.4) 77 ( 1.4)

Nation 2 ( 0.3) 20 ( 1.0) 62 ( 1.4) 38 ( 1.4)

Nonpublic

1996 Guam 2 ( 0.8) 19 ( 3.9) 57 ( 3.9) 43 ( 3.9)

Nation 4 ( 1.2) 33 ( 2.2) 80 ( 2.2) 20 ( 2.2)

Combined

1996 Guam 1 ( 0.2) 6 ( 0.9) 28 ( 1.4) 72 ( 1.4)

Nation 2 ( 0.3) 21 ( 0.9) 64 ( 1.2) 36 ( 1.2)

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). **** Standard

error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

86 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 4.6B provides the percentage of eighth-grade students at or above each

achievement level for the public, nonpublic, and combined populations. Trend results

are not presented for the nonpublic and combined populations because the nonpublic

schools were not included in previous NAEP state mathematics assessments.

1996, Nonpublic School Students, Grade 8

The percentage of nonpublic school students in Guam who performed

at or above the Proficient level (24 percent) was not significantly

different from* that of nonpublic school students across the nation

(33 percent).

1996, Public vs. Nonpublic School Students, Grade 8

The percentage of public school students in Guam who attained the

Proficient level (6 percent) was smaller than the percentage of

nonpublic school students who attained this level (24 percent).

1996, Public and Nonpublic School Students Combined, Grade 8

In Guam, 9 percent of public and nonpublic school students combined

performed at or above the Proficient level. This percentage was smaller

than that of students across the nation (24 percent).

TABLE 4.6B — GRADE 8

Percentage of Students Attaining Mathematics Achievement

Levels by Type of School

Advanced At or Above

Proficient

At or Above

Basic Below Basic

Public

1996 Guam 0 (****) 6 ( 0.8) 29 ( 1.6) 71 ( 1.6)

Nation 4 ( 0.6) 23 ( 1.2) 61 ( 1.3) 39 ( 1.3)

Nonpublic

1996 Guam 7 ( 1.4) 24 ( 3.3) 63 ( 3.4) 37 ( 3.4)

Nation 6 ( 1.2) 33 ( 2.9) 75 ( 2.8) 25 ( 2.8)

Combined

1996 Guam 2 ( 0.4) 9 ( 1.0) 36 ( 1.5) 64 ( 1.5)

Nation 4 ( 0.5) 24 ( 1.1) 62 ( 1.1) 38 ( 1.1)

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). **** Standard

error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

* Although the difference may appear large, recall that “significance” here refers to “statistical significance.”

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 87
Guam

88 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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 PART THREE

Finding a Context for Understanding

Students’ Mathematics Performance in Public

Schools

The mathematics performance of public school students in Guam often can be

better understood when viewed in the context of the environment in which the students

are learning. This educational environment is largely determined by school

characteristics, by characteristics of mathematics instruction in the school, by home

support for academics and other home influences, and by the students’ own views about

mathematics. Information about this environment is gathered by means of the

questionnaires administered to principals, teachers, and students.

Because NAEP is administered to a sample of students that is representative of the

fourth- and eighth-grade student populations in the schools of Guam, NAEP results

provide a broad view of the educational practices in Guam, which is useful for

improving instruction and setting policy. However, despite the richness of the NAEP

results, it is very important to note that NAEP data cannot establish a cause-and-effect

relationship between educational environment and student scores on the NAEP

mathematics assessment.

The variables contained in Part Three are from the school characteristics and

policies questionnaire, teacher questionnaires, and student background questions. These

questionnaires are sometimes refined by revising or reformatting questions between

assessments. Additional questions are sometimes added to questionnaires to track

emerging trends in education. These revisions and additions may make comparisons

with results from previous years unwise or impossible. When appropriate, trends across

assessments are presented; otherwise, only 1996 results are discussed.

Part Three consists of three chapters: Chapter 5 discusses school characteristics

related to mathematics instruction;46 Chapter 6 describes classroom practices related to

mathematics instruction, including calculator and computer use; and Chapter 7 covers

some potential influences from the home and from the students’ own views about

mathematics.

46 Information on teacher preparation is included in Appendix E of this report.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 89
Guam

90 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

CHAPTER 5

School Characteristics Related to

Mathematics Instruction

School programs and conditions, instructional practices, and resource availability

vary from state to state and even among schools within a locality. The information in

this chapter is intended to give insight into those characteristics that are associated with

students’ success in mathematics.

The variables reported here reflect information from the questionnaires completed

by principals and teachers of the public school students in the NAEP 1996 mathematics

assessment. In all cases, analyses are done at the student level. School and

teacher-reported results are given in terms of the percentage of students who attend

schools or who have teachers reporting particular practices.47

Emphasis on Mathematics in the School

In the school characteristics and policies questionnaire, principals were asked

whether their school has identified mathematics as a priority in the last two years (i.e.,

whether mathematics receives special emphasis in school-wide goals and objectives,

instruction, and workshops, etc.). Tables 5.1A and 5.1B present the public school

principals’ reports.

• The percentage of fourth-grade students in Guam who attended schools

that reported that mathematics was a priority (94 percent) was greater

than the national percentage (76 percent).

• The percentage of Guam eighth graders in schools that reported that

mathematics was a priority (76 percent) was not significantly different

from that of students nationwide (74 percent).

47 Appendix A provides more details on the units of analysis used to derive the results presented in this report.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 91
Guam

TABLE 5.1A — GRADE 4

Public Schools’ Reports on Mathematics as a Priority

Has your school identified

mathematics as a priority in the

last two years?

Guam Nation

Percentage and Average Scale Score

Yes 94 ( 0.4) 76 ( 3.9) 

188 ( 1.2) 222 ( 1.2) 

No 6 ( 0.4) 24 ( 3.9) 

*** (**.*) 220 ( 3.1) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). *** Sample size is insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

TABLE 5.1B — GRADE 8

Public Schools’ Reports on Mathematics as a Priority

Has your school identified

mathematics as a priority in the

last two years?

Guam Nation

Percentage and Average Scale Score

Yes 76 ( 0.8) 74 ( 3.3) 

237 ( 2.1) 270 ( 1.7) 

No 24 ( 0.8) 26 ( 3.3) 

245 ( 3.4) 275 ( 2.3) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

92 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Resource Availability to Teachers

Resources available to teachers and schools vary. Past surveys have shown that

teachers’ perceptions of the availability of resources (e.g., instructional materials, staff,

and preparation or planning time) are variable across the country.48 Previous NAEP

assessments in several subject areas have also shown a positive relationship between

teachers’ reports of resource availability and their students’ performance in most

states.49

Availability of Instructional Materials

Teachers often see the lack of resources as a key problem for mathematics

instruction. In 1993 a national survey reported that the average school spent $100 per

year on mathematics software, $1.00 per elementary school student on mathematics

materials and manipulatives, and $0.40 per middle school student on mathematics

materials.50 Teachers were asked to categorize how well their school systems provided

them with the classroom instructional materials they needed. Table 5.2A shows the

percentages of fourth-grade students whose teachers reported receiving varying levels

of support from their public schools.

• The percentage of students whose teachers reported receiving all of the

resources they needed in Guam (3 percent) was smaller than that of

students across the nation (12 percent).

48 National Center for Education Statistics. Schools and Staffing in the United States: A Statistical Profile, 1993-94.

(Washington, DC: National Center for Education Statistics, 1996).

49 Miller, K.E., J.E. Nelson, and M. Naifeh. Cross-State Data Compendium for the NAEP 1994 Grade 4 Reading

Assessment. (Washington, DC: National Center for Education Statistics, 1995).

50 Council of Chief State School Officers. State Indicators of Science and Mathematics Education 1995. (Washington,

DC: Council of Chief State School Officers, State Education Assessment Center, 1995).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 93
Guam

TABLE 5.2A — GRADE 4

Public School Teachers’ Reports on Resource Availability

Which of the following statements is true about

how well your school system provides you with

the instructional materials and other resources

you need to teach your class?

Guam Nation

Percentage and Average Scale Score

I get some or none of the resources I need. 1992 63 ( 1.0) 37 ( 3.5) 

190 ( 1.0) 214 ( 2.0) 

1996 75 ( 1.2)> 34 ( 2.5) 

188 ( 2.1) 221 ( 1.5)> 

I get most of the resources I need. 1992 32 ( 1.0) 52 ( 3.0) 

197 ( 1.8) 221 ( 1.2) 

1996 21 ( 1.1)< 55 ( 2.2) 

191 ( 2.8) 224 ( 1.5) 

I get all the resources I need. 1992 4 ( 0.8) 11 ( 1.7) 

206 ( 4.1) 222 ( 2.7) 

1996 3 ( 0.6) 12 ( 1.8) 

*** (**.*) 224 ( 2.3) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. *** Sample size is

insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

94 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Eighth-grade mathematics teachers were also asked about the availability of

resources. Based on the responses of public school teachers in Guam, the results are

shown in Table 5.2B.

• The percentage of students whose teachers received all of the resources

they needed in Guam (2 percent) was smaller than that of students

nationwide (20 percent).

TABLE 5.2B — GRADE 8

Public School Teachers’ Reports on Resource Availability

Which of the following statements is true about

how well your school system provides you with

the instructional materials and other resources

you need to teach your class?

Guam Nation

Percentage and Average Scale Score

I get some or none of the resources I need. 1990 72 ( 1.0) 31 ( 4.2) 

230 ( 0.9) 260 ( 3.1) 

1992 69 ( 1.1) 33 ( 1.9) 

234 ( 1.3)» 262 ( 1.5) 

1996 68 ( 1.5)« 22 ( 2.7)< 

235 ( 2.2) 265 ( 2.7) 

I get most of the resources I need. 1990 20 ( 0.7) 56 ( 4.0) 

238 ( 2.3) 265 ( 2.0) 

1992 27 ( 1.1)» 53 ( 2.5) 

234 ( 2.6) 270 ( 1.1) 

1996 30 ( 1.5)» 58 ( 3.3) 

230 ( 4.6) 272 ( 1.7)» 

I get all the resources I need. 1990 7 ( 0.6) 13 ( 2.4) 

242 ( 2.9) 264 ( 3.7) 

1992 3 ( 0.4)« 13 ( 2.3) 

*** (**.*) 273 ( 3.3) 

1996 2 ( 0.5)« 20 ( 3.1) 

*** (**.*) 279 ( 2.9)» 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation » («) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1990 at about the 95 percent confidence level. If the notation > (<)

appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992 at

about the 95 percent confidence level. *** Sample size is insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 95
Guam

Availability of Curriculum Specialist in the School

Teachers were asked if there was a curriculum specialist available to help or advise

them in mathematics. Table 5.3A shows the public school fourth-grade teachers’

responses.

• In Guam, about one fifth of the students were taught by teachers who

reported that there was a curriculum specialist available to help or advise

in mathematics (20 percent). This figure was smaller than that of

students across the nation (46 percent).

• The percentage of Guam students whose teachers reported having a

curriculum specialist available in mathematics decreased from 1992

(41 percent) to 1996 (20 percent).

TABLE 5.3A — GRADE 4

Public School Teachers’ Reports on Curriculum Specialists

Is there a curriculum specialist

available to help or advise you in

mathematics?

Guam Nation

Percentage and Average Scale Score

Yes 1992 41 ( 1.4) 50 ( 3.3) 

195 ( 1.5) 218 ( 1.3) 

1996 20 ( 1.0)< 46 ( 3.6) 

189 ( 3.1) 221 ( 2.1) 

No 1992 59 ( 1.4) 50 ( 3.3) 

190 ( 1.0) 219 ( 1.6) 

1996 80 ( 1.0)> 54 ( 3.6) 

189 ( 1.4) 224 ( 1.4) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

96 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 5.3B shows the percentages of eighth-grade students in public schools

whose teachers indicated that they had a curriculum specialist available. At grade 8,

only results from 1996 are available.

• In Guam, less than half of the students were taught by teachers who

reported that there was a curriculum specialist available to help or advise

in mathematics (39 percent). This figure was smaller than that of

students across the nation (52 percent).

TABLE 5.3B — GRADE 8

Public School Teachers’ Reports on Curriculum Specialists

Is there a curriculum specialist

available to help or advise you in

mathematics?

Guam Nation

Percentage and Average Scale Score

Yes 39 ( 1.3) 52 ( 3.8) 

231 ( 3.0) 270 ( 2.1) 

No 61 ( 1.3) 48 ( 3.8) 

235 ( 2.6) 275 ( 1.7) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 97
Guam

In-School Teacher Preparation Time

Teachers were asked to indicate how many school hours they had designated as

preparation time per week. The question did not restrict preparation time to the

mathematics classes of those students who took part in the NAEP assessment or

mathematics classes in general. The question referred to the preparation time allotted

for all classes taught by the teacher. The responses of public school fourth-grade

teachers are shown in Table 5.4A.

• The percentage of students in Guam whose teachers reported having five

or more school hours designated as preparation time per week

(22 percent) was not significantly different from that of students across

the nation (27 percent).

• The percentage of Guam students whose teachers had one to two hours

to prepare each week (37 percent) was greater than that of students

nationwide (21 percent).

TABLE 5.4A — GRADE 4

Public School Teachers’ Reports on Preparation Time

How many school hours do you have

designated as preparation time per

week?

Guam Nation

Percentage and Average Scale Score

Less than 1 22 ( 1.4) 7 ( 1.4) 

188 ( 2.8) 219 ( 4.2)! 

1-2 37 ( 1.4) 21 ( 2.1) 

190 ( 2.7) 222 ( 2.4) 

3-4 19 ( 1.0) 45 ( 2.5) 

189 ( 3.7) 226 ( 1.4) 

5 hours or more 22 ( 1.2) 27 ( 2.6) 

187 ( 2.4) 221 ( 2.1) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

98 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 5.4B shows the percentages of eighth-grade students in public schools

whose teachers reported on school hours designated for preparation. (Note that the

question referred to the total amount of preparation time for all classes taught by the

teacher.)

• The percentage of Guam students whose teachers reported having five

or more school hours designated as preparation time each week

(78 percent) was greater than that of students across the nation

(60 percent).

• The percentage of students whose teachers had one to two hours to

prepare each week in Guam (19 percent) was greater than that of

students nationwide (6 percent).

TABLE 5.4B — GRADE 8

Public School Teachers’ Reports on Preparation Time

How many school hours do you have

designated as preparation time per

week?

Guam Nation

Percentage and Average Scale Score

Less than 1 0 ( ) 3 ( 1.2) 

** * (**.*) 268 (10.6)! 

1-2 19 ( 1.2) 6 ( 1.7) 

230 ( 4.4) 261 ( 6.3)! 

3-4 3 ( 0.4) 30 ( 3.4) 

*** (**.*) 275 ( 2.4) 

5 hours or more 78 ( 1.3) 60 ( 3.7) 

235 ( 1.9) 272 ( 1.7) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic. *** Sample size is insufficient to permit a reliable estimate.

  Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 99
Guam

Parents as Classroom Aides

When school personnel and parents develop a positive line of communication, they

strengthen the learning environment for the students both at school and at home. One

of the most frequent reasons cited by school personnel for contacting parents is to

request parent volunteer time at school.51 The principals of the participating public

schools were asked if parents were used as classroom aides. As shown in Table 5.5A,

principals for fourth graders reported the following.

• About one fifth of the students in Guam (20 percent) were in schools

that reported routinely using parents as aides in classrooms. In contrast,

27 percent of students in Guam attended schools where parents were

not used as classroom aides.

• From 1992 to 1996, the percentage of Guam students in schools that

reported routinely using parents as aides in classrooms increased

somewhat (18 percent in 1992 and 20 percent in 1996).

TABLE 5.5A — GRADE 4

Public Schools’ Reports on Parents as Aides in Classrooms

Does your school use parents as aides

in classrooms?

Guam Nation

Percentage and Average Scale Score

No 1992 8 ( 0.2) 11 ( 2.5) 

** * (**.*) 212 ( 4.5)! 

1996 27 ( 0.5)> 8 ( 1.7) 

191 ( 3.1) 219 ( 3.7)! 

Yes, occasionally 1992 74 ( 0.2) 42 ( 3.3) 

191 ( 0.9) 216 ( 1.4) 

1996 53 ( 0.6)< 44 ( 4.8) 

189 ( 2.0) 219 ( 2.1) 

Yes, routinely 1992 18 ( 0.2) 47 ( 3.4) 

204 ( 2.4) 223 ( 1.5) 

1996 20 ( 0.6)> 48 ( 4.9) 

185 ( 2.8)< 225 ( 1.9) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. ! Interpret with caution

— the nature of the sample does not allow accurate determination of the variability of this statistic. *** Sample size is

insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

51 National Center for Education Statistics. The Condition of Education 1995. (Washington, DC: National Center for

Education Statistics, 1995).

100 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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Table 5.5B shows the percentages of eighth-grade public school students in

schools whose principals reported on the use of parents as classroom aides.

• None of Guam students (0 percent) were in schools that reported

routinely using parents as aides in classrooms. In contrast, 100 percent

of students in Guam attended schools where parents were not used as

classroom aides.

TABLE 5.5B — GRADE 8

Public Schools’ Reports on Parents as Aides in Classrooms

Does your school use parents as aides

in classrooms?

Guam Nation

Percentage and Average Scale Score

No 1992 100 ( ) 48 ( 3.9) 

235 ( 1.2) 268 ( 2.0) 

1996 100 (** **) 41 ( 5.0) 

239 ( 1.7) 267 ( 2.2) 

Yes, occasionally 1992 0 ( ) 40 ( 3.7) 

** * (**.*) 267 ( 2.0) 

1996 0 (****) 46 ( 4.9) 

*** (**.*) 274 ( 2.4) 

Yes, routinely 1992 0 (****) 12 ( 2.7) 

*** (**.*) 266 ( 2.9)! 

1996 0 (****) 13 ( 3.6) 

*** (**.*) 273 ( 5.1)! 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. ! Interpret with caution

— the nature of the sample does not allow accurate determination of the variability of this statistic. *** Sample size is

insufficient to permit a reliable estimate.   Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 101
Guam

Student Absenteeism

School principals were asked if student absenteeism was a serious, moderate, or

minor problem, or not a problem. Table 5.6A shows, for fourth graders, results based

on principals’ reports.

• In Guam, 29 percent of the students attended public schools that

reported that absenteeism was a moderate to serious problem. This

percentage was greater than that of students across the nation

(13 percent).

• The percentage of students in schools reporting that absenteeism was a

moderate to serious problem in Guam increased somewhat from 1992

(27 percent) to 1996 (29 percent).

TABLE 5.6A — GRADE 4

Public Schools’ Reports on Student Absenteeism

To what degree is student absenteeism

a problem in your school?

Guam Nation

Percentage and Average Scale Score

Not a problem 1992 0 (** **) 31 ( 2.7) 

*** (**.*) 226 ( 1.7) 

1996 16 ( 0.3) 43 ( 4.1) 

190 ( 2.9) 230 ( 1.8) 

Minor 1992 73 ( 0.2) 54 ( 3.1) 

192 ( 1.1) 219 ( 1.4) 

1996 55 ( 0.6)< 44 ( 4.3) 

191 ( 1.2) 218 ( 2.3) 

Moderate to serious 1992 27 ( 0.2) 15 ( 2.2) 

194 ( 1.9) 202 ( 2.1) 

1996 29 ( 0.5)> 13 ( 2.3) 

184 ( 2.4)< 210 ( 3.1) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. *** Sample size is

insufficient to permit a reliable estimate.   Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

102 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 5.6B shows the percentages of eighth-grade students in public schools where

principals reported the degree to which absenteeism is a problem.

• In Guam, 66 percent of the students attended public schools that

reported that absenteeism was a moderate to serious problem. This

figure was greater than that of students nationwide (25 percent).

• There was an increase in the percentage of Guam students attending

schools that reported that absenteeism was a moderate to serious

problem from 1992 (34 percent) to 1996 (66 percent).

TABLE 5.6B — GRADE 8

Public Schools’ Reports on Student Absenteeism

To what degree is student absenteeism

a problem in your school?

Guam Nation

Percentage and Average Scale Score

Not a problem 1990 0 (** **) 10 ( 4.1) 

*** (**.*) 277 ( 4.8)! 

1992 0 (****) 19 ( 3.1) 

*** (**.*) 274 ( 3.2) 

1996 0 (****) 22 ( 3.7) 

*** (**.*) 282 ( 3.6) 

Minor 1990 32 ( 0.2) 52 ( 6.2) 

236 ( 1.4) 262 ( 2.1) 

1992 66 ( 0.2)» 52 ( 3.9) 

235 ( 1.2) 270 ( 1.5)» 

1996 34 ( 0.8)< 54 ( 4.4) 

230 ( 2.9) 272 ( 1.6)» 

Moderate to serious 1990 68 ( 0.2) 38 ( 5.5) 

230 ( 0.9) 258 ( 2.6) 

1992 34 ( 0.2)« 29 ( 3.9) 

235 ( 2.7) 258 ( 2.1) 

1996 66 ( 0.8)> 25 ( 3.1) 

239 ( 2.6)» 262 ( 2.4) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation » («) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1990 at about the 95 percent confidence level. If the notation > (<)

appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992 at

about the 95 percent confidence level. ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic. *** Sample size is insufficient to permit a reliable estimate.

  Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 103
Guam

104 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

CHAPTER 6

Classroom Practices Related to Mathematics

Instruction

The mathematics achievement of our nation’s students has been the topic of

considerable discussion in recent years. The mathematics achievement of our students

does not compare well with that of students in other countries52 or with achievement

goals set by the United States for itself.53 Improvements in mathematics performance

during the 1980s and 1990s are encouraging;54 however, policy makers and educators

must continue to evaluate the state of mathematics education and to commit to

improvements to school mathematics programs.

For some of the issues discussed in this chapter, student- and teacher-reported

results for similar questions are presented. In these situations, some discrepancies may

exist between student- and teacher-reported percentages. It is not possible to offer

conclusive reasons for these discrepancies or to determine which reports most accurately

reflect fourth- and eighth-grade classroom activities. The reports presented represent

students’ and teachers’ impressions of the frequency of various activities in the

classrooms.

An important step in the improvement of mathematics education in the nation’s

elementary and secondary schools was the development and adoption of the National

Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for

School Mathematics.

55 Already adopted by the majority of the states,56 the NCTM

Standards represent a basis upon which mathematics instruction can be reformed and

improved. This chapter focuses on curricular and instructional content issues in Guam

public schools and their relationship to students’ mathematics performance.

52 Lapointe, A.E., N.A. Mead, and J.M. Askew. Learning Mathematics. (Washington, DC: The International Assessment

of Educational Progress, National Center for Education Statistics, 1992); Beaton, A.E., I.V.S. Mullis, M.D. Martin, E.S.

Gonzalez, D.L. Kelly, and T.A. Smith. Mathematics Achievement in the Middle School Years. (Chestnut Hill, MA:

TIMSS International Study Center, Boston College, 1996).

53 Reese, C.M., K.E. Miller, J. Mazzeo, and J.A. Dossey. NAEP 1996 Mathematics Report Card. (Washington, DC:

National Center for Education Statistics, 1997).

54 Campbell, J.R., C.M. Reese, C. O'Sullivan, and J.A. Dossey. NAEP 1994 Trends in Academic Progress. (Washington,

DC: National Center for Education Statistics, 1996).

55 National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. (Reston,

VA: NCTM, 1989).

56 Council of Chief State School Officers. Analysis of State Education Indicators: State Profiles and NAEP Results Related

to State Policies and Practices. (Washington, DC: Council of Chief State School Officers, State Education Assessment

Center, 1993).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 105
Guam

NCTM Standards

Since their publication in 1989, the NCTM Standards have received considerable

attention by policy makers and educators. The NCTM Standards outline curriculum and

evaluation recommendations for kindergarten through grade 12 mathematics instruction.

To gauge how knowledgeable teachers are about the standards, teachers were asked

about their familiarity with the NCTM Standards and their involvement in professional

development related to them. Table 6.1A shows the results based on the responses of

fourth-grade public school mathematics teachers.

• A small percentage of the fourth-grade students in Guam (1 percent)

had mathematics teachers who reported being very knowledgeable about

the NCTM Standards. This percentage was smaller than the percentage

whose teachers reported having little or no knowledge of the Standards

(63 percent).

• The percentage of Guam fourth graders whose teachers reported being

very knowledgeable about the NCTM Standards was smaller than the

percentage for the nation (6 percent).

TABLE 6.1A — GRADE 4

Public School Teachers’ Reports on Knowledge of the NCTM

Standards

How knowledgeable are you about the

National Council of Teachers of Mathematics

(NCTM) Curriculum and Evaluation Standards

for School Mathematics?

Guam Nation

Percentage and Average Scale Score

I have little or no knowledge. 63 ( 1.2) 45 ( 2.4) 

185 ( 1.8) 222 ( 1.7) 

Somewhat knowledgeable 25 ( 1.3) 32 ( 2.4) 

192 ( 2.4) 222 ( 1.6) 

Knowledgeable 11 ( 0.8) 18 ( 2.0) 

198 ( 2.9) 222 ( 2.0) 

Very knowledgeable 1 ( 0.2) 6 ( 1.2) 

** * (**.*) 235 ( 4.8)! 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic. *** Sample size is insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

106 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Eighth-grade public school mathematics teachers were also asked about their

knowledge of the NCTM Standards. As presented in Table 6.1B, their responses

indicate the following.

• None of the eighth-grade students in Guam (0 percent) had mathematics

teachers who reported being very knowledgeable about the NCTM

Standards.

TABLE 6.1B — GRADE 8

Public School Teachers’ Reports on Knowledge of the NCTM

Standards

How knowledgeable are you about the

National Council of Teachers of Mathematics

(NCTM) Curriculum and Evaluation Standards

for School Mathematics?

Guam Nation

Percentage and Average Scale Score

I have little or no knowledge. 69 ( 1.4) 16 ( 2.6) 

234 ( 1.8) 264 ( 3.6) 

Somewhat knowledgeable 3 ( 0.7) 34 ( 3.1) 

*** (**.*) 268 ( 2.9) 

Knowledgeable 27 ( 1.4) 33 ( 3.9) 

236 ( 4.1) 275 ( 2.3) 

Very knowledgeable 0 (****) 17 ( 2.7) 

*** (**.*) 282 ( 2.3) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). *** Sample size is insufficient to permit a reliable estimate.   Standard

error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 107
Guam

Teachers were also asked whether they had participated in any professional

development activities that provided them with strategies for implementing the NCTM

Standards. The activities could include local workshops, and regional and national

NCTM meetings. (Teachers were asked to select all activities that applied.) Table 6.2A

presents the results for fourth-grade public school mathematics teachers.

• About three quarters of the students in Guam (78 percent) had

mathematics teachers who reported attending no professional

development activities related to implementing the NCTM Standards.

This percentage was greater than the percentage for the nation

(60 percent).

TABLE 6.2A — GRADE 4

Public School Teachers’ Reports on Professional

Development for Implementing the NCTM Standards

Have you participated in any professional

development activities that have provided

you with strategies for implementing the 1989

NCTM Curriculum and Evaluation Standards

for School Mathematics?

Guam Nation

Percentage and Average Scale Score

Local workshop 18 ( 0.9) 29 ( 2.5) 

196 ( 2.5) 223 ( 1.9) 

Regional or national NCTM meeting 0 (** **) 9 ( 1.4) 

*** (**.*) 229 ( 3.1) 

Other 4 ( 0.5) 12 ( 1.7) 

*** (**.*) 230 ( 3.3) 

No 78 ( 1.0) 60 ( 2.8) 

187 ( 1.5) 222 ( 1.3) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). *** Sample size is insufficient to permit a reliable estimate.   Standard

error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

108 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

When eighth-grade public school mathematics teachers were asked this question

(see Table 6.2B), their responses showed the following.

• About two thirds of the eighth graders in Guam (67 percent) had

mathematics teachers who reported attending no professional

development activities related to implementing the NCTM Standards.

This percentage was greater than the percentage for the nation

(35 percent).

TABLE 6.2B — GRADE 8

Public School Teachers’ Reports on Professional

Development for Implementing the NCTM Standards

Have you participated in any professional

development activities that have provided

you with strategies for implementing the 1989

NCTM Curriculum and Evaluation Standards

for School Mathematics?

Guam Nation

Percentage and Average Scale Score

Local workshop 24 ( 1.4) 51 ( 2.9) 

237 ( 4.6) 276 ( 2.0) 

Regional or national NCTM meeting 0 (** **) 25 ( 3.1) 

*** (**.*) 276 ( 2.2) 

Other 11 ( 0.9) 16 ( 2.4) 

237 ( 6.1) 274 ( 2.6) 

No 67 ( 1.7) 35 ( 3.1) 

234 ( 2.0) 267 ( 2.3) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). *** Sample size is insufficient to permit a reliable estimate. **** Standard

error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 109
Guam

Course-Taking Patterns

To investigate the relationship between the mathematics performance of students

and their study of mathematics in school, information on the types of mathematics

classes in which students were enrolled and the amount of time each week spent on

mathematics instruction in class was collected.

Typically, all fourth-grade students take mathematics. Most eighth graders, with

a few exceptions, also take mathematics. However, by the time a student reaches the

eighth grade, different types of mathematics courses are available. Eighth graders in

Guam were asked about the mathematics class they were currently taking and about the

class they expected to take in the ninth grade. Based on their responses, shown in

Table 6.3:

• In eighth grade, about one third of the students reported taking

eighth-grade mathematics (32 percent), compared to 42 percent taking

prealgebra and 21 percent taking algebra. The percentage of students

taking algebra did not differ significantly from that for the nation

(24 percent).

• About one third of the eighth-grade students expected to take prealgebra

(11 percent) or algebra (24 percent) in the ninth grade. Another

18 percent anticipated taking a geometry class.

110 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 6.3 — GRADE 8

Public School Students’ Reports on their Mathematics Classes

What kind of mathematics class . . .

Guam Nation

Percentage and Average Scale Score

Are you taking this year?*

 Eighth-grade mathematics 32 ( 1.6) 44 ( 2.3)

 221 ( 3.3) 261 ( 1.5)

 Prealgebra 42 ( 1.6) 27 ( 1.9)

 245 ( 2.1) 269 ( 1.6)

 Algebra 21 ( 1.5) 24 ( 1.6)

 264 ( 3.8) 294 ( 1.8)

 Integrated or sequential mathematics 0 ( 0.2) 1 ( 0.3)

 *** (**.*) 280 ( 8.8)!

 Applied mathematics (technical preparation) 1 ( 0.3) 0 ( 0.0)

 *** (**.*) *** (**.*)

 Other mathematics class 4 ( 0.6) 3 ( 0.5)

 *** (**.*) 264 ( 5.8)

Do you expect to take in ninth grade?

 I do not expect to take mathematics

 in ninth grade. 3 ( 0.5) 1 ( 0.2)

 *** (**.*) *** (**.*)

 Basic, general, business, or consumer

 mathematics 7 ( 0.7) 8 ( 0.7)

 215 ( 5.7) 250 ( 2.3)

 Applied mathematics (technical preparation) 1 ( 0.3) 2 ( 0.3)

 *** (**.*) 256 ( 3.9)

 Prealgebra 11 ( 1.1) 11 ( 1.0)

 231 ( 6.7) 257 ( 2.1)

 Algebra I or elementary algebra 24 ( 1.3) 32 ( 1.4)

 251 ( 3.0) 275 ( 1.3)

 Geometry 18 ( 1.5) 20 ( 1.4)

 263 ( 3.8) 293 ( 2.3)

 Integrated or sequential mathematics 1 ( 0.2) 2 ( 0.4)

 *** (**.*) 275 ( 7.2)!

 Other mathematics class 2 ( 0.4) 3 ( 0.5)

 *** (**.*) 292 ( 3.9)

 I don’t know. 35 ( 1.7) 22 ( 1.4)

 230 ( 2.6) 261 ( 1.8)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). * Percentages may not total 100 percent because a small number of students

reported that they are not taking a mathematics class. ! Interpret with caution — the nature of the sample does not allow

accurate determination of the variability of this statistic. *** Sample size is insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 111
Guam

The amount of time spent on mathematics instruction within the classroom also

varies from school to school and from state to state.57 The teachers of the fourth graders

participating in the NAEP assessment were asked about the amount of time spent each

week on mathematics instruction. Table 6.4A presents the public school teachers’

responses.

• In 1996, more than half of the students in Guam had teachers who

reported spending four or more hours on mathematics instruction

(56 percent), compared to 12 percent who reported spending two and

a half hours or less. The average scale score for students receiving four

or more hours of mathematics instruction (188) was not significantly

different from that for students receiving two and a half hours or less

(191).

• The percentage of fourth graders in Guam whose teachers reported

spending four hours or more on mathematics instruction was smaller

than the percentage for the nation (69 percent).

• The percentage of Guam fourth graders in 1996 whose teachers reported

spending four hours or more on mathematics instruction was smaller

than the percentage in 1992 (71 percent).

TABLE 6.4A — GRADE 4

Public School Teachers’ Reports on Time Spent on

Mathematics Instruction

How much time do you spend each week on

mathematics instruction with this class?

Guam Nation

Percentage and Average Scale Score

21⁄2 hours or less 1992 9 ( 0.5) 5 ( 1.0) 

196 ( 2.0) 224 ( 3.7)! 

1996 12 ( 1.1) 5 ( 1.1) 

191 ( 3.8) 225 ( 2.8)! 

More than 21⁄2 hours but less than 4 hours 1992 20 ( 1.1) 21 ( 2.1) 

191 ( 1.8) 222 ( 2.6) 

1996 32 ( 1.3)> 25 ( 2.5) 

191 ( 2.3) 225 ( 1.9) 

4 hours or more 1992 71 ( 1.1) 74 ( 2.5) 

193 ( 1.1) 217 ( 1.1) 

1996 56 ( 1.5)< 69 ( 2.8) 

188 ( 2.6) 222 ( 1.1)> 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. ! Interpret with caution

— the nature of the sample does not allow accurate determination of the variability of this statistic.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

57 National Center for Education Statistics. Schools and Staffing in the United States: A Statistical Profile, 1993-94.

(Washington, DC: National Center for Education Statistics, 1996).

112 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Eighth-grade mathematics teachers were also asked about the amount of time

dedicated to mathematics instruction. Based on the responses of public school teachers

in Guam, the results are shown in Table 6.4B.

• About two thirds of the eighth graders in 1996 had teachers who

reported spending four or more hours on mathematics instruction

(68 percent), compared to 26 percent who reported spending two and

a half hours or less. The average scale score for students receiving four

or more hours of mathematics instruction (234) was not significantly

different from* that for students receiving two and a half hours or less

(228).

• The percentage of eighth graders whose teachers reported spending four

hours or more on mathematics instruction in Guam was greater than the

percentage for the nation (34 percent).

• The percentage of students in 1996 whose teachers reported spending

four hours or more on mathematics instruction was greater than the

percentage in 1992 (28 percent).

TABLE 6.4B — GRADE 8

Public School Teachers’ Reports on Time Spent on

Mathematics Instruction

How much time do you spend each week on

mathematics instruction with this class?

Guam Nation

Percentage and Average Scale Score

21⁄2 hours or less 1992 4 ( 0.3) 13 ( 2.2) 

*** (**.*) 270 ( 3.9) 

1996 26 ( 1.5)> 20 ( 3.2) 

228 ( 3.6) 268 ( 3.2) 

More than 21⁄2 hours but less than 4 hours 1992 68 ( 0.9) 55 ( 2.7) 

233 ( 1.5) 269 ( 1.5) 

1996 6 ( 0.8)< 46 ( 3.5) 

*** (**.*) 274 ( 1.8) 

4 hours or more 1992 28 ( 0.9) 32 ( 3.1) 

237 ( 1.7) 267 ( 2.2) 

1996 68 ( 1.5)> 34 ( 3.5) 

234 ( 2.0) 273 ( 3.1) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. *** Sample size is

insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

* Although the difference may appear large, recall that “significance” here refers to “statistical significance.”

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 113
Guam

Instructional Emphasis

The framework or blueprint that guided the development of the NAEP 1996

mathematics assessment identified three mathematical abilities — conceptual

understanding, procedural knowledge, and problem solving. The NCTM Standards

emphasize the need to give students the opportunity to develop all three abilities.

Focusing on only one of these abilities is limiting to students’ mathematical

development. For example, emphasizing how to do a problem (procedural knowledge)

without understanding why it works (conceptual understanding) or when to use it

(problem solving) offers students, at best, an incomplete picture of mathematics. These

three abilities were reflected in the specifications for the 1990, 1992, and 1996 NAEP

mathematics assessments. Questions assessing all of these abilities were included. Also

identified by the NCTM Standards is the ability to reason which depends upon all three

of the previous abilities, and the need for students to be able to communicate

mathematical ideas. To assess the students’ opportunities to experience a variety of

learning, teachers were asked how often they addressed skills related to these abilities.

Table 6.5A shows the results based on responses given by grade 4 teachers.

• Almost all of the fourth graders had teachers who reported they

addressed the learning of mathematics facts and concepts a lot

(90 percent), while a small percentage (2 percent) had teachers who

reported spending little or no time on the topic.

• A large majority of the students had teachers who reported they

addressed the learning of skills and procedures a lot (82 percent). At

the other extreme, 5 percent of the students had teachers who reported

spending little or no time on the topic.

• Teachers of 32 percent of the students reported they addressed the

developing of reasoning and analytical ability a lot. In contrast,

22 percent had teachers who reported spending little or no time

addressing the topic.

• In terms of addressing the learning of how to communicate ideas in

mathematics clearly, 39 percent of fourth graders had teachers who

reported doing so a lot, while 24 percent of the students had teachers

who reported spending little or no time addressing the topic.

114 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 6.5A — GRADE 4

Public School Teachers’ Reports on Skills Addressed

In this mathematics class, how often do you

address each of the following?

Guam Nation

Percentage and Average Scale Score

Learning mathematics facts and concepts

 A little or none 2 ( 0.5) 0 (****)

 *** (**.*) *** (**.*)

 Some 8 ( 0.6) 7 ( 1.1)

 193 ( 6.2) 221 ( 3.5)

 A lot 90 ( 0.7) 93 ( 1.1)

 189 ( 1.5) 223 ( 1.1)

Learning skills and procedures needed

to solve routine problems

 A little or none 5 ( 0.6) 0 (****)

 *** (**.*) *** (**.*)

 Some 13 ( 1.1) 9 ( 1.3)

 191 ( 3.8) 220 ( 3.9)

 A lot 82 ( 1.2) 91 ( 1.3)

 189 ( 1.8) 223 ( 1.1)

Developing reasoning and analytical

ability to solve unique problems

 A little or none 22 ( 1.1) 7 ( 1.2)

 193 ( 2.7) 222 ( 3.4)

 Some 46 ( 1.3) 39 ( 2.6)

 188 ( 2.3) 219 ( 1.7)

 A lot 32 ( 1.3) 54 ( 2.5)

 188 ( 2.8) 226 ( 1.6)

Learning how to communicate ideas in

 mathematics effectively

 A little or none 24 ( 1.1) 17 ( 1.9)

 192 ( 3.2) 227 ( 2.1)

 Some 37 ( 1.2) 44 ( 2.7)

 190 ( 2.2) 219 ( 2.0)

 A lot 39 ( 1.2) 39 ( 2.6)

 186 ( 2.2) 225 ( 1.6)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). *** Sample size is insufficient to permit a reliable estimate.   Standard

error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 115
Guam

Eighth-grade mathematics teachers were also asked about the degree to which they

addressed the mathematical abilities (Table 6.5B).

• Almost all of the eighth graders had teachers who reported they

addressed the learning of mathematics facts and concepts a lot

(93 percent), while none (0 percent) had teachers who reported

spending little or no time on the topic.

• A large majority of the students had teachers who reported they

addressed the learning of skills and procedures a lot (80 percent). At

the other extreme, 2 percent of the students had teachers who reported

spending little or no time on the topic.

• Teachers of 55 percent of the students reported they addressed the

developing of reasoning and analytical ability a lot. A small percentage

of the students (2 percent) had teachers who reported spending little or

no time addressing the topic.

• In terms of addressing the learning of how to communicate ideas in

mathematics clearly, 58 percent of eighth graders had teachers who

reported doing so a lot while 14 percent of students had teachers who

reported spending little or no time on the topic.

116 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 6.5B — GRADE 8

Public School Teachers’ Reports on Skills Addressed

In this mathematics class, how often do you

address each of the following?

Guam Nation

Percentage and Average Scale Score

Learning mathematics facts and concepts

 A little or none 0 (** **) 5 ( 1.7)

 *** (**.*) 276 ( 5.4)!

 Some 7 ( 0.9) 16 ( 2.4)

 *** (**.*) 269 ( 2.7)

 A lot 93 ( 0.9) 79 ( 3.0)

 234 ( 2.1) 273 ( 1.6)

Learning skills and procedures needed

to solve routine problems

 A little or none 2 ( 0.6) 3 ( 0.9)

 *** (**.*) 278 ( 7.5)!

 Some 18 ( 1.2) 18 ( 2.6)

 238 ( 2.7) 273 ( 2.9)

 A lot 80 ( 1.6) 79 ( 2.7)

 232 ( 2.5) 272 ( 1.5)

Developing reasoning and analytical

ability to solve unique problems

 A little or none 2 ( 0.7) 8 ( 1.6)

 *** (**.*) 251 ( 5.7)!

 Some 44 ( 1.4) 40 ( 3.4)

 233 ( 2.1) 266 ( 2.0)

 A lot 55 ( 1.3) 52 ( 3.3)

 237 ( 2.9) 281 ( 1.5)

Learning how to communicate ideas in

 mathematics effectively

 A little or none 14 ( 1.1) 16 ( 2.0)

 217 ( 4.0) 263 ( 3.8)

 Some 28 ( 1.4) 42 ( 3.2)

 236 ( 2.5) 271 ( 2.3)

 A lot 58 ( 1.3) 42 ( 3.2)

 236 ( 2.9) 278 ( 2.0)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic. *** Sample size is insufficient to permit a reliable estimate.

  Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 117
Guam

Communicating Mathematical Ideas

Much focus in the mathematics education reform effort has been placed on

students’ ability to communicate their understanding of mathematics to others. Results

presented previously in Tables 6.5A and 6.5B examines the level of emphasis teachers

placed on communication in their classroom. As a follow-up, the students participating

in the NAEP assessment, and their teachers, were asked about how often they were

asked to write a few sentences about solving a mathematical problem and how often they

were asked to discuss solutions to mathematics problems with other students.

Based on the responses of the fourth-grade public school teachers in Guam, the

results are shown in Table 6.6A.

• Relatively few of the students were asked to write about solving a

mathematics problem (9 percent) and less than half were asked to

discuss solutions with other students (37 percent) almost every day.

By comparison, 32 percent were never or hardly ever asked to write

about their solutions and 8 percent were never or hardly ever asked to

discuss their solutions.

• The average scale score for students who were asked to discuss solving

a mathematics problem almost every day (185) was not significantly

different from that for students who never or hardly ever discussed their

solutions (189).

When Guam fourth-grade public school students were asked about how often they

wrote about or discussed solutions to mathematics problems, they reported the following:

• Less than one third of the students said they were asked to write about

mathematics solutions (29 percent) and about one quarter said they were

asked to discuss their solutions with other students (24 percent) almost

every day. At the other end of the continuum, 36 percent of students

said they were never or hardly ever asked to write about solutions and

38 percent said they were never or hardly ever asked to discuss their

solutions.

118 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 6.6A — GRADE 4

Public School Teachers’ and Students’ Reports on Writing

About and Discussing Mathematics Problems

How often do the students in this class

(do you) do each of the following?

Guam Nation

Teacher Student Teacher Student

Percentage and Average Scale Score

Write a few sentences about how

to solve a mathematics problem

 Never or hardly ever 32 ( 1.3) 36 ( 1.2) 27 ( 2.4) 33 ( 1.4)

 193 ( 2.2) 197 ( 2.0) 220 ( 1.7) 226 ( 1.3)

 Once or twice a month 31 ( 1.4) 13 ( 0.9) 35 ( 2.8) 17 ( 0.7)

 189 ( 3.2) 185 ( 5.2) 223 ( 2.5) 231 ( 1.3)

 Once or twice a week 27 ( 1.1) 23 ( 1.1) 27 ( 2.2) 27 ( 0.9)

 188 ( 2.9) 189 ( 3.1) 223 ( 1.8) 223 ( 1.6)

 Almost every day 9 ( 0.7) 29 ( 1.3) 10 ( 1.6) 22 ( 1.2)

 182 ( 4.0) 181 ( 2.8) 233 ( 3.2) 211 ( 1.9)

Discuss solutions to mathematics

problems with other students

 Never or hardly ever 8 ( 0.7) 38 ( 1.4) 6 ( 1.4) 33 ( 1.0)

 189 ( 4.3) 190 ( 2.4) 219 ( 3.0)! 222 ( 1.0)

 Once or twice a month 21 ( 1.1) 12 ( 0.9) 22 ( 1.7) 18 ( 0.6)

 192 ( 3.1) 194 ( 4.8) 221 ( 1.9) 227 ( 1.7)

 Once or twice a week 35 ( 1.3) 26 ( 1.4) 37 ( 2.3) 29 ( 0.7)

 193 ( 2.0) 190 ( 2.8) 221 ( 1.9) 224 ( 1.4)

 Almost every day 37 ( 1.3) 24 ( 1.0) 35 ( 2.1) 19 ( 0.8)

 185 ( 2.3) 186 ( 2.2) 227 ( 1.8) 217 ( 1.5)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 119
Guam

Similarly, mathematics teachers of eighth-grade students in Guam’s public schools

were asked about the extent to which they had their students writing or discussing

mathematics solutions. The eighth graders were also asked about the frequency of these

activities. Table 6.6B shows the following on the basis of the reports of teachers in

Guam:

• A small percentage of the students were asked to write about solving a

mathematics problem (3 percent) and a large majority were asked to

discuss solutions with other students (83 percent) almost every day.

By comparison, 22 percent were never or hardly ever asked to write

about their solutions and 0 percent were never or hardly ever asked to

discuss their solutions.

An examination of the responses of eighth-grade public school students in Guam

showed the following (also shown in Table 6.6B):

• Less than one fifth of the students said they were asked to write about

mathematics solutions (14 percent) and less than half said they were

asked to discuss their solutions with other students (42 percent) almost

every day. At the other end of the continuum, 51 percent of students

said they were never or hardly ever asked to write about solutions and

19 percent said they were never or hardly ever asked to discuss their

solutions.

120 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 6.6B — GRADE 8

Public School Teachers’ and Students’ Reports on Writing

About and Discussing Mathematics Problems

How often do the students in this class

(do you) do each of the following?

Guam Nation

Teacher Student Teacher Student

Percentage and Average Scale Score

Write a few sentences about how

to solve a mathematics problem

 Never or hardly ever 22 ( 1.5) 51 ( 1.4) 31 ( 3.3) 47 ( 1.8)

 232 ( 3.9) 245 ( 2.8) 271 ( 2.8) 275 ( 1.6)

 Once or twice a month 30 ( 1.4) 16 ( 1.2) 38 ( 3.0) 19 ( 1.0)

 227 ( 4.1) 240 ( 3.6) 273 ( 2.3) 274 ( 1.7)

 Once or twice a week 45 ( 1.4) 20 ( 1.2) 27 ( 3.1) 21 ( 0.9)

 238 ( 3.7) 232 ( 3.3) 274 ( 2.9) 267 ( 1.7)

 Almost every day 3 ( 0.6) 14 ( 1.2) 5 ( 1.1) 14 ( 0.9)

 ** * (**.*) 226 ( 5.1) 270 ( 4.4)! 261 ( 2.3)

Discuss solutions to mathematics

problems with other students

 Never or hardly ever 0 (****) 19 ( 1.1) 2 ( 0.8) 20 ( 0.8)

 *** (**.*) 228 ( 4.8) 261 ( 5.7)! 266 ( 1.5)

 Once or twice a month 12 ( 1.3) 9 ( 0.9) 12 ( 2.0) 14 ( 0.5)

 *** (**.*) 235 ( 5.5) 264 ( 4.7) 273 ( 2.0)

 Once or twice a week 6 ( 1.0) 29 ( 1.5) 38 ( 3.3) 29 ( 0.8)

 *** (**.*) 236 ( 3.4) 270 ( 2.4) 270 ( 1.5)

 Almost every day 83 ( 1.4) 42 ( 1.6) 48 ( 3.6) 36 ( 1.2)

 237 ( 2.4) 247 ( 2.5) 276 ( 1.4) 274 ( 1.4)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic. *** Sample size is insufficient to permit a reliable estimate.

  Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 121
Guam

Collaboration in Small Groups

In many subject areas, researchers have found benefits from having students work

collaboratively in small groups.58 To examine the extent to which small groups are

being used in instruction, students and their mathematics teachers were asked about the

prevalence of these practices.

Table 6.7A shows the following based on the reports of fourth-grade public school

mathematics teachers:

• About three quarters of the fourth-grade students in Guam worked

mathematics problems in small groups every day (28 percent) or once

or twice a week (49 percent); a small percentage of the fourth graders

never or hardly ever worked in groups (7 percent).

According to fourth graders’ responses:

• In Guam, 19 percent worked mathematics problems in small groups

every day and another 23 percent worked in small groups once or twice

a week. Less than half of the fourth graders reported never or hardly

ever working in groups (47 percent).

TABLE 6.7A — GRADE 4

Public School Teachers’ and Students’ Reports on Solving

Mathematics Problems in Small Groups or With a Partner

How often do the students in this class

(do you) solve mathematics problems

in small groups or with a partner?

Guam Nation

Teacher Student Teacher Student

Percentage and Average Scale Score

Never or hardly ever 7 ( 0.6) 47 ( 1.2) 7 ( 1.6) 42 ( 1.3) 

185 ( 3.9) 193 ( 1.7) 224 ( 2.9)! 222 ( 1.0) 

Once or twice a month 15 ( 1.2) 11 ( 1.0) 18 ( 1.5) 22 ( 0.7) 

188 ( 5.0) 192 ( 3.1) 218 ( 1.7) 233 ( 1.3) 

Once or twice a week 49 ( 1.4) 23 ( 1.0) 50 ( 2.2) 26 ( 1.0) 

190 ( 2.0) 188 ( 3.4) 222 ( 1.6) 221 ( 1.4) 

Almost every day 28 ( 1.5) 19 ( 1.1) 25 ( 2.1) 10 ( 0.7) 

190 ( 2.3) 180 ( 3.3) 227 ( 1.9) 205 ( 2.3) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

58 Mulryan, C.M. “Fifth and Sixth Graders’ Involvement and Participation in Cooperative Small Groups in Mathematics,”

in Elementary School Journal, 95, 4. (1995). pp. 297-310; Reuman, D.A. and D.J. MacIver. Effects on Instructional

Grouping on Seventh Graders’ Academic Motivation and Achievement. (Washington, DC: Office of Educational

Research and Improvement, 1994).

122 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Eighth graders and their mathematics teachers were also asked about working in

small groups. According to public school mathematics teachers in Guam, the following

was true (see Table 6.7B):

• A large majority of the students in Guam worked mathematics problems

in small groups every day (16 percent) or once or twice a week

(65 percent); less than one fifth of the eighth graders never or hardly

ever worked in groups (15 percent).

When eighth-grade students were asked, they reported the following:

• In Guam, 15 percent worked mathematics problems in small groups

every day and another 27 percent worked in small groups once or twice

a week. Less than half of the eighth graders reported never or hardly

ever working in groups (40 percent).

TABLE 6.7B — GRADE 8

Public School Teachers’ and Students’ Reports on Solving

Mathematics Problems in Small Groups or With a Partner

How often do the students in this class

(do you) solve mathematics problems

in small groups or with a partner?

Guam Nation

Teacher Student Teacher Student

Percentage and Average Scale Score

Never or hardly ever 15 ( 1.2) 40 ( 1.3) 7 ( 1.5) 27 ( 1.6) 

236 ( 3.3) 238 ( 2.6) 272 ( 5.8)! 268 ( 1.8) 

Once or twice a month 4 ( 0.7) 18 ( 1.2) 27 ( 3.7) 27 ( 1.2) 

** * (**.*) 243 ( 4.2) 272 ( 3.2) 275 ( 1.5) 

Once or twice a week 65 ( 1.6) 27 ( 1.4) 40 ( 3.4) 29 ( 1.2) 

236 ( 2.8) 239 ( 2.6) 271 ( 2.1) 271 ( 1.5) 

Almost every day 16 ( 1.6) 15 ( 1.0) 27 ( 3.3) 17 ( 1.4) 

220 ( 5.7) 236 ( 4.3) 275 ( 2.2) 269 ( 3.0) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic. *** Sample size is insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 123
Guam

Mathematics Homework

To examine the relationship between homework and mathematics performance,

teachers of assessed students were asked to report the amount of mathematics homework

they assigned each day, and students were asked to report the amount of time they spent

on mathematics homework each day.

Tables 6.8A and 6.8B show the teachers’ and students’ responses for fourth- and

eighth-grade public school students in Guam. (Students had an additional response

choice “I am not taking mathematics this year,” but no analogous option was available

to teachers.) According to fourth-grade teachers’ responses:

• In Guam, about three quarters of the fourth graders in 1996 were

assigned 15 minutes (21 percent) or 30 minutes (58 percent) of

mathematics homework each day.

• A small percentage (1 percent) were not assigned any mathematics

homework each day.

According to students in the fourth grade:

• A small percentage of the fourth graders did not spend any time on

mathematics homework on a typical day (3 percent). By comparison,

34 percent spent 15 minutes and 27 percent spent 30 minutes on their

mathematics homework.

Results based on the responses of the eighth-grade teachers indicated the

following:

• In Guam, less than half of the eighth graders in 1996 were assigned 30

minutes (23 percent) or 45 minutes (14 percent) of mathematics

homework each day.

• A small percentage (6 percent) were not assigned any mathematics

homework each day.

The eighth graders’ reports indicated that:

• Relatively few of the eighth graders did not spend any time on

mathematics homework on a typical day (9 percent). By comparison,

27 percent spent 30 minutes and 19 percent spent 45 minutes on their

mathematics homework.

124 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 6.8A — GRADE 4

Public School Teachers’ and Students’ Reports on Homework

Approximately how much mathematics

homework do you assign (time do you

spend on math homework) each day?

Guam Nation

Teacher Student Teacher Student

Percentage and Average Scale Score

I am not taking mathematics

this year. 1992 --- (--.-) 1 ( 0.2) --- (--.-) 1 ( 0.1) 

 --- (--.-) *** (**.*) --- (--.-) *** (**.*)

1996 --- (--.-) 2 ( 0.4) --- (--.-) 1 ( 0.2) 

 --- (--.-) *** (**.*) --- (--.-) *** (**.*)

None 1992 1 ( 0.1) 4 ( 0.5) 6 ( 1.4) 7 ( 0.6) 

*** (**.*) 180 ( 4.7) 221 ( 2.6)! 222 ( 2.3) 

1996 1 ( 0.2) 3 ( 0.5) 4 ( 0.8) 6 ( 0.6) 

*** (**.*) *** (**.*) 232 ( 3.8) 226 ( 3.2) 

15 minutes 1992 28 ( 1.1) 33 ( 1.3) 53 ( 2.1) 39 ( 1.1) 

189 ( 1.5) 193 ( 1.4) 221 ( 1.4) 221 ( 1.2) 

1996 21 ( 1.4)< 34 ( 1.5) 50 ( 2.6) 40 ( 1.1) 

194 ( 3.2) 189 ( 2.3) 225 ( 1.6) 224 ( 1.3) 

30 minutes 1992 56 ( 1.0) 27 ( 1.2) 36 ( 2.6) 29 ( 0.8) 

194 ( 1.2) 201 ( 1.7) 216 ( 1.8) 222 ( 1.0) 

1996 58 ( 1.3) 27 ( 1.4) 40 ( 2.5) 29 ( 0.8) 

188 ( 1.6) 196 ( 2.3) 220 ( 1.7) 227 ( 1.5) 

45 minutes 1992 9 ( 0.5) 13 ( 0.8) 4 ( 0.9) 12 ( 0.5) 

197 ( 2.4) 194 ( 2.2) 202 ( 4.6)! 218 ( 1.5) 

1996 16 ( 0.7)> 13 ( 1.0) 4 ( 0.9) 13 ( 0.7) 

190 ( 3.7) 195 ( 2.6) 210 ( 5.1)! 225 ( 1.5)> 

One hour or more 1992 6 ( 0.7) 21 ( 1.0) 1 ( 0.4) 12 ( 0.7) 

197 ( 3.1) 187 ( 2.1) *** (**.*) 205 ( 1.8) 

1996 4 ( 0.7) 22 ( 1.2) 2 ( 0.6) 12 ( 0.6) 

*** (**.*) 183 ( 2.6) 208 ( 5.0)! 209 ( 1.9) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. --- Does not apply to

teachers. ! Interpret with caution — the nature of the sample does not allow accurate determination of the variability

of this statistic. *** Sample size is insufficient to permit a reliable estimate.   Standard error estimates cannot be

accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 125
Guam

TABLE 6.8B — GRADE 8

Public School Teachers’ and Students’ Reports on Homework

Approximately how much mathematics

homework do you assign (time do you

spend on math homework) each day?

Guam Nation

Teacher Student Teacher Student

Percentage and Average Scale Score

I am not taking mathematics

this year. 1992 --- (--.-) 0 ( 0.1) --- (--.-) 0 ( 0.1) 

 --- (--.-) ** * (**.*) --- (--.-) *** (**.*)

1996 --- (--.-) 0 ( 0.2) --- (--.-) 0 ( 0.0) 

 --- (--.-) *** (**.*) --- (--.-) *** (**.*)

None 1992 3 ( 0.3) 10 ( 0.9) 3 ( 0.7) 8 ( 0.4) 

*** (**.*) 226 ( 3.9) 233 ( 4.1)! 254 ( 2.4) 

1996 6 ( 0.7) 9 ( 1.1) 1 ( 0.5) 8 ( 0.8) 

*** (**.*) 222 ( 5.8) *** (**.*) 260 ( 2.9) 

15 minutes 1992 32 ( 0.9) 22 ( 1.0) 29 ( 2.1) 27 ( 0.8) 

229 ( 1.9) 234 ( 2.1) 262 ( 1.8) 269 ( 1.4) 

1996 10 ( 0.9)< 23 ( 1.3) 32 ( 2.7) 33 ( 1.1)> 

*** (**.*) 232 ( 3.6) 266 ( 2.3) 273 ( 1.2) 

30 minutes 1992 38 ( 1.1) 29 ( 1.4) 48 ( 2.6) 35 ( 0.7) 

235 ( 1.5) 240 ( 2.0) 268 ( 1.5) 269 ( 1.3) 

1996 23 ( 1.6)< 27 ( 1.3) 52 ( 2.7) 33 ( 0.8) 

233 ( 4.5) 240 ( 3.4) 274 ( 1.9) 274 ( 1.8) 

45 minutes 1992 7 ( 0.8) 14 ( 1.0) 15 ( 2.0) 16 ( 0.6) 

255 ( 4.9) 241 ( 3.0) 282 ( 3.8) 269 ( 1.7) 

1996 14 ( 1.2)> 19 ( 1.3)> 10 ( 1.2) 16 ( 0.7) 

241 ( 6.8) 248 ( 3.7) 284 ( 3.9) 270 ( 2.1) 

One hour or more 1992 19 ( 1.1) 25 ( 1.2) 4 ( 0.9) 13 ( 0.7) 

246 ( 2.0) 237 ( 2.1) 287 ( 5.3)! 266 ( 2.0) 

1996 47 ( 1.2)> 21 ( 1.3) 5 ( 0.8) 10 ( 0.6)< 

234 ( 3.2)< 246 ( 3.2) 281 ( 3.6) 267 ( 3.1) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. --- Does not apply to

teachers. ! Interpret with caution — the nature of the sample does not allow accurate determination of the variability

of this statistic. *** Sample size is insufficient to permit a reliable estimate. **** Standard error estimates cannot be

accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

126 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

In addition to being asked about mathematics homework, students were asked how

often they use a computer at home for schoolwork. The question was not restricted to

mathematics homework, so students’ reports most likely included homework for other

academic areas such as English and science. Given that home computers are steadily

assuming more importance in completing homework assignments,59 it is important that

NAEP monitor the prevalence of this practice and its relationship to performance.

Based on the reports of fourth graders in Guam, as shown in Table 6.9A:

• More than half of the students reported that there was no computer at

home (62 percent) and another 20 percent reported never or hardly ever

using their home computer to do homework.

• Less than one fifth of the fourth graders reported using their home

computer to do homework almost every day (7 percent) or once or twice

a week (7 percent).

• The average scale score for students who used a computer almost every

day for homework (178) was lower than that of students who never or

hardly ever did so (197).

• The average scale score for students who used a computer almost every

day for homework was lower than that of students who did not have a

computer at home (186).

TABLE 6.9A — GRADE 4

Public School Students’ Reports on Using Computers at

Home

How often do you use a computer at

home for schoolwork?

Guam Nation

Percentage and Average Scale Score

There is no computer at home. 62 ( 1.1) 44 ( 1.4) 

186 ( 1.7) 214 ( 1.3) 

Never or hardly ever 20 ( 1.1) 26 ( 0.9) 

197 ( 3.3) 229 ( 1.3) 

Once or twice a month 5 ( 0.6) 11 ( 0.6) 

205 ( 3.8) 239 ( 1.6) 

Once or twice a week 7 ( 0.7) 10 ( 0.6) 

186 ( 4.2) 228 ( 2.4) 

Almost every day 7 ( 0.6) 8 ( 0.5) 

178 ( 3.8) 214 ( 2.4) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

59 National Center for Education Statistics. Digest of Education Statistics 1995. (Washington, DC: National Center for

Education Statistics, 1995).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 127
Guam

When eighth-grade public school students in Guam (see Table 6.9B) were asked

about the use of home computers to complete homework assignments, they reported the

following:

• Less than half of the students reported that there was no computer at

home (47 percent) and another 17 percent reported never or hardly ever

using their home computer to do homework.

• About one quarter of the eighth graders reported using their home

computer to do homework almost every day (9 percent) or once or twice

a week (14 percent).

• The average scale score for students who used a computer almost every

day for homework (246) was not significantly different from* that of

students who never or hardly ever did so (235).

• The average scale score for students who used a computer almost every

day for homework did not differ significantly from that of students who

did not have a computer at home (242).

TABLE 6.9B — GRADE 8

Public School Students’ Reports on Using Computers at

Home

How often do you use a computer at

home for schoolwork?

Guam Nation

Percentage and Average Scale Score

There is no computer at home. 47 ( 1.5) 37 ( 1.2) 

242 ( 2.6) 262 ( 1.3) 

Never or hardly ever 17 ( 1.2) 15 ( 0.8) 

235 ( 3.8) 269 ( 1.9) 

Once or twice a month 13 ( 1.2) 19 ( 0.8) 

261 ( 4.4) 282 ( 1.5) 

Once or twice a week 14 ( 1.3) 17 ( 0.8) 

244 ( 4.8) 282 ( 2.1) 

Almost every day 9 ( 1.0) 11 ( 0.6) 

246 ( 6.2) 276 ( 2.7) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

* Although the difference may appear large, recall that “significance” here refers to “statistical significance.”

128 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Calculator and Computer Use in the Mathematics

Classroom

Recommendations for facilitating mathematics instruction in the nation’s schools

often include more use of calculators and computers.60 The NCTM Standards recognize

the technological world in which students are living and the opportunities that

technology provides for students to learn and use mathematics. The increasingly

technical workplace demands that students have a deep understanding of mathematics

that permits solving complex problems.

Given the importance of using technology in mathematics instruction, NAEP asked

students and their teachers about their use of calculators and computers. Teachers in

Guam were also asked about the availability of computers for mathematics instruction.

Calculators

Recent analysis of data from the NAEP 1992 assessment suggests a positive

relationship between calculator use and the effectiveness of the school.61 The same

research also found that the use of calculators in mathematics classes varied widely from

school to school. As part of the NAEP assessment, students and their mathematics

teachers were asked to report on the frequency of use of calculators in mathematics

classes and teachers were asked about the use of calculators on tests. This latter question

is relevant to NAEP since the students are allowed to use a calculator on a portion of

the assessment. (The question concerning calculator use on tests was not asked of

students.) Reports from public school teachers of the fourth graders in Guam (shown

in Tables 6.10A and 6.11A) indicate the following:

• Less than one fifth of the students used a calculator in their mathematics

class almost every day (1 percent) or once or twice a week (15 percent).

More than half of the students never or hardly ever used a calculator

(64 percent). The percentage of students using a calculator almost

every day was smaller than that for the nation (5 percent).

• Teachers of 5 percent of fourth graders reported permitting students to

use calculators for tests. The average scale score for students who were

allowed to use calculators (190) was not significantly different from that

of students who were not (189).

• The percentage of students in 1996 who were permitted to use

calculators on tests was not significantly different from that in 1992

(6 percent).

When fourth graders were asked about the use of calculators in their mathematics

class, their responses (as shown in Table 6.10A) indicated the following:

• About one quarter of the students reported using a calculator almost

every day (13 percent) or once or twice a week (14 percent). In

comparison, 63 percent of students reported never or hardly ever using

calculators in their mathematics class.

60 National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. (Reston,

VA: NCTM, 1989).

61 Mullis, I.V.S., F. Jenkins, and E.G. Johnson. Effective Schools in Mathematics. (Washington, DC: U.S. Department

of Education, 1994).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 129
Guam

TABLE 6.10A — GRADE 4

Public School Teachers’ and Students’ Reports on the

Frequency of Calculator Use

How often do the students in this

class (do you) use a calculator?

Guam Nation

Teacher Student Teacher Student

Percentage and Average Scale Score

Never or hardly ever 64 ( 1.3) 63 ( 1.4) 24 ( 2.5) 40 ( 1.4) 

187 ( 2.3) 192 ( 1.2) 216 ( 2.3) 220 ( 1.3) 

Once or twice a month 20 ( 1.0) 10 ( 0.7) 42 ( 2.6) 26 ( 0.8) 

193 ( 2.8) 194 ( 4.4) 223 ( 1.6) 233 ( 1.0) 

Once or twice a week 15 ( 1.0) 14 ( 0.9) 29 ( 2.4) 23 ( 1.0) 

192 ( 4.5) 186 ( 4.5) 229 ( 1.8) 223 ( 1.4) 

Almost every day 1 ( 0.4) 13 ( 1.0) 5 ( 0.9) 11 ( 0.6) 

*** (**.*) 174 ( 4.2) 227 ( 5.0) 206 ( 1.9) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). *** Sample size is insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

TABLE 6.11A — GRADE 4

Public School Teachers’ Reports on the Use of Calculators

for Tests

Do you permit students in this class to

use calculators for tests?

Guam Nation

Percentage and Average Scale Score

Yes 1992 6 ( 0.5) 5 ( 1.2) 

192 ( 3.4) 228 ( 4.3)! 

1996 5 ( 0.7) 10 ( 1.8) 

190 ( 5.7) 222 ( 2.4) 

No 1992 94 ( 0.5) 95 ( 1.2) 

193 ( 0.9) 218 ( 1.0) 

1996 95 ( 0.7) 90 ( 1.8) 

189 ( 1.6) 223 ( 1.2)> 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. ! Interpret with caution

— the nature of the sample does not allow accurate determination of the variability of this statistic.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

130 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Eighth-grade students and their mathematics teachers were asked the same

questions about calculator use, and the results are shown in Tables 6.10B and 6.11B.

Based on the responses of eighth-grade public school teachers in Guam, results showed

that:

• About three quarters of the students used a calculator in their

mathematics class almost every day (57 percent) or once or twice a

week (18 percent). Less than one fifth of the students never or hardly

ever used a calculator (14 percent). The percentage of students using

a calculator almost every day did not differ significantly from that for

the nation (57 percent).

• In 1996, when asked if they allowed students to use a calculator for tests,

teachers of 49 percent of eighth graders reported permitting students to

use them. The average scale score for students allowed to use

calculators (239) was not significantly different from* that of students

who were not (230).

• The percentage of students in 1996 who were permitted to use a

calculator on tests was larger than the percentage in 1992 (7 percent)

and larger than the percentage in 1990 (9 percent).

Responses from eighth-grade students (Table 6.10B) showed the following:

• More than half of the students reported using a calculator almost every

day (36 percent) or once or twice a week (27 percent). In comparison,

25 percent of students reported never or hardly ever using a calculator

in their mathematics class.

* Although the difference may appear large, recall that “significance” here refers to “statistical significance.”

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 131
Guam

TABLE 6.10B — GRADE 8

Public School Teachers’ and Students’ Reports on the

Frequency of Calculator Use

How often do the students in this

class (do you) use a calculator?

Guam Nation

Teacher Student Teacher Student

Percentage and Average Scale Score

Never or hardly ever 14 ( 1.1) 25 ( 1.4) 8 ( 1.5) 11 ( 1.1) 

228 ( 5.2) 236 ( 4.7) 251 ( 5.0) 254 ( 2.7) 

Once or twice a month 12 ( 1.6) 12 ( 1.2) 15 ( 2.3) 13 ( 0.9) 

*** (**.*) 237 ( 6.0) 260 ( 3.3) 265 ( 2.0) 

Once or twice a week 18 ( 1.1) 27 ( 1.4) 20 ( 2.6) 27 ( 1.4) 

229 ( 5.4) 240 ( 3.1) 269 ( 3.5) 267 ( 1.5) 

Almost every day 57 ( 1.7) 36 ( 1.5) 57 ( 3.0) 49 ( 2.5) 

241 ( 2.9) 241 ( 2.4) 280 ( 1.7) 278 ( 1.6) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). *** Sample size is insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

TABLE 6.11B — GRADE 8

Public School Teachers’ Reports on the Use of Calculators

for Tests

Do you permit students in this class to

use calculators for tests?

Guam Nation

Percentage and Average Scale Score

Yes 1990 9 ( 0.4) 33 ( 4.5) 

233 ( 2.9) 271 ( 2.9) 

1992 7 ( 0.7)« 49 ( 3.1)» 

264 ( 4.3)» 275 ( 1.9) 

1996 49 ( 1.5)»> 70 ( 3.0)»> 

239 ( 3.2)< 279 ( 1.6) 

No 1990 91 ( 0.4) 67 ( 4.5) 

232 ( 0.8) 258 ( 1.8) 

1992 93 ( 0.7)» 51 ( 3.1)« 

234 ( 1.1) 262 ( 1.6) 

1996 51 ( 1.5)«< 30 ( 3.0)«< 

230 ( 3.2) 259 ( 2.3) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation » («) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1990 at about the 95 percent confidence level. If the notation > (<)

appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992 at

about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

132 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Computers

Computers are potentially valuable instructional tools for the mathematics

classroom and can be used to demonstrate mathematics concepts, diagnose learning

problems, deliver instruction, and analyze data. Computers are increasingly important

in students’ homes, where they are used for homework as well as for other pursuits.

Since 1984, the percentage of students in grades 7 through 12 who use a computer at

school or at home has increased.62

Teachers of the students assessed were asked about the availability and

accessibility of computers for use in their mathematics classroom. Based on the

responses of fourth-grade teachers, the results are shown in Table 6.12A.

• In Guam, 20 percent of students had teachers who reported that no

computers were available for use in their mathematics class and

28 percent had teachers who reported that computers were available in

a computer laboratory but difficult to access or schedule. In comparison,

1 percent of students were in mathematics classes where four or more

computers were available within the classroom and 48 percent where

computers were available in a laboratory and easy to access or schedule.

• The percentage of students in mathematics classes where computers

were not available was larger than the percentage for the nation

(6 percent).

TABLE 6.12A — GRADE 4

Public School Teachers’ Reports on the Availability of

Computers

Which best describes the availability of

computers for use by students in your

mathematics classes?

Guam Nation

Percentage and Average Scale Score

None available 20 ( 0.9) 6 ( 1.3) 

189 ( 4.0) 218 ( 4.0)! 

One within the classroom 0 ( 0.2) 35 ( 3.3) 

*** (**.*) 225 ( 1.7) 

Two or three within the classroom 2 ( 0.3) 22 ( 2.2) 

*** (**.*) 222 ( 2.1) 

Four or more within the classroom 1 ( 0.0) 7 ( 1.5) 

*** (**.*) 224 ( 7.5)! 

Available in a computer laboratory but

difficult to access or schedule 28 ( 1.3) 13 ( 1.9) 

190 ( 3.2) 222 ( 4.5) 

Available in a computer laboratory and

easy to access or schedule 48 ( 1.2) 16 ( 2.7) 

187 ( 2.1) 224 ( 2.0) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic. *** Sample size is insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

62 National Center for Education Statistics. Digest of Education Statistics 1995. (Washington, DC: National Center for

Education Statistics, 1995).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 133
Guam

As presented in Table 6.12B, when eighth-grade mathematics teachers were asked

about availability of computers, their responses indicated the following:

• In Guam, 53 percent of the students had teachers who reported that no

computers were available for use in their mathematics classes and

32 percent had teachers who reported computers were available in a

computer laboratory but difficult to access or schedule. In comparison,

8 percent of the students were in mathematics classes where four or

more computers were available within the classroom and 6 percent

where computers were available in a laboratory and easy to access or

schedule.

• The percentage of students in mathematics classes where computers

were not available was larger than the percentage for the nation

(26 percent).

TABLE 6.12B — GRADE 8

Public School Teachers’ Reports on the Availability of

Computers

Which best describes the availability of

computers for use by students in your

mathematics classes?

Guam Nation

Percentage and Average Scale Score

None available 53 ( 1.5) 26 ( 3.7) 

236 ( 2.2) 269 ( 3.1) 

One within the classroom 0 ( ) 19 ( 3.0) 

** * (**.*) 271 ( 3.9) 

Two or three within the classroom 0 (****) 5 ( 1.5) 

*** (**.*) 274 (10.2)! 

Four or more within the classroom 8 ( 0.6) 7 ( 2.1) 

*** (**.*) 274 ( 4.4)! 

Available in a computer laboratory but

difficult to access or schedule 32 ( 1.5) 26 ( 3.6) 

230 ( 4.5) 270 ( 2.6) 

Available in a computer laboratory and

easy to access or schedule 6 ( 0.7) 18 ( 2.8) 

*** (**.*) 278 ( 4.1) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic. *** Sample size is insufficient to permit a reliable estimate.

  Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

134 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

In addition to a range of availability from school to school, the uses of computers

can vary widely from class to class. There are a variety of ways that computers can be

used to help students learn and use mathematics, such as exploring new mathematical

ideas, analyzing information to solve problems, practicing skills, and playing

mathematical games. Also, the frequency of use can vary regardless of the primary use

of the computers in the classroom. Teachers in Guam were asked how they used

computers and how often they were used in their mathematics classroom. The responses

of fourth-grade public school teachers, shown in Table 6.13A, indicate the following:

• About one third of the fourth graders had teachers who reported not

using a computer for mathematics instruction (31 percent). This

percentage was larger than the percentage for the nation (23 percent).

• In Guam, 25 percent of students had teachers who reported never or

hardly ever using a computer with their classes, compared to about two

thirds who reported doing so almost every day (1 percent) or once or

twice a week (64 percent).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 135
Guam

TABLE 6.13A — GRADE 4

Public School Teachers’ Reports on the Primary Use and

Frequency of Use of Computers

Guam Nation

Percentage and Average Scale Score

If you do use computers, what is the

primary use of these computers for

mathematics instruction?

Drill and practice 43 ( 1.3) 27 ( 2.4) 

188 ( 1.7) 222 ( 2.1) 

Demonstration of new topics in mathematics 4 ( 0.7) 2 ( 0.6) 

** * (**.*) 222 ( 7.5)! 

Playing mathematical/learning games 8 ( 0.5) 41 ( 2.6) 

199 ( 4.0) 225 ( 1.5) 

Simulations and applications 13 ( 0.9) 6 ( 1.2) 

188 ( 4.0) 225 ( 3.6) 

I do not use computers for instruction. 31 ( 1.1) 23 ( 2.9) 

189 ( 3.0) 220 ( 3.4) 

How often do the students in this class

use a computer?

Never or hardly ever 25 ( 1.2) 21 ( 2.4) 

194 ( 2.9) 221 ( 2.6) 

Once or twice a month 9 ( 0.8) 19 ( 1.9) 

186 ( 4.5) 227 ( 2.1) 

Once or twice a week 64 ( 1.5) 46 ( 2.5) 

188 ( 1.6) 222 ( 1.4) 

Almost every day 1 ( 0.4) 14 ( 1.8) 

*** (**.*) 225 ( 2.8) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic. *** Sample size is insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

136 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 6.13B presents the eighth-grade teachers’ reports on uses for computers in

their mathematics classrooms.

• About half of the eighth graders had teachers who reported not using a

computer for mathematics instruction (52 percent). This percentage did

not differ significantly from the percentage for the nation (52 percent).

• In Guam, 84 percent of students had teachers who reported never or

hardly ever using a computer with their classes, compared to a small

percentage who reported doing so almost every day (0 percent) or once

or twice a week (7 percent).

TABLE 6.13B — GRADE 8

Public School Teachers’ Reports on the Primary Use and

Frequency of Use of Computers

Guam Nation

Percentage and Average Scale Score

If you do use computers, what is the

primary use of these computers for

mathematics instruction?

Drill and practice 25 ( 1.6) 18 ( 2.5) 

236 ( 4.2) 270 ( 4.3) 

Demonstration of new topics in mathematics 11 ( 1.3) 5 ( 1.5) 

*** (**.*) 280 ( 3.8)! 

Playing mathematical/learning games 12 ( 0.9) 13 ( 2.4) 

*** (**.*) 266 ( 4.3) 

Simulations and applications 0 (****) 13 ( 2.9) 

*** (**.*) 281 ( 4.5)! 

I do not use computers for instruction. 52 ( 1.7) 52 ( 3.9) 

231 ( 3.7) 270 ( 1.5) 

How often do the students in this class

use a computer?

Never or hardly ever 84 ( 1.0) 70 ( 3.9) 

234 ( 2.2) 273 ( 1.4) 

Once or twice a month 9 ( 0.7) 22 ( 3.9) 

*** (**.*) 277 ( 3.9) 

Once or twice a week 7 ( 0.7) 8 ( 1.5) 

*** (**.*) 262 ( 5.5) 

Almost every day 0 (****) 1 ( 0.4) 

*** (**.*) 250 ( 8.6)! 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic. *** Sample size is insufficient to permit a reliable estimate.

**** Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 137
Guam

Finally, students were asked how often they used computers when doing

mathematics in school. The question was not limited to using the computer in their

mathematics class. Therefore, students’ responses could include use of computers to

do mathematics assignments at other times throughout the school day or in before/after

school programs. On the basis of the responses of fourth-grade public school students,

as shown in Table 6.14A, results indicated that:

• In Guam, 71 percent of students never or hardly ever used computers

to do mathematics in school. About one quarter of the fourth graders

used computers for this purpose almost every day (8 percent) or once

or twice a week (17 percent).

TABLE 6.14A — GRADE 4

Public School Students’ Reports on the Frequency of

Computer Use

When you do mathematics in school,

how often do you use a computer?

Guam Nation

Percentage and Average Scale Score

Never or hardly ever 71 ( 1.4) 56 ( 1.0) 

191 ( 1.7) 223 ( 1.2) 

Once or twice a month 4 ( 0.5) 10 ( 0.7) 

190 ( 7.8) 226 ( 2.4) 

Once or twice a week 17 ( 1.0) 20 ( 1.0) 

191 ( 4.3) 225 ( 1.3) 

Almost every day 8 ( 0.7) 14 ( 0.8) 

175 ( 4.1) 218 ( 1.8) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

138 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Table 6.14B presents results for eighth-grade public school students who were

asked the same question.

• In Guam, 60 percent of students never or hardly ever used computers

to do mathematics in school. About one quarter of the eighth graders

used computers for this purpose almost every day (9 percent) or once

or twice a week (17 percent).

TABLE 6.14B — GRADE 8

Public School Students’ Reports on the Frequency of

Computer Use

When you do mathematics in school,

how often do you use a computer?

Guam Nation

Percentage and Average Scale Score

Never or hardly ever 60 ( 1.7) 57 ( 1.4) 

239 ( 2.0) 270 ( 1.3) 

Once or twice a month 14 ( 1.3) 16 ( 0.9) 

242 ( 4.3) 275 ( 2.2) 

Once or twice a week 17 ( 1.2) 15 ( 0.9) 

239 ( 4.3) 270 ( 2.0) 

Almost every day 9 ( 0.9) 12 ( 0.6) 

234 ( 6.5) 270 ( 2.2) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 139
Guam

140 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

CHAPTER 7

Influences Beyond School That Facilitate

Learning Mathematics

The home environment can be an important support for the school environment.

To examine the relationship between mathematics scale scores and home factors, the

NAEP assessment considered students’ responses to questions about home factors and

principals’ responses to questions about parental involvement in the school. To examine

the impact of student mobility on academic achievement, students were also asked how

often they had changed schools because of household moves.

The students’ attitudes toward mathematics can also be expected to relate to their

performance in the assessment. As the NCTM Curriculum and Evaluation Standards

for School Mathematics warns, the beliefs that students develop influence not only their

thinking and performance but also their attitude and decisions about studying

mathematics in future years. The NCTM Standards describes specific attitudes that

should be given increased attention in the curriculum.

Discussing Studies at Home

When students discuss academic work at home, they create an important link

between home and school. How often schoolwork is discussed at home can be a

measure of the importance of school for students and their families. Recent NAEP

assessments in a variety of subject areas have found a positive relationship between

discussing studies at home and student performance.63

63 Campbell, J.R., P.L. Donahue, C.M. Reese, and G.W. Phillips. NAEP 1994 Reading Report Card for the Nation and

the States. (Washington, DC: National Center for Education Statistics, 1996); Beatty, A.S., C.M. Reese, H.R. Persky,

and P. Carr. NAEP 1994 U.S. History Report Card. (Washington, DC: National Center for Education Statistics, 1996);

Persky, H.R., C.M. Reese, C.Y. O'Sullivan, S. Lazer, J. Moore, and S. Shakrani. NAEP 1994 Geography Report Card.

(Washington, DC: National Center for Education Statistics, 1996).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 141
Guam

Students were asked to report on the frequency of home discussion about

schoolwork. As shown in Table 7.1A, the 1996 results for fourth graders attending

public schools in Guam indicate that

• Less than half of the fourth graders (46 percent) said they discussed

their schoolwork at home almost every day. This percentage was larger

than the percentage who said they never or hardly ever had such

discussions (22 percent).

• The average scale score for students who discussed their schoolwork

almost every day (189) was not significantly different from that for

students who never or hardly ever did so (186).

TABLE 7.1A — GRADE 4

Public School Students’ Reports on Discussing Studies at

Home

How often do you discuss things you

have studied in school with someone

at home?

Guam Nation

Percentage and Average Scale Score

Never or hardly ever 1992 28 ( 1.2) 20 ( 0.6) 

190 ( 1.5) 209 ( 1.2) 

1996 22 ( 1.3)< 17 ( 0.6)< 

186 ( 3.9) 213 ( 1.4) 

Once or twice a month 1992 7 ( 0.5) 6 ( 0.3) 

189 ( 2.9) 220 ( 2.9) 

1996 7 ( 0.7) 5 ( 0.3) 

189 ( 6.5) 226 ( 2.8) 

Once or twice a week 1992 26 ( 1.0) 21 ( 0.6) 

197 ( 1.5) 225 ( 1.1) 

1996 25 ( 1.4) 22 ( 0.7) 

191 ( 2.4) 227 ( 1.4) 

Almost every day 1992 39 ( 1.2) 53 ( 0.7) 

193 ( 1.1) 220 ( 0.9) 

1996 46 ( 1.5)> 56 ( 0.9) 

189 ( 2.0) 223 ( 1.3) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

142 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Based on the reports of eighth graders, Table 7.1B indicates the following

relationship between discussing studies at home and mathematics performance on the

NAEP 1996 assessment.

• In Guam, about one third of the eighth-grade students (32 percent) said

they discussed their schoolwork at home almost every day. This

percentage was larger than the percentage who said they never or hardly

ever had such discussions (24 percent).

• The average scale score for students who discussed their schoolwork

almost every day (250) was higher than that for students who never or

hardly ever did so (235).

TABLE 7.1B — GRADE 8

Public School Students’ Reports on Discussing Studies at

Home

How often do you discuss things you

have studied in school with someone

at home?

Guam Nation

Percentage and Average Scale Score

Never or hardly ever 1992 34 ( 1.1) 23 ( 0.6) 

235 ( 2.0) 257 ( 1.2) 

1996 24 ( 1.3)< 21 ( 1.0) 

235 ( 3.2) 263 ( 1.8)> 

Once or twice a month 1992 10 ( 0.8) 10 ( 0.4) 

244 ( 4.8) 267 ( 1.8) 

1996 12 ( 1.1) 10 ( 0.4) 

245 ( 4.7) 271 ( 2.6) 

Once or twice a week 1992 30 ( 0.9) 28 ( 0.6) 

243 ( 1.6) 271 ( 1.1) 

1996 33 ( 1.5) 29 ( 0.8) 

242 ( 3.4) 275 ( 1.5) 

Almost every day 1992 26 ( 1.0) 39 ( 0.9) 

245 ( 2.4) 272 ( 1.5) 

1996 32 ( 1.6)> 40 ( 1.0) 

250 ( 2.6) 274 ( 1.2) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 143
Guam

Literacy Materials in the Home

Students can learn much about mathematics and its role in real-world situations

by reading materials outside the classroom. Research findings and results from opinion

polls are often found in magazine and newspaper articles. Also, the availability of

reading and reference materials at home may be an indicator of the value placed by

parents on learning.64 In past NAEP assessments, a positive relationship has consistently

been reported between print materials in the home and average scale scores.65

As part of the NAEP assessment, students were asked whether their families have

more than 25 books, an encyclopedia, receive a newspaper regularly, and receive any

magazines regularly. Table 7.2A shows the percentages of fourth-grade public school

students reporting that their families have all four types, only three types, or two or fewer

types of these literacy materials and students’ average scale scores. Based on their

responses:

• Less than one fifth of the students in Guam (17 percent) reported having

all four types of literacy materials in their homes. This percentage was

smaller than the percentage for the nation (34 percent).

• In comparison, the percentage reporting having two or fewer types of

these materials (51 percent) was greater than the percentage having all

four types. The percentage having two or fewer types was greater than

the percentage for the nation (32 percent).

• In 1996 the average mathematics scale score for students with all four

types of literacy materials (197) was higher than that for students with

two or fewer types (184).

64 Rogoff, B. Apprenticeship in Thinking: Cognitive Development in Social Context. (New York: Oxford University Press,

1990).

65 Campbell, J.R., P.L. Donahue, C.M. Reese, and G.W. Phillips. NAEP 1994 Reading Report Card for the Nation and

the States. (Washington, DC: National Center for Education Statistics, 1996); Beatty, A.S., C.M. Reese, H.R. Persky,

and P. Carr. NAEP 1994 U.S. History Report Card. (Washington, DC: National Center for Education Statistics, 1996);

Persky, H.R., C.M. Reese, C.Y. O'Sullivan, S. Lazer, J. Moore, and S. Shakrani. NAEP 1994 Geography Report Card.

(Washington, DC: National Center for Education Statistics, 1996).

144 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 7.2A — GRADE 4

Public School Students’ Reports on Literacy Materials in the

Home

How many of the following types of

reading materials are in your home

(more than 25 books, an encyclopedia,

a newspaper, magazines)?

Guam Nation

Percentage and Average Scale Score

Zero to two 1992 56 ( 1.0) 31 ( 1.3) 

188 ( 1.2) 208 ( 1.1) 

1996 51 ( 1.5)< 32 ( 0.9) 

184 ( 1.9) 212 ( 1.7) 

Three 1992 28 ( 1.1) 35 ( 0.7) 

199 ( 1.7) 220 ( 1.0) 

1996 32 ( 1.4) 34 ( 0.7) 

193 ( 2.0) 224 ( 1.2)> 

Four 1992 16 ( 0.9) 34 ( 1.2) 

201 ( 1.7) 228 ( 1.2) 

1996 17 ( 1.0) 34 ( 0.9) 

197 ( 3.3) 231 ( 1.3) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 145
Guam

Table 7.2B shows the results based on eighth-grade public school students’ reports

on literacy materials in the home and their average scale scores.

• About one third of the eighth graders in Guam (33 percent) reported

having all four types of literacy materials in their homes. This

percentage was smaller than the percentage for the nation (47 percent).

• In comparison, the percentage reporting having two or fewer types of

these materials (37 percent) was not significantly different from the

percentage having all four types. The percentage having two or fewer

types was greater than the percentage for the nation (21 percent).

• Based on the 1996 results for Guam, the average mathematics scale

score for students with all four types of literacy materials (253) was

higher than that for students with two or fewer types (231).

TABLE 7.2B — GRADE 8

Public School Students’ Reports on Literacy Materials in the

Home

How many of the following types of

reading materials are in your home

(more than 25 books, an encyclopedia,

a newspaper, magazines)?

Guam Nation

Percentage and Average Scale Score

Zero to two 1990 36 ( 1.2) 21 ( 1.0) 

221 ( 1.3) 244 ( 2.1) 

1992 39 ( 1.1) 21 ( 0.7) 

226 ( 1.5)» 248 ( 1.2) 

1996 37 ( 1.5) 21 ( 0.7) 

231 ( 3.1)» 254 ( 1.6)»> 

Three 1990 37 ( 1.5) 30 ( 1.0) 

235 ( 1.4) 259 ( 1.6) 

1992 35 ( 1.1) 31 ( 0.7) 

238 ( 1.7) 266 ( 1.3)» 

1996 31 ( 1.3)«< 31 ( 0.9) 

235 ( 4.3) 268 ( 1.2)» 

Four 1990 27 ( 1.0) 48 ( 1.3) 

243 ( 1.5) 272 ( 1.5) 

1992 26 ( 1.0) 48 ( 1.0) 

246 ( 2.3) 276 ( 1.1) 

1996 33 ( 1.6)»> 47 ( 1.1) 

253 ( 2.6)» 281 ( 1.4)»> 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation » («) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1990 at about the 95 percent confidence level. If the notation > (<)

appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992 at

about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

146 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Television Viewing Habits

Past NAEP assessments have shown that over 40 percent of fourth- and

eighth-grade students reported watching four or more hours of television each day. A

major concern is that time spent watching television results in less time available for

homework and related academic activities. The effects of such extensive television

exposure are difficult to document, but there is a generally negative relationship between

NAEP score results and hours watched.66

Students were asked how much television they usually watched each day. The

results for fourth- and eighth-grade public school students in Guam are shown in Tables

7.3A and 7.3B, respectively.

• Among fourth graders, 16 percent reported watching six or more hours

of television on a typical day. This percentage was smaller than the

percentage who reported watching one hour or less (40 percent).

• The percentage of fourth graders in Guam who reported watching six

or more hours of television a day was smaller than the percentage for

the nation (20 percent).

• Based on the 1996 state results, the average mathematics scale score for

fourth-grade students who reported watching two to three hours of

television a day (192) was higher than that for students who reported

watching one hour or less (185).

• The average scale score for fourth graders who reported watching two

to three hours of television a day did not differ significantly from that

for students who reported watching six hours or more (187).

• Among eighth graders, 17 percent reported watching six or more hours

of television on a typical day. This percentage did not differ

significantly from the percentage who reported watching one hour or

less (21 percent).

• The percentage of eighth graders in Guam who reported watching six

or more hours of television a day was not significantly different from

the percentage for the nation (14 percent).

• Based on the 1996 state results, the average mathematics scale score for

eighth-grade students who reported watching two to three hours of

television a day (242) was higher than that for students who reported

watching one hour or less (229).

• The average scale score for eighth graders who reported watching two

to three hours of television a day did not differ significantly from* that

for students who reported watching six hours or more (235).

* Although the difference may appear large, recall that “significance” here refers to “statistical significance.”

66 Campbell, J.R., P.L. Donahue, C.M. Reese, and G.W. Phillips. NAEP 1994 Reading Report Card for the Nation and

the States. (Washington, DC: National Center for Education Statistics, 1996); Beatty, A.S., C.M. Reese, H.R. Persky,

and P. Carr. NAEP 1994 U.S. History Report Card. (Washington, DC: National Center for Education Statistics, 1996);

Persky, H.R., C.M. Reese, C.Y. O'Sullivan, S. Lazer, J. Moore, and S. Shakrani. NAEP 1994 Geography Report Card.

(Washington, DC: National Center for Education Statistics, 1996).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 147
Guam

TABLE 7.3A — GRADE 4

Public School Students’ Reports on Television Viewing Habits

How much television do you usually

watch each day?

Guam Nation

Percentage and Average Scale Score

1 hour or less 1992 34 ( 1.1) 21 ( 0.8) 

188 ( 1.3) 221 ( 1.6) 

1996 40 ( 1.4)> 24 ( 1.1) 

185 ( 1.8) 223 ( 1.8) 

2 to 3 hours 1992 30 ( 1.2) 35 ( 0.8) 

199 ( 1.4) 225 ( 1.1) 

1996 28 ( 1.3) 36 ( 0.7) 

192 ( 2.2)< 228 ( 1.2) 

4 to 5 hours 1992 15 ( 0.7) 22 ( 0.8) 

200 ( 2.4) 221 ( 1.3) 

1996 16 ( 1.0) 20 ( 0.7) 

195 ( 2.6) 224 ( 1.5) 

6 hours or more 1992 21 ( 0.9) 22 ( 0.8) 

186 ( 1.8) 204 ( 1.1) 

1996 16 ( 1.0)< 20 ( 0.8) 

187 ( 3.6) 208 ( 1.5) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

148 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 7.3B — GRADE 8

Public School Students’ Reports on Television Viewing Habits

How much television do you usually

watch each day?

Guam Nation

Percentage and Average Scale Score

1 hour or less 1990 19 ( 0.9) 12 ( 0.8) 

218 ( 2.0) 269 ( 2.4) 

1992 22 ( 0.8)» 15 ( 0.6)» 

223 ( 2.3) 276 ( 2.2) 

1996 21 ( 1.4) 17 ( 0.6)» 

229 ( 3.8) 277 ( 2.7) 

2 to 3 hours 1990 38 ( 1.2) 43 ( 1.1) 

236 ( 1.5) 267 ( 1.4) 

1992 38 ( 1.2) 45 ( 0.6) 

240 ( 1.9) 274 ( 1.1)» 

1996 41 ( 1.6) 45 ( 0.9) 

242 ( 2.2) 276 ( 1.1)» 

4 to 5 hours 1990 23 ( 1.1) 28 ( 1.1) 

239 ( 2.1) 262 ( 1.6) 

1992 20 ( 1.0) 26 ( 0.7) 

248 ( 2.3)» 261 ( 1.1) 

1996 22 ( 1.3) 24 ( 0.7)« 

246 ( 3.3) 268 ( 1.4)»> 

6 hours or more 1990 20 ( 1.1) 16 ( 1.0) 

230 ( 2.6) 245 ( 2.0) 

1992 20 ( 0.9) 13 ( 0.4) 

231 ( 2.6) 243 ( 1.5) 

1996 17 ( 1.3) 14 ( 0.6) 

235 ( 5.2) 252 ( 1.4)»> 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation » («) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1990 at about the 95 percent confidence level. If the notation > (<)

appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992 at

about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 149
Guam

Parental Support

When parents are involved in their children’s education, both children and parents

are likely to benefit. Research on students at risk has shown that parents’ participation

in their children’s education has more effect on the child’s performance than parent

income or parent education.67 Parental involvement is naturally part of the home

environment, but it is also increasingly sought in the school.

As part of the NAEP assessment, the principals of participating students were

asked about parental involvement in their schools. Tables 7.4A and 7.4B present the

results for fourth and eighth graders, respectively, in public schools in Guam. According

to these results:

• Overall, all of the fourth-grade students attended schools where

principals characterized parental support as very positive (48 percent)

or somewhat positive (52 percent).

• Overall, more than half of the eighth-grade students attended schools

where principals characterized parental support as very positive

(0 percent) or somewhat positive (58 percent).

TABLE 7.4A — GRADE 4

Public Schools’ Reports on Parental Support

How would you characterize parental

support for student achievement within

your school?

Guam Nation

Percentage and Average Scale Score

Somewhat to very negative 1992 0 (****) 5 ( 1.2) 

*** (**.*) 202 ( 4.9)! 

1996 0 (****) 5 ( 1.5) 

*** (**.*) 200 ( 5.8)! 

Somewhat positive 1992 71 ( 0.2) 54 ( 3.2) 

194 ( 1.1) 215 ( 1.3) 

1996 52 ( 0.6)< 52 ( 3.7) 

192 ( 1.5) 220 ( 1.3)> 

Very positive 1992 29 ( 0.2) 41 ( 3.2) 

189 ( 1.2) 225 ( 1.7) 

1996 48 ( 0.6)> 43 ( 3.9) 

185 ( 1.6) 227 ( 1.7) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. ! Interpret with caution

— the nature of the sample does not allow accurate determination of the variability of this statistic. *** Sample size is

insufficient to permit a reliable estimate.   Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

67 Office of Educational Research and Improvement. Mapping out the National Assessment of Title I: The Interim Report

— 1996. (Washington, DC: Office of Educational Research and Improvement, U.S. Department of Education, 1996).

150 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 7.4B — GRADE 8

Public Schools’ Reports on Parental Support

How would you characterize parental

support for student achievement within

your school?

Guam Nation

Percentage and Average Scale Score

Somewhat to very negative 1992 87 ( 0.3) 10 ( 2.3) 

237 ( 1.3) 258 ( 2.4)! 

1996 42 ( 0.9)< 7 ( 2.3) 

243 ( 2.5) 271 ( 3.4)!> 

Somewhat positive 1992 13 ( 0.3) 62 ( 3.2) 

216 ( 3.4) 265 ( 1.2) 

1996 58 ( 0.9)> 57 ( 4.8) 

231 ( 2.4)> 268 ( 1.5) 

Very positive 1992 0 (** **) 28 ( 3.0) 

*** (**.*) 276 ( 2.1) 

1996 0 (****) 35 ( 4.5) 

*** (**.*) 277 ( 2.7) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. ! Interpret with caution

— the nature of the sample does not allow accurate determination of the variability of this statistic. *** Sample size is

insufficient to permit a reliable estimate. **** Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 151
Guam

Student Mobility

Research indicates that moving more than once or twice during the school year

lowers student achievement. Students who attend the same school throughout their

career are most likely to graduate, whereas the most mobile of the school populations

have the highest rates of failure and dropping out.68

In order to look at the relationship between mobility and mathematics

achievement, students were asked how many times within the past two years they had

changed schools because they had changed where they lived. Table 7.5A shows results

for fourth-grade public school students.

• In terms of student mobility, 52 percent of fourth graders reported not

moving over the last two years while 14 percent of students reported

doing so three or more times. The students with the highest reported

mobility had an average scale score (184) that did not differ significantly

from* that of those who reported not moving (191).

• The percentage of students in Guam who reported moving three or more

times (14 percent) was somewhat greater than the percentage for the

nation (11 percent).

TABLE 7.5A — GRADE 4

Public School Students’ Reports on Mobility

Within the past two years, how many

times have you changed schools

because you changed where you

lived?

Guam Nation

Percentage and Average Scale Score

None 1992 45 ( 1.1) 60 ( 0.9) 

194 ( 1.2) 225 ( 0.9) 

1996 52 ( 1.3)> 62 ( 1.1) 

191 ( 2.0) 227 ( 1.2) 

One 1992 21 ( 0.9) 19 ( 0.6) 

194 ( 2.1) 216 ( 1.6) 

1996 22 ( 1.2) 19 ( 0.7) 

192 ( 2.3) 221 ( 1.9) 

Two 1992 15 ( 0.8) 9 ( 0.4) 

192 ( 2.1) 206 ( 1.7) 

1996 12 ( 0.9) 8 ( 0.5) 

177 ( 4.0)< 210 ( 2.1) 

Three or more 1992 18 ( 0.8) 13 ( 0.5) 

191 ( 2.0) 201 ( 1.6) 

1996 14 ( 1.0)< 11 ( 0.8) 

184 ( 4.5) 207 ( 2.0) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

* Although the difference may appear large, recall that “significance” here refers to “statistical significance.”

68 ERIC Clearinghouse on Urban Education. Highly Mobile Students: Educational Problems and Possible Solutions. (New

York, NY: ERIC Clearinghouse on Urban Education, ERIC/CUE Digest, Number 73, 1991).

152 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Eighth-grade public school students were also asked about their mobility. As

shown in Table 7.5B, the results based on 1996 eighth graders’ reports of mobility

indicate the following:

• In terms of student mobility, 62 percent of eighth graders reported not

having moved over the last two years, while 9 percent of students

reported doing so three or more times. The students with the highest

reported mobility had an average scale score (224) that was lower than

that of those who reported not moving (246).

• In Guam, the percentage of students who reported moving three or more

times (9 percent) was greater than the percentage for the nation

(6 percent).

TABLE 7.5B — GRADE 8

Public School Students’ Reports on Mobility

Within the past two years, how many

times have you changed schools

because you changed where you

lived?

Guam Nation

Percentage and Average Scale Score

None 1992 69 ( 1.3) 78 ( 0.7) 

240 ( 1.2) 271 ( 1.0) 

1996 62 ( 1.9)< 74 ( 0.7)< 

246 ( 1.8)> 276 ( 1.1)> 

One 1992 17 ( 1.0) 14 ( 0.4) 

238 ( 2.1) 262 ( 1.8) 

1996 19 ( 1.4) 14 ( 0.5) 

242 ( 3.4) 262 ( 2.0) 

Two 1992 7 ( 0.7) 5 ( 0.4) 

240 ( 4.7) 250 ( 2.9) 

1996 10 ( 1.1) 5 ( 0.4) 

231 ( 6.3) 253 ( 2.7) 

Three or more 1992 7 ( 0.8) 4 ( 0.3) 

230 ( 4.5) 245 ( 2.3) 

1996 9 ( 0.9) 6 ( 0.3)> 

224 ( 6.6) 254 ( 2.6)> 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 153
Guam

Students’ Views About Mathematics

The attitudes children form about mathematics can affect the depth to which they

learn the concepts. These same attitudes can also affect decisions that middle school

students make about what mathematics courses they will study. Failure to study

mathematics can close the doors to education beyond high school, and to many

interesting and exciting careers. Thus, students’ attitudes and beliefs about mathematics

can be a contributing factor affecting the skills they will acquire.

Do Students Believe That Math Is Useful for Everyday Problems?

If children view mathematics as a practical, useful subject, they may better

understand that it can be applied to a wide variety of real-world problems and

phenomena. The NCTM Standards explain that, even though most mathematical ideas

in the kindergarten through fourth grade curriculum arise from the everyday world, they

must be regularly applied to real-world situations. Further, children need to understand

that mathematics is an integral part of real-world situations and activities in other

curricular areas. One major purpose of mathematics is to help children understand and

interpret their world and solve problems that occur in it. This important view of

mathematics must continue through the curriculum for grades 5 through 8. Teachers

should emphasize the application of mathematics to real-world problems as well as to

other settings relevant to middle school students.

In order to examine whether mathematics has been made relevant to the students,

they were asked the degree to which they agreed or disagreed with the statement that

mathematics is useful for solving everyday problems. Responses by fourth-grade public

school students are reported in Table 7.6A. According to their responses:

• More than half of the fourth graders in Guam agreed with the statement

that mathematics is useful for solving everyday problems (57 percent).

This percentage was greater than that of students disagreeing with the

statement (18 percent).

• The percentage of students in the state agreeing that mathematics is

useful for everyday problems (57 percent) was smaller than the

percentage seen nationally (68 percent).

154 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 7.6A — GRADE 4

Public School Students’ Views on the Usefulness of

Mathematics

To what degree do you agree with the

statement “Mathematics is useful for

solving everyday problems?”

Guam Nation

Percentage and Average Scale Score

Disagree 1992 17 ( 0.8) 13 ( 0.6) 

187 ( 2.1) 207 ( 1.7) 

1996 18 ( 1.2) 14 ( 0.7) 

182 ( 3.8) 211 ( 2.0) 

Undecided 1992 27 ( 1.0) 21 ( 0.9) 

192 ( 1.7) 218 ( 1.3) 

1996 25 ( 1.3) 18 ( 0.7)< 

189 ( 3.4) 221 ( 1.5) 

Agree 1992 56 ( 1.3) 66 ( 1.1) 

198 ( 1.1) 223 ( 0.9) 

1996 57 ( 1.3) 68 ( 0.9) 

195 ( 2.2) 228 ( 1.0)> 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 155
Guam

Eighth graders were also asked about the usefulness of mathematics to solve

everyday problems. According to the responses of eighth-grade public school students

in Guam, as shown in Table 7.6B, the following was true:

• Overall, a large majority of the eighth graders strongly agreed

(43 percent) or agreed (37 percent) that mathematics was useful for

solving everyday problems. A small percentage strongly disagreed

(2 percent) or disagreed (4 percent).

• The percentage of students in Guam strongly agreeing that mathematics

is useful for everyday problems (43 percent) was not significantly

different from the percentage seen nationally (41 percent).

TABLE 7.6B — GRADE 8

Public School Students’ Views on the Usefulness of

Mathematics

To what degree do you agree with the

statement “Mathematics is useful for

solving everyday problems?”

Guam Nation

Percentage and Average Scale Score

Strongly disagree 1992 1 ( 0.3) 2 ( 0.2) 

*** (**.*) 246 ( 3.5) 

1996 2 ( 0.6) 2 ( 0.2) 

*** (**.*) 251 ( 4.3) 

Disagree 1992 4 ( 0.7) 5 ( 0.4) 

*** (**.*) 262 ( 3.1) 

1996 4 ( 0.6) 5 ( 0.4) 

*** (**.*) 258 ( 2.8) 

Undecided 1992 16 ( 1.0) 12 ( 0.5) 

236 ( 3.2) 267 ( 1.9) 

1996 13 ( 1.4) 12 ( 0.6) 

229 ( 4.2) 273 ( 2.9) 

Agree 1992 38 ( 1.5) 43 ( 0.7) 

240 ( 2.1) 270 ( 1.1) 

1996 37 ( 1.9) 40 ( 0.8)< 

238 ( 3.0) 274 ( 1.1) 

Strongly agree 1992 41 ( 1.3) 38 ( 0.7) 

244 ( 1.8) 269 ( 1.2) 

1996 43 ( 1.9) 41 ( 1.2) 

248 ( 2.6) 272 ( 1.2) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level. *** Sample size is

insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

156 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

Do Students Believe Mathematics Is a Static Discipline?

Do students believe that mathematics is a static, unchanging, rule-bound discipline

or a dynamic, flexible way of approaching problem-solving situations? This question

is key to the mathematics curricula described in the NCTM Standards. Curricula should

emphasize the development of students’ mathematical thinking and reasoning abilities.

Although learning the basic facts and rules remains important, memorization of facts and

rules without understanding and not being able to use them appropriately is not helpful.

Curricula should also emphasize the importance of flexibility in choosing strategies and

techniques for solving mathematical problems. Successful problem solving, employing

flexibility in approach and technique, should lead to confidence and perseverance in

solving higher level problems.

Students were asked whether they agreed or disagreed with the two statements that

learning mathematics is mostly memorizing facts and that there is only one way to solve

a mathematical problem. Responses by fourth-grade public school students are reported

in Table 7.7A. According to their responses, the following is true:

• Relatively few of the fourth graders in Guam disagreed with the

statement that mathematics is mostly memorizing facts (10 percent).

This percentage was smaller than that of students agreeing with the

statement (68 percent).

• When asked if there is only one way to solve a mathematics problem,

38 percent of fourth graders disagreed. This percentage was greater

than that of students agreeing with this belief (32 percent).

• The percentage of students in the state disagreeing that mathematics is

the memorization of facts (10 percent) was smaller than the percentage

in the nation (21 percent). Similarly, the percentage disagreeing with

the belief that there is only one solution to a mathematics problem

(38 percent) was smaller than the national percentage (63 percent).

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 157
Guam

TABLE 7.7A — GRADE 4

Public School Students’ Views on the Nature of Mathematics

To what degree do you agree with the

following statements?

Guam Nation

Percentage and Average Scale Score

Learning mathematics is mostly

 memorizing facts.

Disagree 10 ( 1.0) 21 ( 0.9) 

185 ( 4.6) 233 ( 1.6) 

Undecided 21 ( 1.2) 25 ( 0.6) 

192 ( 3.5) 226 ( 1.3) 

Agree 68 ( 1.3) 55 ( 0.9) 

192 ( 1.7) 220 ( 1.0) 

There is only one correct way to

solve a mathematics problem.

Disagree 38 ( 1.5) 63 ( 0.9) 

202 ( 2.4) 231 ( 1.0) 

Undecided 30 ( 1.2) 20 ( 0.7) 

189 ( 2.8) 219 ( 1.7) 

Agree 32 ( 1.3) 17 ( 0.6) 

180 ( 2.4) 205 ( 1.6) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

Eighth graders were also asked about their beliefs about the nature of mathematics.

The responses of eighth-grade public school students in Guam, as shown in Table 7.7B,

indicate that:

• Overall, less than one fifth of the eighth graders strongly disagreed

(4 percent) or disagreed (11 percent) that mathematics is mostly

memorizing facts. More than half strongly agreed (18 percent) or

agreed (36 percent).

• The percentage of students in the state strongly disagreeing that

mathematics is mostly memorizing facts was smaller than the percentage

seen nationally (7 percent).

• Overall, more than half of the eighth graders strongly disagreed

(27 percent) or disagreed (35 percent) that there was only one way to

solve a mathematical problem. Relatively few strongly agreed

(4 percent) or agreed (9 percent).

• The percentage of students in the state strongly disagreeing that there is

one way to solve a mathematics problem was smaller than the

percentage seen nationally (34 percent).

158 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

TABLE 7.7B — GRADE 8

Public School Students’ Views on the Nature of Mathematics

To what degree do you agree with the

following statements?

Guam Nation

Percentage and Average Scale Score

Learning mathematics is mostly

 memorizing facts.

Strongly disagree 4 ( 0.8) 7 ( 0.4) 

*** (**.*) 282 ( 2.8) 

Disagree 11 ( 1.0) 22 ( 0.9) 

257 ( 6.7) 283 ( 2.0) 

Undecided 30 ( 1.5) 28 ( 0.7) 

241 ( 3.3) 274 ( 1.4) 

Agree 36 ( 1.6) 30 ( 0.7) 

239 ( 2.8) 265 ( 1.1) 

Strongly agree 18 ( 1.3) 12 ( 0.6) 

232 ( 4.4) 255 ( 1.9) 

There is only one correct way to

solve a mathematics problem.

Strongly disagree 27 ( 1.5) 34 ( 0.9) 

253 ( 3.1) 279 ( 1.3) 

Disagree 35 ( 1.8) 43 ( 0.7) 

245 ( 2.5) 273 ( 1.2) 

Undecided 25 ( 1.2) 14 ( 0.6) 

232 ( 2.7) 263 ( 1.9) 

Agree 9 ( 1.0) 5 ( 0.4) 

218 ( 6.0) 243 ( 2.7) 

Strongly agree 4 ( 0.7) 2 ( 0.2) 

*** (**.*) 245 ( 3.6) 

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). *** Sample size is insufficient to permit a reliable estimate.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 159
Guam

160 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
Guam

 APPENDIX A

Reporting NAEP 1996 Mathematics Results

for Guam

A.1 Participation Guidelines

As was discussed in the Introduction, unless the overall participation rate is

sufficiently high for a jurisdiction, there is a risk that the assessment results for that

jurisdiction will be subject to appreciable nonresponse bias. Moreover, even if the

overall participation rate is high, there may be significant nonresponse bias if the

nonparticipation that does occur is heavily concentrated among certain types of schools

or students. The following guidelines concerning school and student participation rates

in the state assessment program were established to address four significant ways in

which nonresponse bias could be introduced into the jurisdiction sample estimates. The

guidelines determining a jurisdiction’s eligibility to have its results published are

presented below. Also presented below are the conditions that will result in a

jurisdiction’s receiving a notation in the 1996 reports. Note that in order for a

jurisdiction’s results to be published with no notations, that jurisdiction must satisfy all

guidelines. (A more complete discussion of the NAEP participation guidelines can be

found in the Technical Report of the NAEP 1996 State Assessment Program in

Mathematics.)

Guidelines on the Publication of NAEP Results

Guideline 1 — Publication of Public School Results

A jurisdiction will have its public school results published in the NAEP

1996 Mathematics Report Card (or in other reports that include all

state-level results) if and only if its weighted participation rate for the

initial sample of public schools is greater than or equal to 70 percent.

Similarly, a jurisdiction will receive a separate NAEP 1996 Mathematics

State Report if and only if its weighted participation rate for the initial

sample of public schools is greater than or equal to 70 percent.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 161
Guam

Guideline 2 — Publication of Nonpublic School Results

A jurisdiction will have its nonpublic school results published in the

NAEP 1996 Mathematics Report Card (or in other reports that include

all state-level results) if and only if its weighted participation rate for

the initial sample of nonpublic schools is greater than or equal to 70

percent AND meets minimum sample size requirements.1 A

jurisdiction eligible to receive a separate NAEP 1996 Mathematics State

Report under guideline 1 will have its nonpublic school results included

in that report if and only if that jurisdiction’s weighted participation rate

for the initial sample of nonpublic schools is greater than or equal to

70 percent AND meets minimum sample size requirements. If a

jurisdiction meets guideline 2 but fails to meet guideline 1, a separate

NAEP 1996 Mathematics State Report will be produced containing only

nonpublic school results.

Guideline 3 — Publication of Combined Public and

Nonpublic School Results

A jurisdiction will have its combined results published in the NAEP

1996 Mathematics Report Card (or in other reports that include all

state-level results) if and only if both guidelines 1 and 2 are satisfied.

Similarly, a jurisdiction eligible to receive a separate NAEP 1996

Mathematics State Report under guideline 1 will have its combined

results included in that report if and only if guideline 2 is also met.

Guidelines for Notations of NAEP Results

Guideline 4 — Notation for Overall Public School

Participation Rate

A jurisdiction that meets guideline 1 will receive a notation if its

weighted participation rate for the initial sample of public schools was

below 85 percent AND the weighted public school participation rate

after substitution was below 90 percent.

Guideline 5 — Notation for Overall Nonpublic School

Participation Rate

A jurisdiction that meets guideline 2 will receive a notation if its

weighted participation rate for the initial sample of nonpublic schools

was below 85 percent AND the weighted nonpublic school participation

rate after substitution was below 90 percent.

1

 Minimum participation size requirements for reporting nonpublic school data consist of two components: (1) a school

sample size of six or more participating schools and (2) an assessed student sample size of at least 62.

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Guideline 6 — Notation for Strata-Specific Public

School Participation Rate

A jurisdiction that is not already receiving a notation under

guideline 4 will receive a notation if the sample of public schools

included a class of schools with similar characteristics that had a

weighted participation rate (after substitution) of below 80 percent, and

from which the nonparticipating schools together accounted for more

than five percent of the jurisdiction’s total weighted sample of public

schools. The classes of schools from each of which a jurisdiction

needed minimum school participation levels were determined by degree

of urbanization, minority enrollment, and median household income of

the area in which the school is located.

Guideline 7 — Notation for Strata-Specific Nonpublic

School Participation Rate

A jurisdiction that is not already receiving a notation under

guideline 5 will receive a notation if the sample of nonpublic schools

included a class of schools with similar characteristics that had a

weighted participation rate (after substitution) of below 80 percent, and

from which the nonparticipating schools together accounted for more

than five percent of the jurisdiction’s total weighted sample of

nonpublic schools. The classes of schools from each of which a

jurisdiction needed minimum school participation levels were

determined by type of nonpublic school (Catholic versus non-Catholic)

and location (metropolitan versus nonmetropolitan).

Guideline 8 — Notation for Overall Student Participation

Rate in Public Schools

A jurisdiction that meets guideline 1 will receive a notation if the

weighted student response rate within participating public schools was

below 85 percent.

Guideline 9 — Notation for Overall Student Participation

Rate in Nonpublic Schools

A jurisdiction that meets guideline 2 will receive a notation if the

weighted student response rate within participating nonpublic schools

was below 85 percent.

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Guideline 10 — Notation for Strata-Specific Student

Participation Rates in Public Schools

A jurisdiction that is not already receiving a notation under

guideline 8 will receive a notation if the sampled students within

participating public schools included a class of students with similar

characteristics that had a weighted student response rate of below 80

percent, and from which the nonresponding students together accounted

for more than five percent of the jurisdiction’s weighted assessable

public school student sample. Student groups from which a jurisdiction

needed minimum levels of participation were determined by the age of

the student, whether or not the student was classified as a student with

a disability (SD) or of limited English proficiency (LEP), and the type

of assessment session (monitored or unmonitored), as well as school

level of urbanization, minority enrollment, and median household

income of the area in which the school is located.

Guideline 11 — Notation for Strata-Specific Student

Participation Rates in Nonpublic Schools

A jurisdiction that is not already receiving a notation under

guideline 9 will receive a notation if the sampled students within

participating nonpublic schools included a class of students with similar

characteristics that had a weighted student response rate of below 80

percent, and from which the nonresponding students together accounted

for more than five percent of the jurisdiction’s weighted assessable

nonpublic school student sample. Student groups from which a

jurisdiction needed minimum levels of participation were determined

by the age of the student, whether or not the student was classified as

a student with a disability (SD) or of limited English proficiency (LEP),

and the type of assessment session (monitored or unmonitored), as well

as type and location of school.

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A.2 NAEP Reporting Groups

The state assessment program provides results for groups of students defined by

shared characteristics — region of the country, gender, race/ethnicity, parental education,

location of the school, type of school, participation in Title I programs, and eligibility

for the free/reduced-price lunch component of the National School Lunch Program.

Based on criteria described later in this appendix, results are reported for subpopulations

only when sufficient numbers of students and adequate school representation are present.

For public school students, the minimum requirement is at least 62 students in a

particular subgroup from at least 5 primary sampling units (PSUs).2 For nonpublic

school students, the minimum requirement is 62 students from at least 6 different schools

for the state assessment program or from at least 5 PSUs for the national assessment.

However, the data for all students, regardless of whether their subgroup was reported

separately, were included in computing overall results. Definitions of the subpopulations

referred to in this report are presented on the following pages.

Region

Results are reported for four regions of the nation: Northeast, Southeast, Central,

and West. States included in each region are shown in Figure A.1. All 50 states and

the District of Columbia are listed. Territories and the two Department of Defense

Educational Activities jurisdictions were not assigned to any region.

Regional results are based on national assessment samples, not on aggregated state

assessment program samples. Thus, the regional results are based on a sample that is

different and separate from that used to report the state results.

NORTHEAST SOUTHEAST CENTRAL WEST

 Connecticut Alabama Illinois Alaska

 Delaware Arkansas Indiana Arizona

District of Columbia Florida Iowa California

 Maine Georgia Kansas Colorado

 Maryland Kentucky Michigan Hawaii

 Massachusetts Louisiana Minnesota Idaho

New Hampshire Mississippi Missouri Montana

New Jersey North Carolina Nebraska Nevada

New York South Carolina North Dakota New Mexico

 Pennsylvania Tennessee Ohio Oklahoma

Rhode Island Virginia* South Dakota Oregon

Vermont West Virginia Wisconsin Texas

 Virginia* Utah

 Washington

Wyoming

* The part of Virginia that is included in the Washington, DC, metropolitan area is included in the Northeast region; the

remainder of the state is in the Southeast region.

FIGURE A.1

Regions of the Country

2

 For the State Assessment Program, a PSU is most often a single school; for the national assessment, a PSU is a selected

geographic region (a county, group of counties, or a metropolitan statistical area).

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Gender

Results are reported separately for males and females.

Race/Ethnicity

The race/ethnicity variable is derived from two questions asked of students and

schools’ records, and it is used for race/ethnicity subgroup comparisons. Two questions

from the set of general student background questions were used to determine

race/ethnicity:

If you are Hispanic, what is your Hispanic background?

° I am not Hispanic.

° Mexican, Mexican American, or Chicano

° Puerto Rican

° Cuban

° Other Spanish or Hispanic background

Students who responded to this question by filling in the second, third, fourth, or

fifth oval were considered Hispanic. For students who filled in the first oval, did not

respond to the question, or provided information that was illegible or could not be

classified, responses to the question below were examined in an effort to determine

race/ethnicity.

Which best describes you?

° White (not Hispanic)

° Black (not Hispanic)

° Hispanic (“Hispanic” means someone who is from a Mexican,

Mexican American, Chicano, Puerto Rican, Cuban,

or other Spanish or Hispanic background.)

° Asian or Pacific Islander (“Asian or Pacific Islander”

means someone who is from a Chinese, Japanese, Korean,

Filipino, Vietnamese, or other Asian or Pacific Island background.)

° American Indian or Alaskan Native (“American Indian or

Alaskan Native” means someone who is from one of the American

Indian tribes, or one of the original people of Alaska.)

° Other (specify)

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Students’ race/ethnicity was then assigned on the basis of their response. For

students who filled in the sixth oval (“Other”) or provided illegible information or

information that could not be classified, or did not respond at all, race/ethnicity was

assigned as determined by school records.3

Race/ethnicity could not be determined for students who did not respond to either

of the demographic questions and whose schools did not provide information about

race/ethnicity.

The details of how race/ethnicity classifications were derived is presented so that

readers can determine how useful the results are for their particular purposes. Also,

some students indicated that they were from a Hispanic background (e.g., Puerto Rican

or Cuban) and that a racial/ethnic category other than Hispanic best described them.

These students were classified as Hispanic based on the rules described above.

Furthermore, information from the schools did not always correspond to how students

described themselves. Therefore, the racial/ethnic results presented in this report attempt

to provide a clear picture based on several sources of information.

As noted in Chapters 2 and 4, national scale score and achievement level results

for eighth-grade Asian/Pacific Islander students are not included in the main body of this

report. The decision not to publish these results is discussed in Appendix F.

Parents’ Highest Level of Education

The variable representing level of parental education is derived from responses to

two questions from the set of general student background questions. Students were

asked to indicate the extent of their mother’s education:

How far in school did your mother go?

° She did not finish high school.

° She graduated from high school.

° She had some education after high school.

° She graduated from college.

° I don’t know.

Students were asked a similar question about their father’s education level:

How far in school did your father go?

° He did not finish high school.

° He graduated from high school.

° He had some education after high school.

° He graduated from college.

° I don’t know.

3

 The procedure for assigning race/ethnicity was modified for Hawaii. See the Technical Report for the NAEP 1996 State

Assessment Program in Mathematics for details.

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The information was combined into one parental education reporting variable

determined through the following process. If a student indicated the extent of education

for only one parent, that level was included in the data. If a student indicated the extent

of education for both parents, the higher of the two levels was included in the data. If

a student did not know the level of education for both parents or did not know the level

for one parent and did not respond for the other, the parental education level was

classified as “I don’t know.” If the student did not respond for either parent, the student

was recorded as having provided no response. (Nationally, 36 percent of fourth graders

and 11 percent of eighth graders reported that they did not know the education level of

either of their parents.)

Type of Location

Results are provided for students attending public schools in three mutually

exclusive location types — central city, urban fringe/large town, and rural/small town

— as defined below. The type of location variable is defined in such a way as to indicate

the geographical location of a student’s school. The intention is not to indicate, or

imply, social or economic meanings for these location types. The type of location

variable, on which the current NAEP sampling is based, does not support the reporting

of regional results. Therefore, only state and national results will be presented.

Central City: The Central City category includes central cities of all

Metropolitan Statistical Areas (MSAs).4 Central City is a geographic

term and is not synonymous with “inner city.”

Urban Fringe/Large Town: An Urban Fringe includes all densely

settled places and areas within MSAs that are classified as urban by the

Bureau of the Census. A Large Town is defined as places outside

MSAs with a population greater than or equal to 25,000.

Rural/Small Town: Rural includes all places and areas with a

population of less than 2,500 that are classified as rural by the Bureau

of the Census. A Small Town is defined as places outside MSAs with

a population of less than 25,000 but greater than or equal to 2,500.

4

 Each Metropolitan Statistical Area (MSA) is defined by the Office of Management and Budget.

168 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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Type of School

Samples for the 1996 state assessment program were expanded to include students

attending nonpublic schools (Catholic schools and other religious and private schools)

in addition to students attending public schools. The expanded coverage was instituted

for the first time in 1994. Samples for the 1990 and 1992 Trial State Assessment

programs had been restricted to public school students only. For those jurisdictions

meeting pre-established participation rate standards (see earlier section of this appendix),

separate results are reported for public schools, for nonpublic schools, and for the

combined public and nonpublic school samples. The combined sample for each

jurisdiction also contains students attending Bureau of Indian Affairs (BIA) schools and

Department of Defense Domestic Dependent Elementary and Secondary Schools

(DDESS) in that jurisdiction. These two categories of schools are not included in either

the public or nonpublic school samples.

Note that the DDESS and Department of Defense Dependents Schools

(DoDDS)5 were assessed in 1996 as separate jurisdictions, reported as jurisdictions with

public school samples only.

Title I Participation

Based on available school records, students were classified as either currently

participating in a Title I program or receiving Title I services, or as not receiving such

services. The classification applies only to the school year when the assessment was

administered (i.e., the 1995-96 school year) and is not based on participation in previous

years. If the school did not offer any Title I programs or services, all students in that

school were classified as not participating.

Eligibility for the Free/Reduced-Price School Lunch Program

Based on available school records, students were classified as either currently

eligible for the free/reduced-price lunch component of the Department of Agriculture’s

National School Lunch Program or not eligible. The classification refers only to the

school year when the assessment was administered (i.e., the 1995-96 school year) and

is not based on eligibility in previous years. If school records were not available, the

student was classified as “Information not available.” If the school did not participate

in the program, all students in that school were classified as “Information not available.”

A.3 Guidelines for Analysis and Reporting

This report describes mathematics performance for fourth and eighth graders and

compares the results for various groups of students within these populations — for

example, those who have certain demographic characteristics or who responded to a

specific background question in a particular way. The report examines the results for

individual demographic groups and individual background questions. It does not include

an analysis of the relationships among combinations of these subpopulations or

background questions.

5

 The Department of Defense Dependents Schools (DoDDS) refers to overseas schools (i.e., schools outside the United

States). Department of Defense Domestic Dependent Elementary and Secondary Schools (DDESS) refers to domestic

schools (i.e., schools in the United States).

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Drawing Inferences from the Results

Because the percentages of students in these subpopulations and their average

scale scores are based on samples — rather than on the entire population of fourth and

eighth graders in a jurisdiction — the numbers reported are necessarily estimates. As

such, they are subject to a measure of uncertainty, reflected in the standard error of the

estimate. When the percentages or average scale scores of certain groups are compared,

it is essential to take the standard error into account, rather than to rely solely on

observed similarities or differences. Therefore, the comparisons discussed in this report

are based on statistical tests that consider both the magnitude of the difference between

the averages or percentages and the standard errors of those statistics.

One of the goals of the state assessment program is to estimate scale score

distributions and percentages of students in the categories described in A.2 for the

overall populations of fourth- and eighth-grade students in each participating jurisdiction

based on the particular samples of students assessed. The use of confidence intervals,

based on the standard errors, provides a way to make inferences about the population

average scale scores and percentages in a manner that reflects the uncertainty associated

with the sample estimates. An estimated sample average scale score ± 2 standard errors

approximates a 95 percent confidence interval for the corresponding population average

or percentage. This means that one can conclude with approximately 95 percent

confidence that the average scale score of the entire population of interest (e.g., all

fourth-grade students in public schools in a jurisdiction) is within ± 2 standard errors

of the sample average.

As an example, suppose that the average mathematics scale score of the students

in a particular jurisdiction’s eighth-grade sample were 256 with a standard error of 1.2.

A 95 percent confidence interval for the population average would be as follows:

Mean ± 2 standard errors = 256 ± 2 × (1.2) = 256 ± 2.4 =

256 - 2.4 and 256 + 2.4 = (253.6, 258.4)

Thus, one can conclude with 95 percent confidence that the average scale score

for the entire population of eighth-grade students in public schools in that jurisdiction

is between 253.6 and 258.4.

Similar confidence intervals can be constructed for percentages, if the percentages

are not extremely large or extremely small. For extreme percentages, confidence

intervals constructed in the above manner may not be appropriate, and accurate

confidence intervals can be constructed only by using procedures that are quite

complicated.

Extreme percentages, defined by both the magnitude of the percentage and the size

of the sample from which it was derived, should be interpreted with caution. (The

forthcoming Technical Report of the NAEP 1996 State Assessment Program in

Mathematics contains a more complete discussion of extreme percentages.)

170 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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Analyzing Subgroup Differences in Averages and Percentages

The statistical tests determine whether the evidence — based on the data from the

groups in the sample — is strong enough to conclude that the averages or percentages

are really different for those groups in the population. If the evidence is strong (i.e., the

difference is statistically significant), the report describes the group averages or

percentages as being different (e.g., one group performed higher than or lower than

another group) — regardless of whether the sample averages or sample percentages

appear to be about the same or not. If the evidence is not sufficiently strong (i.e., the

difference is not statistically significant), the averages or percentages are described as

being not significantly different — again, regardless of whether the sample averages or

sample percentages appear to be about the same or widely discrepant. The reader is

cautioned to rely on the results of the statistical tests — rather than on the apparent

magnitude of the difference between sample averages or percentages — to determine

whether those sample differences are likely to represent actual differences between the

groups in the population.

In addition to the overall results, this report presents outcomes separately for a

variety of important subgroups. Many of these subgroups are defined by shared

characteristics of students, such as their gender or race/ethnicity and the type of location

in which their school is situated. Other subgroups are defined by the responses of the

assessed students’ mathematics teachers to questions in the mathematics teacher

questionnaire.

In Chapter 1 of this report, differences between the jurisdiction and the nation were

tested for overall mathematics scale score and for each of the mathematics content areas.

In Chapter 2, significance tests were conducted for the overall scale score for each of

the subpopulations. Chapter 3 reports differences between the jurisdiction and nation

for the percentage of students at or above the Proficient level, and Chapter 4 contains

significance tests for the percentage of students at or above the Proficient level for each

of the subpopulations. In Chapters 5 through 7, comparisons were made across

subgroups for responses to various background questions.

As an example of comparisons across subgroups, consider the question: Do

students who reported discussing studies at home almost every day exhibit higher average

mathematics scale scores than students who report never or hardly ever doing so?

To answer the question posed above, begin by comparing the average mathematics

scale score for the two groups being analyzed. If the average for the group that reported

discussing their studies at home almost every day is higher, it may be tempting to

conclude that that group does have a higher mathematics scale score than the group that

reported never or hardly ever discussing their studies at home. However, even though

the averages differ, there may be no real difference in performance between the two

groups in the population because of the uncertainty associated with the estimated average

scale scores of the groups in the sample. Remember that the intent is to make a

statement about the entire population, not about the particular sample that was assessed.

The data from the sample are used to make inferences about the population as a whole.

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As discussed in the previous section, each estimated sample average scale score

(or percentage) has a degree of uncertainty associated with it. It is therefore possible

that if all students in the population (rather than a sample of students) had been assessed

or if the assessment had been repeated with a different sample of students or a different,

but equivalent, set of questions, the performances of various groups would have been

different. Thus, to determine whether there is a real difference between the average

scale score (or percentage of a certain attribute) for two groups in the population, an

estimate of the degree of uncertainty associated with the difference between the scale

score averages or percentages of those groups must be obtained for the sample. This

estimate of the degree of uncertainty — called the standard error of the difference

between the groups — is obtained by taking the square of each group’s standard error,

summing these squared standard errors, and then taking the square root of this sum.

In a manner similar to that in which the standard error for an individual group

average or percentage is used, the standard error of the difference can be used to help

determine whether differences between groups in the population are real. The difference

between the mean scale score or percentage of the two groups — 2 standard errors of

the difference — represents an approximate 95 percent confidence interval. If the

resulting interval includes zero, there is insufficient evidence to claim a real difference

between groups in the population. If the interval does not contain zero, the difference

between groups is statistically significant (different) at the .05 level.

As another example, to determine whether the average mathematics scale score

of fourth-grade males is higher than that of fourth-grade females in a particular

jurisdiction’s public schools, suppose that the sample estimates of the average scale

scores and standard errors for males and females were as follows:

The difference between the estimates of the average sale scores of males and

females is two points (218 - 216). The standard error of this difference is

√ 0.92 + 1.12 = 1.4

Thus, an approximate 95 percent confidence interval for this difference is

Mean difference ± 2 standard errors of the difference =

2 ± 2 × (1.4) = 2 ± 2.8 = 2 - 2.8 and 2 + 2.8 = (-0.8, 4.8)

Group Average Scale Score Standard Error

Males 218 0.9

Females 216 1.1

172 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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The value zero is within this confidence interval, which extends from -0.8 to 4.8

(i.e., zero is between -0.8 and 4.8). Thus, there is insufficient evidence to claim a

difference in average mathematics scale score between the populations of fourth-grade

males and females in public schools in the hypothetical jurisdiction.6

Throughout this report, when the average scale scores or percentages for two

groups were compared, procedures like the one described above were used to draw the

conclusions that are presented. If a statement appears in the report indicating that a

particular group had a higher (or lower) average scale score than a second group, the

95 percent confidence interval for the difference between groups did not contain zero.

An attempt was made to distinguish between group differences that were statistically

significant but rather small in a practical sense and differences that were both statistically

and practically significant. A procedure based on effect sizes was used. Statistically

significant differences that are rather small are described in the text as somewhat higher

or somewhat lower. When a statement indicates that the average scale score or

percentage of some attribute was not significantly different for two groups, the

confidence interval included zero, and thus no difference could be assumed between the

groups. The information described in this section also pertains to comparisons across

years. The reader is cautioned to avoid drawing conclusions solely on the basis of the

magnitude of the difference. A difference between two groups in the sample that

appears to be slight may represent a statistically significant difference in the population

because of the magnitude of the standard errors. Conversely, a difference that appears

to be large may not be statistically significant.

The procedures described in this section, and the certainty ascribed to intervals

(e.g., a 95% confidence interval), are based on statistical theory that assumes that only

one confidence interval or test of statistical significance is being performed. However,

in each chapter of this report, many different groups are being compared (i.e., multiple

sets of confidence intervals are being calculated). In sets of confidence intervals,

statistical theory indicates that the certainty associated with the entire set of intervals is

less than that attributable to each individual comparison from the set. To hold the

certainty level for the set of comparisons at a particular level (e.g., 0.95), adjustments

(called multiple comparison procedures) must be made to the methods described in the

previous section. One such procedure — the Bonferroni method — was used in the

analyses described in this report to form confidence intervals for the differences between

groups whenever sets of comparisons were considered.7 Thus, the confidence intervals

in the text that are based on sets of comparisons are more conservative than those

described on the previous pages.

6

 The procedure described above (especially the estimation of the standard error of the difference) is, in a strict sense,

only appropriate when the statistics being compared come from independent samples. For certain comparisons in the

report, the groups were not independent. In those cases, a different (and more appropriate) estimate of the standard

error of the difference was used.

7

 Miller, R.G. Simultaneous Statistical Inference. (New York, NY: Wiley, 1966).

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Most of the multiple comparisons in this report pertain to relatively small sets or

“families” of comparisons. For example, when comparisons were discussed concerning

students’ reports of parental education, six comparisons were conducted — all pairs of

the four parental education levels. In these situations, Bonferroni procedures were

appropriate. However, the maps in Chapter 1 of this report display comparisons between

Guam and all other participating jurisdictions. The “family” of comparisons in this case

was as many as 46. To control the certainty level for a large family of comparisons, the

False Discovery rate (FDR) criterion8 was used. Unlike the Bonferroni procedures

which control the familywise error rate (i.e., the probability of making even one false

rejection in the set of comparisons), the Benjamini and Hochberg (BH) approach using

the FDR criterion controls the expected proportion of falsely rejected hypotheses as a

proportion of all rejected hypotheses. Bonferroni procedures may be considered

conservative for large families of comparisons.9 In other words, using the Bonferroni

method would produce more statistically nonsignificant comparisons than using the BH

approach. Therefore, the BH approach is potentially more powerful for comparing

Guam to all other participating jurisdictions. A more detailed description of the

Bonferroni and BH procedures appears in the Technical Report of the NAEP 1996 State

Assessment Program in Mathematics.

Statistics with Poorly Estimated Standard Errors

Not only are the averages and percentages reported in NAEP subject to

uncertainty, but their standard errors are as well. In certain cases, typically when the

standard error is based on a small number of students or when the group of students is

enrolled in a small number of schools, the amount of uncertainty associated with the

standard errors may be quite large. Throughout this report, estimates of standard errors

subject to a large degree of uncertainty are followed by the symbol “!”. In such cases,

the standard errors — and any confidence intervals or significance tests involving these

standard errors — should be interpreted cautiously. Further details concerning

procedures for identifying such standard errors are discussed in the Technical Report of

the NAEP 1996 State Assessment Program in Mathematics.

Minimum Subgroup Sample Sizes

Results for mathematics performance and background variables were tabulated and

reported for groups defined by gender, race/ethnicity, parental education, location of the

school, type of school, participation in federally funded Title I programs, and eligibility

for the free/reduced-price lunch component of the National School Lunch Program.

NAEP collects data for five racial/ethnic subgroups (White, Black, Hispanic,

Asian/Pacific Islander, and American Indian/Alaskan Native), three types of locations

(Central City, Urban Fringe/Large Town, and Rural/Small Town),10 and five levels of

parents’ education (Graduated From College, Some Education After High School,

Graduated From High School, Did Not Finish High School, and I Don’t Know).

8

 Benjamini, Y. and Y. Hochberg. “Controlling the false discovery rate: A practical and powerful approach to multiple

testing,” in Journal of the Royal Statistical Society, Series B, 57(1). (pp. 289—300, 1994).

9

 Williams, V.S.L., L.V. Jones, and J.W. Tukey. Controlling Error in Multiple Comparisons, with Special Attention to the

National Assessment of Educational Progress. (Research Triangle Park, NC: National Institute of Statistical Sciences,

December 1994).

10 Previous NAEP reports reported data for four types of communities, rather than for the three types of location. These

types of communities were Advantaged Urban, Disadvantaged Urban, Extreme Rural, and Other types of communities.

174 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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In many jurisdictions, and for some regions of the country, the number of students

in some of these groups was not sufficiently high to permit accurate estimation of

performance and/or background variable results. As a result, data are not provided for

the subgroups with students from very few schools or for the subgroups with very small

sample sizes. For results to be reported for any state assessment program subgroup,

public school results must represent at least 5 primary sampling units (PSUs) and

nonpublic school results must represent 6 schools. For results to be reported for any

national assessment subgroup, at least 5 PSUs must be represented in the subgroup. In

addition, a minimum sample of 62 students per subgroup is required. For statistical tests

pertaining to subgroups, the sample size for both groups has to meet the minimum

sample size requirements.

The minimum sample size of 62 was determined by computing the sample size

required to detect an effect size of 0.5 total-group standard deviation units with a

probability of 0.8 or greater. The effect size of 0.5 pertains to the true difference

between the average scale score of the subgroup in question and the average scale score

for the total fourth- or eighth-grade public school population in the jurisdiction, divided

by the standard deviation of the scale score in the total population. If the true difference

between subgroup and total group mean is 0.5 total-group standard deviation units, then

a sample size of at least 62 is required to detect such a difference with a probability

of 0.8. Further details about the procedure for determining minimum sample size appear

in the Technical Report of the NAEP 1996 State Assessment Program in Mathematics.

Describing the Size of Percentages

Some of the percentages reported in the text of the report are given qualitative

descriptions. For example, the number of students currently taking an algebra class

might be described as “relatively few” or “almost all,” depending on the size of the

percentage in question. Any convention for choosing descriptive terms for the

magnitude of percentages is to some degree arbitrary. The descriptive phrases used in

the report and the rules used to select them are shown below.

Percentage

p = 0

0 < p ≤ 8

8 < p ≤ 13

13 < p ≤ 18

18 < p ≤ 22

22 < p ≤ 27

27 < p ≤ 30

30 < p ≤ 36

36 < p ≤ 47

47 < p ≤ 53

53 < p ≤ 64

64 < p ≤ 71

71 < p ≤ 79

79 < p ≤ 89

89 < p < 100

p = 100

Descriptive Term Used in Report

None

A small percentage

Relatively few

Less than one fifth

About one fifth

About one quarter

Less than one third

About one third

Less than half

About half

More than half

About two thirds

About three quarters

A large majority

Almost all

All

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A.4 Revisions to the NAEP 1990 and 1992 Mathematics Findings

After the NAEP 1994 assessment has been conducted, two technical problems

were discovered in the procedures used to develop the NAEP mathematics scale and

achievement levels determined for the 1990 and 1992 mathematics assessments. These

errors affected the mathematics scale scores reported in 1992 and the achievement level

results reported in 1990 mathematics scale scores reported in 1992 and the achievement

level results reported in 1990 and 1992. The National Center for Education Statistics

(NCES) and the National Assessment Governing Board (NAGB) have evaluated the

impact of these errors and have reanalyzed and reported the revised results from both

mathematics assessments. The technical errors have been corrected and the revised

national and state scale score results for 1992 and achievement level results for 1990

and 1992 are presented in the NAEP 1996 mathematics reports.

Although the two technical problems that were discovered are discussed in greater

detail in the NAEP 1996 Technical Report and NAEP 1996 Technical Report of the State

Assessment in Mathematics, a brief summary is presented below.

The first technical problem resulted from an error in the computer program used

to compute NAEP scale score results. The error occurred in the convention used to

handle omitted responses in the item response theory (IRT) scaling of the partial-credit

constructed-response questions, and it was limited only to those questions. In Analyses

of the NAEP 1992 response questions, and it was limited only to those questions. In

analyses of the NAEP 1992 mathematics assessment, this error caused all blank

responses to partial-credit constructed-response questions (both omitted and not-reached

responses) to be treated as missing — an acceptable treatment, but not the conventional

choice for NAEP. (Because the NAEP 1990 mathematics assessment did not include

these types of questions, the error did not occur.) The national and state assessments

results were recalculated using the intended convention for the treatment of omitted

responses.

In general, the effect of this technical problem on the previously reported NAEP

1992 mathematics findings was minimal, and it had little impact on policy-related

interpretations. The recalculated 1992 mathematics scale score results, at the national

and state levels, are quite similar to those published in the 1992 mathematics reports.

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The second technical problem involved the development of the NAEP

mathematics achievement level cut scores, and it concerned the mapping of the

NAGB-approved achievement levels onto the NAEP mathematics scale. This error

affected the achievement level results reported for the 1990 and 1992 mathematics

assessments. In deriving the final levels recommended to NAGB, panelists’ ratings for

the multiple-choice and constructed-response questions were combined to obtain an

overall rating for the questions. When combined, the ratings were weighted based on

the amount of information provided by each type of question. In other words, some of

the questions “counted more” toward the overall cut scores than others. However,

because the weighting was carried out incorrectly, the constructed-response questions

received more weight than intended. Therefore, the cut scores established by mapping

the achievement levels onto the NAEP mathematics scale were incorrect, and the

percentages of students at or above these levels were incorrectly estimated.

The program that mapped the achievement levels to the NAEP scale was corrected

to appropriate weight the constructed-response questions, and revised mathematics

achievement level cut scores were developed based on the corrected scaling procedures.

As a result, the cut scores for the three achievement levels at each grade were raised,

and the percentages of students at or above the achievement levels were recalculated

based on the corrected cut scores. Revised 1990 and 1992 percentages, for the national

and state assessments, are presented in this report.

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178 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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 APPENDIX B

The NAEP 1996 Mathematics Assessment

The 1996 assessment was the first update of the NAEP mathematics assessment

framework1 since the release of the National Council of Teachers of Mathematics

(NCTM) Curriculum and Evaluation Standards for School Mathematics.

2 This update

reflected refinements in the specifications governing the development of the 1996

assessment while assuring comparability of results across the 1990, 1992, and 1996

assessments. The refinements that distinguish the framework of the assessment

conducted in 1996 from the framework of the assessments conducted in 1990 and 1992

include the following:

• moving away from the rigid content-strand-by-cognitive-process matrix

that governed the development of earlier assessments. Classifying

specific questions into cells of a matrix had required those questions to

measure a unique content strand at a unique cognitive level. This

stipulation often decontextualized the questions and limited the

possibility of assessing students’ abilities to reason in rich

problem-solving situations and to make connections among content

strands within mathematics.

• allowing individual questions on the assessment to be classified in one

or more content strands when appropriate. Knowledge or skills from

more than one content strand is often needed to answer a question. The

option to classify questions in multiple ways provides a greater

opportunity to measure student ability in content settings that closely

approximate real-world reasoning and problem-solving situations.

(However, to develop content strand scales, the primary content

classification was used for questions with multiple classifications.)

• including the mathematics ability categories (conceptual understanding,

procedural knowledge, and problem solving) as well as the process goals

from the NCTM Standards (i.e., communication and connections) to

achieve a balance of questions that measured a range of cognitive

outcomes.

1

 National Assessment Governing Board. Mathematics Framework for the 1996 National Assessment of Educational

Progress. (Washington, DC: National Assessment Governing Board, 1994).

2

 National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. (Reston,

VA: NCTM, 1989).

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• continuing the move towards including more constructed-response

questions.

• creating “families” of questions that probe a student’s understanding of

mathematics vertically within a content strand or horizontally across

content strands.

• revising the number sense, properties, and operations and geometry and

spatial sense content strands to reflect the NCTM Standards emphasis

on developing and assessing students’ abilities to make sense of both

number and operation and spatial settings.

These refinements to the NAEP mathematics framework were made so that the

1996 assessment would: (1) more adequately reflect recent curricular emphases and

objectives and yet (2) maintain a connection with the 1990 and 1992 assessments to

measure trends in student performance. Prior to the 1996 assessment, investigations

were conducted to ensure that results from the assessment could be reported on the

existing NAEP mathematics scale. The conclusion drawn from these investigations was

that results from the 1990, 1992, and 1996 assessments could be reported on a common

scale and trends in mathematics performance since 1990 examined.

The Assessment Design

Each student in the state assessment program in mathematics received a booklet

containing a set of general background questions, a set of subject-specific background

questions, and a combination of cognitive questions grouped in sets called blocks. At

each grade level, the blocks of questions consisted of multiple-choice and

constructed-response questions. Two types of constructed-response questions were

included — short and extended constructed-response. Short constructed-response

questions required students to provide answers to computation problems or to describe

solutions in one or two sentences. Extended constructed-response questions required

students to provide longer answers (e.g., a description of possibilities, a more involved

computational analysis, or a description of a pattern and its implications). Students were

expected to adequately answer the short constructed-response questions in about 2 to 3

minutes and the extended constructed-response questions in approximately 5 minutes.

Short constructed-response questions which first appeared in the assessment in 1996

were graded to allow for partial credit (i.e., giving students credit for answers that are

partially correct) according to a unique scoring rubric developed for each

constructed-response question. Short constructed-response questions included in the

1990 and 1992 mathematics assessments were dichotomously scored (i.e., correct or

incorrect). The extended constructed-response questions included in the 1992 and 1996

assessments were scored allowing for partial credit.

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The blocks of questions contained several other features. Five to seven of the

blocks at each grade level allowed calculator usage. At grade 4, students were provided

four-function calculators, and at grade 8, students were provided scientific calculators.

Prior to the assessment, all students were trained in the use of these calculators. For

several blocks, students were given manipulatives (including geometric shapes,

three-dimensional models, and spinners). For two of the blocks at each grade level,

students were given rulers (at grade 4) or rulers and protractors (at grade 8) so the

student could answer questions dealing with measurements and draw specified geometric

shapes.

As part of the national assessment, other blocks of questions were developed for

each of the grade levels. Each grade level had two estimation blocks that employed a

paced-audiotape format to measure students’ estimation skills. Each grade level also

had two 30-minute theme blocks consisting of a mixture of multiple-choice and

constructed-response questions. All of the questions in these blocks related to some

aspect of a rich problem setting that served as a unifying theme for the entire block.

Neither the estimation nor the theme block component were included in the state

assessment program. Results for the estimation and theme blocks will be featured in

future reports on the NAEP 1996 mathematics assessment.

Of the 17 blocks in the national sample at the fourth grade and the 19 blocks in

the national sample at the eighth grade, 3 were carried forward from the 1990 assessment

and 5 were carried forward from the 1992 assessment to allow for the measurement of

trends across time. The remaining blocks of questions at each grade level contained new

questions developed for the 1996 assessment as specified by the updated framework.

The data in Table B.1 reflect the number of questions by type by grade level for

the 1990, 1992, and 1996 assessments. As mentioned earlier, the 1996 assessment

continued NAEP’s shift toward more constructed-response questions, including extended

constructed-response questions that required students to provide an answer and a

corresponding explanation.

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TABLE B.1

Distribution of Questions by Question Type

Grade 4 Grade 8 Grade 12

1990 1992 1996 1990 1992 1996 1990 1992 1996

Multiple-Choice 102 99 81 149 118 102 156 115 99 

Short Constructed-Response* 41 59 64 42 65 69 47 64 74 

Extended Constructed-Response** --- 5 13 --- 6 12 --- 6 11 

Total 143 163 158 191 189 183 203 185 184 

* Short constructed-response questions included in the 1990 and 1992 assessments were scored dichotomously. New

short constructed-response questions included in the 1996 assessment were scored to allow for partial credit.

** No extended constructed-response questions were included in the 1990 assessment.

Each booklet in the state assessment program included three sets of student

background questions. The first, consisting of general background questions, included

questions about race or ethnicity, mother’s and father’s level of education, reading

materials in the home, homework, attendance, and academic expectations. The second

set, consisting of mathematics background questions, included questions about

instructional activities, courses taken, use of specialized resources such as calculators in

mathematics classes, and views on the utility and value of the subject. (Students were

given 5 minutes to complete each set of questions, with the exception of the fourth

graders, who were given more time because the general background questions were read

aloud to them.) The third set of questions followed the cognitive question blocks and

contained five questions about students’ motivation to do well on the assessment, their

perception of the difficulty of the assessment, and their familiarity with the types of

cognitive questions included.

The blocks of cognitive and background questions were carefully balanced to

ensure that the blocks could be completed within the time provided to the students, using

information gathered from the field test. For more information on the design of the

assessment, the reader is referred to Appendix C.

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 APPENDIX C

Technical Appendix: The Design,

Implementation, and Analysis of the 1996

State Assessment Program in Mathematics

C.1 Overview

The purpose of this appendix is to provide technical information about the 1996

state assessment program in mathematics. It provides a description of the design for the

assessment and gives an overview of the steps involved in the implementation of the

program from the planning stages through to the analysis of the data.

This appendix is one of several documents that provide technical information

about the 1996 state assessment program. Those interested in more details are referred

to the forthcoming Technical Report of the NAEP 1996 State Assessment Program in

Mathematics. Theoretical information about the models and procedures used in NAEP

can be found in the special NAEP-related issue of the Journal of Educational Statistics

(Summer 1992/Volume 17, Number 2) as well as previous national technical reports.

Educational Testing Service (ETS) was awarded the cooperative agreement for the

1996 NAEP programs, including the state assessment program. ETS was responsible

for overall management of the programs as well as for development of the overall

design, the cognitive questions and questionnaires, data analysis, and reporting. National

Computer Systems (NCS) was a subcontractor to ETS on both the national and state

NAEP programs. NCS was responsible for printing, distribution, and receipt of all

assessment materials, and for scanning and professional scoring. All aspects of sampling

and field operations for both the national and state assessment programs were the

responsibility of Westat, Inc. NCES awarded a separate cooperative agreement to

Westat for these services for the national and state assessments.

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Organization of the Technical Appendix

This appendix provides a brief description of the design for the state assessment

program in mathematics and gives an overview of the steps involved in implementing

the program from the planning stages to the analysis of the data. (A more detailed

discussion of the technical aspects of the NAEP state assessment program can be found

in the forthcoming Technical Report of the NAEP 1996 State Assessment Program in

Mathematics.) The organization of this appendix is as follows:

• Section C.2 provides an overview of the design of the 1996 state

assessment program in mathematics.

• Section C.3 discusses the balanced incomplete block (BIB) spiral design

that was used to assign cognitive questions to assessment booklets and

assessment booklets to students.

• Section C.4 outlines the sampling design used for the 1996 state

assessment program.

• Section C.5 summarizes Westat’s field administration procedures.

• Section C.6 describes the flow of the data from their receipt at NCS

through data entry and professional scoring.

• Section C.7 summarizes the procedures used to weight the assessment

data and to obtain estimates of the sampling variability of subpopulation

estimates.

• Section C.8 describes the initial analyses performed to verify the quality

of the data.

• Section C.9 describes the item response theory scales and the overall

mathematics composite scale that were created for the final analyses of

the state assessment program data.

• Section C.10 provides an overview of the linking of the scaled results

from the state assessment program in mathematics to those from the

national assessment.

C.2 Design of the NAEP 1996 State Assessment Program in

Mathematics

The major aspects of the design for the state assessment program in mathematics

included the following:

• Participation at the jurisdiction level was voluntary.

• Fourth- and eighth-grade students from public and nonpublic schools

were assessed. Nonpublic schools included Catholic schools, other

religious schools, private schools, Department of Defense Domestic

Elementary and Secondary Schools (DDESS), and Bureau of Indian

Affairs schools. Separate representative samples of public and

nonpublic schools were selected in each participating jurisdiction and

students were randomly sampled within schools. The size of a

jurisdiction’s nonpublic school samples was proportional to the

percentage of students in that jurisdiction attending such schools.

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• The fourth- and eighth-grade mathematics assessment instruments used

for the state assessment program and the national assessment consisted

of 13 blocks of questions. Eight of these blocks were previously

administered as part of the 1990 and 1992 national and Trial State

Assessments. The type of questions — constructed-response or

multiple-choice — was determined by the nature of the task. In addition,

the constructed-response questions were of two types: short

constructed-response questions required students to provide answers to

computation problems or to describe solutions in one or two sentences,

while extended constructed-response questions required students to

provide longer responses when answering the question. Each student

was given 3 of the 13 blocks of questions.

• A complex form of matrix sampling called a balanced incomplete block

(BIB) spiraling design was used. With BIB spiraling, students in an

assessment session received different booklets, which provided for

greater mathematics content coverage than would have been possible

had every student been administered the identical set of questions,

without imposing an undue testing burden on the student.

• Background questionnaires given to the students, the students’

mathematics teachers, and the principals or other administrators

provided a variety of contextual information. The background

questionnaires for the state assessment program were identical to those

used in the national fourth- and eighth-grade assessments.

• The total assessment time for each student was approximately one hour

and 40 minutes. Each assessed student was assigned a mathematics

booklet that contained two 5-minute background questionnaires,

followed by 3 of the 13 blocks of mathematics questions requiring 15

minutes each, and a 3-minute motivation questionnaire. Twenty-six

different booklets were assembled.

• The assessments were scheduled to take place in the five-week period

between January 29 and March 4, 1996. One-fourth of the schools in

each jurisdiction were to be assessed each week throughout the first four

weeks; however, due to the severe weather throughout much of the

country, the fifth week was used for regular testing as well as for

makeup sessions.

• Data collection was, by law, the responsibility of each participating

jurisdiction. Security and uniform assessment administration were high

priorities. Extensive training of state assessment personnel was

conducted to assure that the assessment would be administered under

standard, uniform procedures. For jurisdictions that had participated in

previous NAEP state assessments, 25 percent of both public and

nonpublic school assessment sessions were monitored by the Westat

staff. For the jurisdictions new to NAEP, 50 percent of both public and

nonpublic school sessions were monitored.

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C.3 Assessment Instruments

The assembly of cognitive questions into booklets and their subsequent assignment

to assessed students was determined by a BIB design with spiraled administration. This

design is a variant of a matrix sampling design. The full set of mathematics questions

was divided into 13 unique blocks, each requiring 15 minutes for completion. Each

assessed student received a booklet containing 3 of the 13 blocks according to a design

that ensured that each block was administered to a representative sample of students

within each jurisdiction.

In addition to the student assessment booklets, three other instruments provided

data relating to the assessment — a mathematics teacher questionnaire, a school

characteristics and policies questionnaire, and an SD/LEP student questionnaire.

The student assessment booklets contained five sections and included both

cognitive and noncognitive questions. In addition to three 15-minute sections of

cognitive questions, each booklet included two 5-minute sets of general and mathematics

background questions designed to gather contextual information about students, their

experiences in mathematics, and their attitudes toward the subject, and one 3-minute

section of motivation questions designed to gather information about the student’s level

of motivation while taking the assessment.

The teacher questionnaire was administered to the mathematics teachers of the

fourth- and eighth-grade students participating in the assessment. The questionnaire

consisted of three sections and took approximately 20 minutes to complete. The first

section focused on the teacher’s general background and experience; the second, on the

teacher’s background related to mathematics; and the third, on classroom information

about mathematics instruction.

The school characteristics and policies questionnaire was given to the principal

or other administrator in each participating school and took about 20 minutes to

complete. The questions asked about the principal’s background and experience, school

policies, programs, and facilities, and the demographic composition and background of

the students and teachers.

The SD/LEP student questionnaire was completed by the staff member most

familiar with any student selected for the assessment who was classified in either of two

ways: students with disabilities (SD) had an Individualized Education Plan (IEP) of

equivalent special education plan (for reasons other than being gifted and talented);

students with limited English proficiency were classified as LEP students. The

questionnaire took approximately three minutes to complete and asked about the student

and the special programs in which the student participated. It was completed for all

selected SD or LEP students regardless of whether or not they participated in the

assessment. Selected SD or LEP students participated in the assessment if they were

determined by the school to be able to participate, considering the terms of their IEP

and accommodations provided by the school or by NAEP.

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C.4 The Sampling Design

The sampling design for NAEP is complex, in order to minimize burden on

schools and students while maximizing the utility of the data; for further details see the

forthcoming Technical Report for the NAEP 1996 State Assessment Program in

Mathematics. The target populations for the state assessment program in mathematics

consisted of fourth- and eighth-grade students enrolled in either public or nonpublic

schools. The representative samples of public school fourth and eighth graders assessed

in the state assessment program came from about 100 schools (per grade) in most

jurisdictions. However, if a jurisdiction had fewer than 100 public schools with a

particular grade, all or almost all schools were asked to participate. If a jurisdiction had

smaller numbers of students in each school than expected, more than 100 schools were

selected for participation. The nonpublic school samples differed in size across the

jurisdictions, with the number of schools selected proportional to the nonpublic school

enrollment within each jurisdiction. Typically, about 20 to 25 nonpublic schools (per

grade) were included for each jurisdiction. The school sample in each jurisdiction was

designed to produce aggregate estimates for the jurisdiction and for selected

subpopulations (depending upon the size and distribution of the various subpopulations

within the jurisdiction) and also to enable comparisons to be made, at the jurisdiction

level, between administration of assessment tasks with monitoring and without

monitoring. The public schools were stratified by urbanization, percentage of Black and

Hispanic students enrolled, and median household income within the ZIP code area of

the school. The nonpublic schools were stratified by type of control (Catholic,

private/other religious, other nonpublic), metropolitan status, and enrollment size per

grade.

The national and regional results presented in this report are based on nationally

representative samples of fourth- and eighth-grade students. The samples were selected

using a complex multistage sampling design involving the sampling of students from

selected schools within selected geographic areas across the country. The sample design

had the following stages:

(1) selection of geographic areas (a county, group of counties, or metropolitan

 statistical area)

(2) selection of schools (public and nonpublic) within the selected areas

(3) selection of students within selected schools

Each selected school that participated in the assessment, and each student assessed,

represent a portion of the population of interest. To make valid inferences from student

samples to the respective populations from which they were drawn, sampling weights

are needed. Discussions of sampling weights and how they are used in analyses are

presented in sections C.7 and C.8.

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The state results provided in this report are based on state-level samples of fourthand eighth-grade students. The samples of both public and nonpublic school students

were selected based on a two-stage sample design that entailed selecting students within

schools. The first-stage samples of schools were selected with a probability proportional

to the fourth- or eighth-grade enrollment in the schools. Special procedures were used

for jurisdictions with many small schools and for jurisdictions with a small number of

schools. As with the national samples, the state samples were weighted to allow for

valid inferences about the populations of interest.

The results presented for a particular jurisdiction are based on the representative

sample of students who participated in the 1996 state assessment program. The results

for the nation and regions of the country are based on the nationally and regionally

representative samples of students who were assessed as part of the national NAEP

program. Using the national and regional results from the 1996 national assessment

was necessary because of the voluntary nature of the state assessment program. Because

not every state participated in the program, the aggregated data across states did not

necessarily provide representative national or regional results.

In most jurisdictions, up to 30 students were selected from each school, with the

aim of providing an initial sample size of approximately 3,000 public school students

per jurisdiction per grade. The student sample size of 30 for each school was chosen

to ensure that at least 2,000 public school students (per grade) participated from each

jurisdiction, allowing for school nonresponse, exclusion of students, inaccuracies in the

measures of enrollment, and student absenteeism from the assessment. In jurisdictions

with fewer schools, larger numbers of students per school were often required to ensure

initial samples of roughly 3,000 students. In certain jurisdictions, all eligible fourth or

eighth graders were targeted for assessment. Jurisdictions were given the option to

reduce the expected student sample size in order to reduce testing burden and the number

of multiple-testing sessions for participating schools. At grade 4, two jurisdictions

(Delaware and Guam) and at grade 8, four jurisdictions (Alaska, Delaware, Hawaii, and

Rhode Island) elected to exercise this option. Using this option can involve

compromises such as higher standard errors and accompanying loss of precision.

In order to provide for wider inclusion of students with disabilities and limited

English proficiency, the 1996 state assessments in mathematics involved dividing the

sample of students at each grade level into two subsamples, referred to as S1 and S2.

S1 provided continuity with the 1992 mathematics assessment and thus allowed for the

reporting of performance over time by using the same exclusion criteria for students

with disabilities and limited English proficiency as was used in that assessment. S2

provided for wider inclusion of students with disabilities and limited English proficiency

by incorporating new exclusion rules. For further discussion, see the NAEP 1996

Mathematics Report Card. The 1996 national assessment in mathematics involved an

additional subsample, S3, in which accommodations were provided for certain students

with disabilities or limited English proficiency, again in order to make NAEP more

inclusive.

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For both the national and state mathematics assessments, scaling and analysis

procedures (discussed in sections C.8 to C.10) were applied to a combination of students

from S1 and S2. Specifically, all assessed students from S1 were combined with those

students from S2 who were not identified as SD or LEP. This combination of segments

of the S1 and S2 subsamples provided for maximizing the use of available data while

allowing for comparisons to the student population in the national sample. This

combination, referred to as the “reporting sample,” was the sample used in linking the

state assessment to the national assessment (see Section C.10).

Additional analyses will be conducted on the national samples in order to study

the effects of changing the exclusion rules and the presence of accommodations.

Preliminary discussion can be found in the NAEP 1996 Mathematics Report Card and

more detailed discussion will follow in future NAEP publications.

C.5 Field Administration

The administration of the 1996 program required collaboration between staff in

the participating jurisdictions and schools and the NAEP contractors, especially Westat,

the field administration contractor.

Each jurisdiction volunteering to participate in the 1996 state assessment program

was asked to appoint a state coordinator as liaison between NAEP staff and the

participating schools. In addition, Westat hired and trained a supervisor for each

jurisdiction and six field managers, each of whom was assigned to work with groups

of jurisdictions. The state supervisors were responsible for working with the state

coordinators, overseeing assessment activities, training school district personnel to

administer the assessment, and coordinating the quality-control monitoring efforts. Each

field manager was responsible for working with the state coordinators of seven to eight

jurisdictions and for the supervision of the state supervisors assigned to those

jurisdictions. An assessment administrator was responsible for preparing for and

conducting the assessment session in one or more schools. These individuals were

usually school or district staff and were trained by Westat. Westat also hired and trained

three to five quality control monitors in each jurisdiction. For jurisdictions that had

previously participated in the state assessment program, 25 percent of the public and

nonpublic school sessions were monitored. For jurisdictions new to the program, 50

percent of all sessions were monitored. The assessment sessions were conducted during

a five-week period beginning in late January 1996.

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C.6 Materials Processing, Professional Scoring, and Database

Creation

Upon completion of each assessment session, school personnel shipped the

assessment booklets and forms to NCS for professional scoring, entry into computer

files, and checking. The files were then sent to ETS for creation of the database.

After NCS received all appropriate materials from a school, they were forwarded

to the professional scoring area where the responses to the constructed-response question

were evaluated by trained staff using guidelines prepared by ETS. Each

constructed-response question had a unique scoring guide that defined the criteria to be

used in evaluating students’ responses. The extended constructed-response questions

were evaluated with four- or five-level rubrics, and the short constructed-response

questions first used in 1996 were rated according to three-level rubrics that permit partial

credit to be given. Short constructed-response questions used previously were scored

dichotomously (i.e., correct or incorrect).

For the national mathematics assessment and the state assessment program in

mathematics, over 4.8 million constructed responses were scored. This figure includes

rescoring to monitor inter-rater reliability and trend reliability. In other words, scoring

reliability was calculated both within year (1996) and across years (1990, 1992, and

1996). The overall within-year percentages of agreement for the 1996 national

within-year reliability samples were 96 percent at grade 4 and 96 percent at grade 8.

The percentages of agreement across the assessment years for the national inter-year

reliability samples were 96 percent (1990 to 1996) and 94 percent (1992 to 1996) at

grade 4 and 95 percent (1990 to 1996) and 94 percent (1992 to 1996) at grade 8.

Data transcription and editing procedures were used to generate the disk and tape

files containing various assessment information, including the sampling weights required

to make valid statistical inferences about the population from which the state assessment

program sample was drawn. Prior to analysis, the data from these files underwent a

quality control check at ETS. The files were then merged into a comprehensive,

integrated database.

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C.7 Weighting and Variance Estimation

A complex sample design was used to select the students to be assessed in each

of the participating jurisdictions. The properties of a sample from a complex design are

very different from those of a simple random sample in which every student in the target

population has an equal chance of selection and in which the observations from different

sampled students can be considered to be statistically independent of one another. The

properties of the sample from the complex state assessment program design were taken

into account in the analysis of the assessment data.

One way that the properties of the sample design were addressed was by using

sampling weights to account for the fact that the probabilities of selection were not

identical for all students. These weights also included adjustments for school and

student nonresponse. All population and subpopulation characteristics based on the state

assessment program data used sampling weights in their estimation.

In addition to deriving appropriate estimates of population characteristics, it is

essential to obtain appropriate measures of the degree of uncertainty of those statistics.

One component of uncertainty results from sampling variability, which is a measure of

the dependence of the results on the particular sample of students actually assessed.

Because of the effects of cluster selection (schools are selected first, then students are

selected within those schools), observations made on different students cannot be

assumed to be independent of each other (and, in fact, are generally positively

correlated). As a result, classical variance estimation formulas will produce incorrect

results. Instead, a jackknife variance estimation procedure that takes the characteristics

of the sample into account was used for all analyses.

Jackknife variance estimation provides a reasonable measure of uncertainty for any

statistic based on values observed without error. Statistics such as the percentage of

students correctly answering a given question meet this requirement, but other statistics

based on estimates of student mathematics performance, such as the average

mathematics scale score of a subpopulation, do not. Because each student typically

responds to relatively few questions from a particular content strand (e.g., Algebra and

Functions or Geometry and Spatial Sense) there exists a nontrivial amount of

imprecision in the measurement of the scale score of a given student. This imprecision

adds an additional component of variability to statistics based on estimates of individual

scale scores.

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C.8 Preliminary Data Analysis

After the computer files of student responses were received from NCS and merged

into an integrated database, all cognitive and noncognitive questions were subjected to

an extensive item analysis. For each question, this analysis yielded the number of

respondents, the percentage of responses in each category, the percentage who omitted

the question, the percentage who did not reach the question, and the correlation between

the question score and the block score. In addition, the item analysis program provided

summary statistics for each block, including a reliability (internal consistency)

coefficient. These analyses were used to check the scoring of the questions, to verify

the appropriateness of the difficulty level of the questions, and to check for speededness.

The results were reviewed by knowledgeable project staff in search of aberrations that

might signal unusual results or errors in the database.

The question and block-level analyses were done using rescaled versions of the

final sampling weights provided by Westat (see Section C.7). The rescaling was carried

out within each jurisdiction. The sum of the sampling weights for the public school

students within each jurisdiction was constrained to be equal. The same transformation

was then applied to the weights of the nonpublic school students in that jurisdiction.

The sum of the weights for each of the DoDEA samples (i.e., DDESS and DoDDS) was

constrained to be equal to the same value as the public school students in other

jurisdictions. Use of rescaled weights does nothing to alter the value of statistics

calculated separately within each jurisdiction. However, for statistics obtained from

samples that combine students from different jurisdictions, use of the rescaled weights

results in a roughly equal contribution of each jurisdiction's data to the final value of the

estimate. Equal contribution of each jurisdiction's data to the results of the item response

theory (IRT) scaling was viewed as a desirable outcome. The original final sampling

weights provided by Westat were used in reporting.

Additional analyses comparing the data from the monitored sessions with those

from the unmonitored sessions were conducted to determine the comparability of the

assessment data from the two types of administrations. Differential item functioning

(DIF) analyses were carried out using the national assessment data. DIF analyses

identify questions that were differentially difficult for various subgroups, affording the

opportunity to reexamine such questions with respect to their fairness and their

appropriateness for inclusion in the scaling process.

192 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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C.9 Scaling the Assessment Questions

The primary analysis and reporting of the results from the state assessment

program used item response theory (IRT) scale-score models. Scaling models quantify

a respondent’s tendency to provide correct answers to the domain of questions

contributing to a scale as a function of a parameter called performance, estimated by a

scale score. The scale scores can be viewed as a summary measure of performance

across the domain of questions that make up the scale. Three distinct IRT models were

used for scaling: 1) 3-parameter logistic models for multiple-choice questions; 2)

2-parameter logistic models for short constructed-response questions that were scored

correct or incorrect; and 3) generalized partial credit models for short and extended

constructed-response questions that were scored on a multipoint (i.e., greater than two

levels) scale.

Five distinct scales were created for the state assessment program in mathematics

to summarize fourth- and eighth-grade students’ abilities according to the five defined

content strands (Number Sense, Properties, and Operations; Measurement; Geometry and

Spatial Sense; Data Analysis, Statistics, and Probability; and Algebra and Functions).

These scales were defined identically to, but separately from, those used for the scaling

of the national NAEP fourth- and eighth-grade mathematics data. Although the

questions comprising each scale were identical to those used in the national assessment

program, the item parameters for the state assessment program scales were estimated

from combined public school data from the jurisdictions participating in the state

assessment program.1 Item parameter estimation was carried out on an item calibration

subsample. The calibration subsample consisted of an approximately 25 percent sample

of all available public school data. To ensure equal representation in the scaling process,

each jurisdiction contributed the same number of students to the item calibration sample.

Within each jurisdiction, 50 percent of the calibration sample was taken from monitored

administrations and the other 50 percent came from unmonitored administrations.

The fit of the IRT model to the observed data was examined within each scale

by comparing the estimates of the empirical item characteristic functions with the

theoretic curves. For correct-incorrect questions, nonmodel-based estimates of the

expected proportions of correct responses to each question for students with various

levels of scale proficiency were compared with the fitted item response curve; for the

short and extended partial-credit constructed-response questions, the comparisons were

based on the expected proportions of students with various levels of scale proficiency

who achieved each score level. In general, the question-level results were well fit by

the scaling models.

1

 Schools from the DoDEA jurisdictions were not included in the item calibration sample.

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Using the item parameter estimates, estimates of various population statistics were

obtained for each jurisdiction. The NAEP methods use random draws (“plausible

values”) from estimated proficiency distributions for each student to compute population

statistics. Plausible values are not optimal estimates of individual student proficiencies;

instead, they serve as intermediate values to be used in estimating population

characteristics. Under the assumptions of the scaling models, these population estimates

will be consistent, in the sense that the estimates approach the model-based population

values as the sample size increases, which would not be the case for population estimates

obtained by aggregating optimal estimates of individual performance.

In addition to the plausible values for each scale, a composite of the five content

strand scales was created as a measure of overall mathematics proficiency. This

composite was a weighted average of the five mathematics scales in which the weights

were proportional to the relative importance assigned to each content strand in the

mathematics framework. The definition of the composite for the state assessment

program was identical to that used for the national fourth- and eighth-grade mathematics

assessments.

C.10 Linking the State Results to the National Results

A major purpose of the state assessment program was to allow each participating

jurisdiction to compare its 1996 results with those for the nation as a whole and with

those for the region of the country in which that jurisdiction is located. For meaningful

comparisons to be made between each jurisdiction and the relevant national sample,

results from these two assessments had to be expressed in terms of a similar system of

scale units.

The results from the state assessment program were linked to those from the

national assessment through linking functions determined by comparing the results for

the aggregate of all students assessed in the state assessment program with the results

for students of the matching grade within the National Linking Sample of the national

NAEP. The National Linking Sample of the national NAEP for a given grade is a

representative sample of the population of all grade-eligible public school students

within the aggregate of 45 participating states and the District of Columbia. Guam and

the two Department of Defense Education Activity (DoDEA) jurisdictions were not

included in the aggregate. Specifically, the fourth- and eighth-grade National Linking

Samples consist of all fourth- and eighth-grade students in public schools in the states

and the District of Columbia who were assessed in the national cross-sectional

mathematics assessment.

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For each grade, a linear equating within each scale was used to link the results

of the state assessment program to the national assessment. For each scale, the adequacy

of the linear equating was evaluated by comparing the distribution of mathematics scale

scores based on the aggregation of all assessed students at each grade from the

participating states and the District of Columbia with the equivalent distribution based

on the students in the National Linking Sample. In the estimation of these distributions,

the students were weighted to represent the target population of public school students

in the specified grade in the aggregation of the states and the District of Columbia. If

a linear equating were adequate, the distribution for the aggregate of states and the

District of Columbia and that for the National Linking Sample will have, to a close

approximation, the same shape in terms of the skewness, kurtosis, and higher moments

of the distributions. The only differences in the distributions allowed by linear equating

are in the means and variances. Generally, this has been found to be the case.

Each mathematics content-strand scale was linked by matching the mean and

standard deviation of the scale scores across all students in the state assessment

(excluding Guam and the two DoDEA jurisdictions) to the corresponding scale mean

and standard deviation across all students in the National Linking Sample.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 195
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196 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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 APPENDIX D

Setting the Achievement Levels

Setting achievement levels is a test-centered method for setting standards on the

NAEP assessment that identifies what students should know and should be able to do.

The method depends on securing and summarizing a set of judgmental ratings of

expectations for student educational performance on specific questions comprising the

NAEP mathematics assessment. The NAEP mathematics scale is a numerical index of

students’ performance in mathematics ranging from 0 to 500. The three achievement

levels — Basic, Proficient, and Advanced — are mapped onto the scale for each grade

level assessed.

The NAEP mathematics achievement levels were set following the 1990

assessment and further refined following the 1992 assessment. In developing the

threshold values for the levels, a broadly constituted panel of judges — including

teachers (50%), non-teacher educators (20%), and the general public

(noneducators)1 (30%) — rated a grade-specific item pool using the policy definitions

of the National Assessment Governing Board (NAGB) for Basic, Proficient, and

Advanced. The policy definitions were operationalized by the judges in terms of specific

mathematical skills, knowledge, and behaviors that were judged to be appropriate

expectations for students in each grade and were in accordance with the current

mathematics assessment framework. The policy definitions are as follows:

Basic

This level denotes partial mastery of the prerequisite knowledge and

skills that are fundamental for proficient work at each grade.

Proficient

This level represents solid academic performance for each grade

assessed. Students reaching this level have demonstrated competency

over challenging subject matter and are well prepared for the next level

of schooling.

Advanced

This higher level signifies superior performance beyond proficient

grade-level mastery at each grade.

1

 Noneducators represented business, labor, government service, parents, and the general public.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 197
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The judges’ operationalized definitions were incorporated into lists of descriptors

that represent what borderline students should be able to do at each of the levels defined

by policy. The purpose of having panelists develop their own operational definitions

of the achievement levels was to ensure that all panelists would have a common

understanding of borderline performances and a common set of content-based referents

to use during the item-rating process.

The judges (24 at grade 4 and 22 at grade 8) each rated half of the questions in

the NAEP pool in terms of the expected probability that a student at a borderline

achievement level would answer the question correctly, based on the judges’

operationalization of the policy definitions and the factors that influence question

difficulty. To assist the judges in generating consistently scaled ratings, the rating

process was repeated twice, with feedback. Information on consistency among different

judges and on the difficulty of each question2 was fed back into the first repetition

(round 2), while information on consistency within each judge’s set of ratings was fed

back into the second repetition (round 3). The third round of ratings permitted the

judges to discuss their ratings among themselves to resolve problematic ratings. The

mean final rating of the judges aggregated across questions yielded the threshold values

in the percent correct metric. These cut scores were then mapped onto the NAEP scale

(which is defined and scored using item response theory, rather than percent correct) to

obtain the scale scores for the achievement levels.3 The judges’ ratings, in both metrics,

and their associated errors of measurement are shown below. NAGB accepted the

panel’s achievement levels and, for reporting purposes, set final cutpoints one standard

error (a measure of consistency among the judges’ ratings) below the mean levels.

Mean Percent Standard

Correct Error of

Grade Level (Round 3) Scale Score* Scale Score**

 4 Basic 39 214 1.9

 4 Proficient 65 249 4.1

 4 Advanced 84 282 4.0

 8 Basic 48 262 2.4

 8 Proficient 71 299 5.7

 8 Advanced 87 333 4.8

* Scale score is derived from a weighted average of the mean percent correct for multiple-choice and short

constructed-response questions after both were mapped onto the NAEP scale.

** The standard error of the scale score is estimated from the difference in mean scale scores for the two equivalent

subgroups of judges.

FIGURE D.1

Cutpoints for Achievement Levels at Grades 4 and 8

2

 Item difficulty estimates were based on a preliminary, partial set of responses to the national assessment.

3

 See Appendix A for a discussion of the technical errors that resulted in the reanalysis and rereporting of 1990 and 1992

mathematics achievement level results.

198 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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After the ratings were completed, the judges for each grade level reviewed the

operationalized descriptions developed by the judges of the other grade levels as well

as their own descriptions and defined achievement level descriptions that were generally

acceptable to all three grade-group judges. However, the descriptions varied in format,

sharpness of language, and degree of specificity of the statements. Therefore, another

panel at a subsequent validation meeting improved the wording and modified the

language of the achievement level descriptions to reflect more closely the terminology

of the National Council of Teachers of Mathematics Curriculum and Evaluation

Standards for School Mathematics.

4 The achievement level descriptions, though based

on the 1992 NAEP pool, apply to the current assessment and will not change from

assessment to assessment (that is, until the framework changes).

Figure 3.1 in Chapter 3 provides the detailed descriptions of the three achievement

levels for grades 4 and 8. In addition, exemplar questions are presented to illustrate each

level.

4

 National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. (Reston,

VA: NCTM, 1989).

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200 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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 APPENDIX E

Teacher Preparation

Teachers are key to improving mathematics learning, and so it is important to

examine their background and professional development. Fourth- and eighth-grade

mathematics teachers completed questionnaires concerning their background and

training, including their experience, certification, undergraduate and graduate course

work in mathematics, and involvement in pre-service education.

Consistent with procedures used throughout this report, the student was the unit

of analysis. That is, the mathematics teachers’ responses were linked to their students,

and the data reported are the percentages of students taught by teachers with particular

characteristics.

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TABLE E.1A — GRADE 4

Public School Teachers’ Reports on Their Highest Level of

Education

What is the highest academic degree

you hold?

Guam Nation

Percentage of Students

Bachelor’s degree 1992 67 ( 1.3) 53 ( 2.4) 

1996 77 ( 1.0)> 60 ( 2.8) 

Master’s degree 1992 31 ( 1.2) 41 ( 2.4) 

1996 23 ( 1.0)< 32 ( 2.3)< 

Education specialist’s or

professional diploma 1992 2 ( 0.5) 6 ( 1.2) 

1996 0 ( 0.1) 8 ( 1.2) 

Doctorate or professional degree 1992 0 ( ) 0 ( 0.3) 

1996 0 (** **) 0 ( 0.0) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level.   Standard error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

TABLE E.1B — GRADE 8

Public School Teachers’ Reports on Their Highest Level of

Education

What is the highest academic degree

you hold?

Guam Nation

Percentage of Students

Bachelor’s degree 1990 80 ( 0.6) 56 ( 4.2) 

1992 79 ( 0.9) 53 ( 2.9) 

1996 81 ( 1.5) 59 ( 3.4) 

Master’s degree 1990 16 ( 0.5) 35 ( 4.3) 

1992 21 ( 0.9)» 41 ( 2.7) 

1996 18 ( 1.5) 35 ( 3.2) 

Education specialist’s or

professional diploma 1990 4 ( 0.3) 6 ( 1.8) 

1992 0 (** **) 6 ( 1.3) 

1996 0 ( ) 5 ( 1.2) 

Doctorate or professional degree 1990 0 (** **) 2 ( 1.4) 

1992 0 ( ) 0 ( 0.3) 

1996 0 (** **) 1 ( 0.4) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

» («) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1990

at about the 95 percent confidence level. If the notation > (<) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1992 at about the 95 percent confidence level.   Standard error

estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

202 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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TABLE E.2 — GRADES 4 AND 8

Public School Teachers’ Reports on Their Undergraduate

Majors

What were your undergraduate major

fields of study?

Guam Nation

Percentage of Students

GRADE 4

Education 91 ( 0.8) 88 ( 1.5) 

Mathematics 5 ( 0.7) 7 ( 1.4) 

Mathematics Education 6 ( 0.7) 6 ( 1.2) 

Special Education 11 ( 0.8) 8 ( 1.5) 

ESL 3 ( 0.7) 3 ( 0.9) 

Other 28 ( 1.4) 37 ( 2.5) 

GRADE 8

Education 78 ( 1.3) 59 ( 3.2) 

Mathematics 34 ( 1.3) 47 ( 3.0) 

Mathematics Education 0 (** **) 23 ( 2.9) 

Special Education 2 ( 0.6) 1 ( 0.4) 

ESL 0 ( ) 0 ( 0.2) 

Other 40 ( 1.3) 37 ( 3.3) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). ** ** Standard

error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

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TABLE E.3 — GRADES 4 AND 8

Public School Teachers’ Reports on Their Graduate Majors

What were your graduate major fields

of study?

Guam Nation

Percentage of Students

GRADE 4

Education 56 ( 1.3) 59 ( 2.7) 

Mathematics 3 ( 0.5) 4 ( 1.0) 

Mathematics Education 2 ( 0.6) 5 ( 1.3) 

Special Education 7 ( 0.6) 5 ( 1.2) 

Bilingual 0 ( 0.0) 2 ( 0.6) 

Admin./Supervision/Curric. 7 ( 0.7) 15 ( 1.8) 

Counseling 3 ( 0.4) 2 ( 0.7) 

Other 21 ( 1.1) 16 ( 1.7) 

No graduate study 31 ( 1.3) 31 ( 2.4) 

GRADE 8

Education 74 ( 1.8) 47 ( 2.9) 

Mathematics 5 ( 0.8) 18 ( 2.4) 

Mathematics Education 24 ( 1.5) 19 ( 2.8) 

Special Education 1 ( 0.5) 1 ( 0.3) 

Bilingual 0 ( ) 0 (** **)

Admin./Supervision/Curric. 13 ( 1.0) 19 ( 3.2) 

Counseling 5 ( 1.0) 3 ( 1.0) 

Other 22 ( 1.4) 18 ( 2.6) 

No graduate study 18 ( 1.1) 24 ( 2.5) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). **** Standard

error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

204 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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TABLE E.4 — GRADES 4 AND 8

Public School Teachers’ Reports on Their Teaching

Certification

What type of teaching certification do

you have in this state in your main

assignment field?

Guam Nation

Percentage of Students

GRADE 4

None, Accreditation other than state,

Temporary, or Probationary 9 ( 1.3) 5 ( 1.0) 

Regular 74 ( 1.3) 79 ( 2.0) 

Advanced 17 ( 0.9) 16 ( 1.8) 

GRADE 8

None, Accreditation other than state,

Temporary, or Probationary 16 ( 1.1) 8 ( 1.4) 

Regular 59 ( 1.6) 79 ( 2.6) 

Advanced 25 ( 1.4) 14 ( 2.4) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

TABLE E.5A — GRADE 4

Public School Teachers’ Reports on Years Teaching

Experience

Counting this year, how many years in

total have you taught . . . 

Guam Nation

Percentage of Students

At either the elementary or

 secondary level

 2 years or less 1992 11 ( 1.0) 8 ( 1.1)

 1996 20 ( 1.0)> 8 ( 1.3)

 3-5 years 1992 13 ( 0.7) 13 ( 1.7)

 1996 20 ( 1.4)> 14 ( 1.6)

 6-10 years 1992 12 ( 0.8) 14 ( 1.6)

 1996 13 ( 1.1) 23 ( 2.0)>

 11-24 years 1992 53 ( 1.3) 46 ( 2.4)

 1996 36 ( 1.4)< 35 ( 2.6)<

 25 years or more 1992 11 ( 0.6) 19 ( 1.6)

 1996 11 ( 0.8) 20 ( 2.5)

Mathematics*

 2 years or less 1996 20 ( 1.0) 11 ( 1.6)

 3-5 years 1996 20 ( 1.2) 14 ( 1.9)

 6-10 years 1996 13 ( 1.1) 26 ( 2.0)

 11-24 years 1996 37 ( 1.4) 33 ( 2.8)

 25 years or more 1996 9 ( 0.6) 16 ( 2.1)

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level. * This question was not asked of fourth-grade teachers in 1992.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

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TABLE E.5B — GRADE 8

Public School Teachers’ Reports on Years Teaching

Experience

Counting this year, how many years in

total have you taught . . . 

Guam Nation

Percentage of Students

At either the elementary or

 secondary level

 2 years or less 1992 17 ( 0.9) 9 ( 1.6)

 1996 43 ( 1.4)> 8 ( 1.7)

 3-5 years 1992 10 ( 0.7) 11 ( 1.4)

 1996 15 ( 1.1)> 11 ( 2.2)

 6-10 years 1992 10 ( 0.9) 15 ( 1.4)

 1996 5 ( 0.7)< 19 ( 2.5)

 11-24 years 1992 53 ( 1.0) 48 ( 2.1)

 1996 21 ( 1.2)< 37 ( 3.9)

 25 years or more 1992 10 ( 0.5) 17 ( 1.7)

 1996 16 ( 1.3)> 25 ( 3.1)

Mathematics

 2 years or less 1992 27 ( 1.2) 11 ( 1.6)

 1996 43 ( 1.4)> 11 ( 1.8)

 3-5 years 1992 5 ( 0.7) 14 ( 1.7)

 1996 15 ( 1.1)> 14 ( 2.1)

 6-10 years 1992 10 ( 0.8) 18 ( 1.8)

 1996 6 ( 0.8)< 21 ( 2.7)

 11-24 years 1992 48 ( 1.1) 44 ( 2.4)

 1996 18 ( 1.2)< 37 ( 3.8)

 25 years or more 1992 10 ( 0.5) 13 ( 1.8)

 1996 18 ( 1.2)> 17 ( 2.8)

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

206 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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TABLE E.6 — GRADES 4 AND 8

Public School Teachers’ Reports on Courses in Mathematics

or Mathematics Education

During the last two years, how many

college or university courses have you

taken in mathematics or mathematics

education?

Guam Nation

Percentage of Students

GRADE 4

None 74 ( 1.2) 78 ( 2.4) 

One 12 ( 0.9) 14 ( 1.8) 

Two 8 ( 0.7) 5 ( 1.1) 

Three or more 5 ( 0.5) 4 ( 1.2) 

GRADE 8

None 30 ( 1.1) 74 ( 3.1) 

One 6 ( 0.7) 10 ( 2.2) 

Two 5 ( 0.8) 5 ( 1.3) 

Three or more 59 ( 1.2) 11 ( 2.0) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

TABLE E.7 — GRADES 4 AND 8

Public School Teachers’ Reports on Coursework in the Use

of Technology

During the past five years, have you taken

courses or participated in professional

development activities in the use of

technology such as computers?

Guam Nation

Percentage of Students

GRADE 4

Yes 50 ( 1.5) 83 ( 1.8) 

GRADE 8

Yes 50 ( 1.2) 76 ( 2.9) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details).

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

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TABLE E.8A — GRADE 4

Public School Teachers’ Reports on Studies of Mathematics

Instruction Techniques

Have you ever studied any of the following, either

in college or university courses or in professional

development workshops or seminars?

Guam Nation

Percentage of Students

Estimation 1992 80 ( 1.0) 82 ( 1.9) 

1996 74 ( 1.1)< 77 ( 1.7) 

Problem solving in mathematics 1992 88 ( 1.1) 92 ( 1.3) 

1996 85 ( 1.0) 90 ( 1.6) 

Use of manipulatives in mathematics instruction 1992 88 ( 1.0) 93 ( 1.0) 

1996 92 ( 0.8)> 91 ( 1.2) 

Use of calculators in mathematics instruction 1992 52 ( 1.1) 60 ( 2.7) 

1996 57 ( 1.5)> 72 ( 2.1)> 

Understanding students’ thinking about math 1992 65 ( 1.3) 72 ( 2.1) 

1996 67 ( 1.3) 71 ( 1.9) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

TABLE E.8B — GRADE 8

Public School Teachers’ Reports on Studies of Mathematics

Instruction Techniques

Have you ever studied any of the following, either

in college or university courses or in professional

development workshops or seminars?

Guam Nation

Percentage of Students

Estimation 1992 57 ( 1.4) 79 ( 2.2) 

1996 90 ( 0.9)> 77 ( 2.4) 

Problem solving in mathematics 1992 80 ( 1.1) 94 ( 1.2) 

1996 96 ( 0.6)> 94 ( 1.9) 

Use of manipulatives in mathematics instruction 1992 90 ( 0.5) 90 ( 1.6) 

1996 84 ( 1.5)< 89 ( 2.3) 

Use of calculators in mathematics instruction 1992 67 ( 0.7) 77 ( 2.7) 

1996 88 ( 1.1)> 80 ( 2.7) 

Understanding students’ thinking about math 1992 42 ( 1.4) 66 ( 2.6) 

1996 80 ( 1.5)> 72 ( 2.6) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

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TABLE E.9A — GRADE 4

Public School Teachers’ Reports on Studies of Gender and

Cultural Issues

Have you ever studied any of the

following, either in college or

university courses or in professional

development workshops or seminars?

Guam Nation

Percentage of Students

Gender issues in the teaching

of mathematics 1992 44 ( 1.2) 33 ( 2.4) 

1996 36 ( 1.6)< 46 ( 2.5)> 

Teaching students from different

cultural backgrounds 1992 71 ( 1.0) 43 ( 2.5) 

1996 69 ( 1.2) 50 ( 2.7) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

TABLE E.9B — GRADE 8

Public School Teachers’ Reports on Studies of Gender and

Cultural Issues

Have you ever studied any of the

following, either in college or

university courses or in professional

development workshops or seminars?

Guam Nation

Percentage of Students

Gender issues in the teaching

of mathematics 1992 25 ( 1.1) 42 ( 2.7) 

1996 58 ( 1.7)> 48 ( 3.4) 

Teaching students from different

cultural backgrounds 1992 53 ( 1.0) 51 ( 2.4) 

1996 82 ( 1.2)> 52 ( 3.0) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). If the notation

> (<) appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992

at about the 95 percent confidence level.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1992 and

1996 Mathematics Assessments.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 209
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TABLE E.10 — GRADES 4 AND 8

Public School Teachers’ Reports on Professional

Development

During the last year, how much time in

total have you spent in professional

development workshops or seminars in

mathematics or mathematics education?

Guam Nation

Percentage of Students

GRADE 4

None 39 ( 1.4) 15 ( 2.1) 

Less than 6 hours 30 ( 1.6) 29 ( 2.2) 

6-15 hours 20 ( 1.4) 28 ( 2.4) 

16-35 hours 6 ( 0.7) 15 ( 2.0) 

More than 35 hours 4 ( 0.4) 13 ( 1.6) 

GRADE 8

None 68 ( 1.4) 5 ( 1.2) 

Less than 6 hours 24 ( 1.3) 19 ( 3.1) 

6-15 hours 2 ( 0.5) 28 ( 2.7) 

16-35 hours 0 (****) 21 ( 2.6) 

More than 35 hours 5 ( 0.8) 27 ( 2.9) 

The standard errors of the statistics appear in parentheses. It can be said with about 95 percent confidence that, for each

population of interest, the value for the entire population is within ± 2 standard errors of the estimate for the sample. In

comparing two estimates, one must use the standard error of the difference (see Appendix A for details). **** Standard

error estimates cannot be accurately determined.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

210 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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 APPENDIX F

Discussion of the Grade 8 Asian/Pacific

Islander Sample

As noted in Chapters 2 and 4, national scale score and achievement level results

for eighth-grade Asian/Pacific Islander students are not included in the main body of this

report. The decision to present these results in a separate appendix was made following

a thorough investigation by the current NAEP grantees (Westat and ETS)1 into the

quality and credibility of these results, as well as an independent review by a committee

of statisticians from the National Institute of Statistical Sciences (NISS).2 Collateral

results from the grade 8 state assessment program in mathematics suggested that the

1996 national results may substantially underestimate actual achievement of the

Asian/Pacific Islander group. Because of its potential to misinform, NCES decided to

omit the national grade 8 Asian/Pacific Islander results from the body of the report.

The results are, however, included in this appendix along with a description of the

findings that led to this decision.

Concerns about the accuracy of the national grade 8 Asian/Pacific Islander results

were initially noted during routine quality control of the NAEP 1996 mathematics

results. Despite statistically significant gains from 1992 to 1996 in average scale scores

for the nation as a whole at all three grade levels, a large apparent decline in average

scores was observed for the grade 8 Asian/Pacific Islander subgroup. Table F.1 contains

national average mathematics scale score estimates, and their standard errors, for the

Asian/Pacific Islander subgroup for the 1990, 1992 and 1996 assessment years. From

1992 to 1996, the estimated decline in average scores for this subgroup was

approximately 14 scale score points (about .4 within-grade standard deviation units) on

the NAEP 500-point scale. Despite the large magnitude of this apparent decline, it is

not statistically significant at the .05 level, after controlling for multiple comparisons.

1

 Carlson, J. and P. Williams. ETS/NAEP Technical Memorandum on 1996 Mathematics Grade 8 results for Asian/Pacific

Islander Subpopulation. (October 29, 1996); Rust, K. Westat Memorandum to Gary Phillips on 1996 Mathematics

Grade 8 Results for Asian and Pacific Islander Students. (November 1, 1996).

2

 Letter from Jerome Sacks to Gary Phillips, dated November 21, 1996.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 211
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TABLE F.1

Average Mathematics Scale Scores for the Grade 8

Asian/Pacific Islander Subgroup

1990 1992 1996

Percentage Average

Scale Score Percentage AverageScale Score Percentage AverageScale Score

All students 100 263 (1.3) 100 268 (0.9)» 100 272 (1.1)»>

Students who indicated

their Race/Ethnicity as...

 Asian/Pacific Islander 2 (0.5)! 279 (4.8)! 3 (0.2) 288 (5.4) 3 (0.2) 274 (3.9)

The NAEP mathematics scale ranges from 0 to 500. The standard errors of the statistics appear in parentheses. It can

be said with about 95 percent confidence that, for each population of interest, the value for the entire population is within

± 2 standard errors of the estimate for the sample. In comparing two estimates, one must use the standard error of the

difference (see Appendix A for details). If the notation » («) appears, it signifies that the value for public school students

was significantly higher (lower) than the value for 1990 at about the 95 percent confidence level. If the notation > (<)

appears, it signifies that the value for public school students was significantly higher (lower) than the value for 1992 at

about the 95 percent confidence level. ! Interpret with caution — the nature of the sample does not allow accurate

determination of the variability of this statistic.

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1990, 1992,

and 1996 Mathematics Assessments.

The data from the NAEP state assessment program in mathematics provided an

independent data source to aid in evaluating the accuracy of the national grade 8 NAEP

results for Asian/Pacific Islander students as well as for other subgroups. Forty states

and the District of Columbia participated in the state assessment. Results based on the

combined data from these jurisdictions are quite stable in that they are based on a sample

of approximately 4,000 schools and over 100,000 students. Because of the voluntary

nature of the state assessment program, these aggregated state results are not nationally

representative. They can, however, be compared to restricted national results, calculated

using public-school data from only those states participating in the state assessment, to

obtain valuable insight into the quality of the national estimates for the grade 8

race/ethnicity subgroups.

Table F.2 contains restricted national results. Results are presented separately for

four of the race/ethnicity subgroups: White, Black, Hispanic, and Asian/Pacific Islander.

Aggregated state results are also presented for these same four subgroups. For three of

the four subgroups, the difference between the restricted national estimates and

aggregated state estimates are quite small. However, for the Asian/Pacific subgroup, the

difference between the two estimates, though again within reasonable bounds of

sampling variability, is of considerably greater magnitude and the restricted national

estimates are substantially lower than those obtained from the aggregated state data.

These results suggest that the national grade 8 Asian/Pacific Islander results may

substantially underestimate the performance of this subgroup. NCES was concerned that

publishing the national results in the absence of the kind of discussion included in this

appendix was potentially misinforming. Hence, they made the decision to omit the

results from the body of the report and to include them in this appendix.

212 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
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TABLE F.2

Average Mathematics Scale Scores by Race/Ethnicity for

Restricted National and Aggregated State Samples

Restricted National

Sample

Aggregated State

Sample Difference

Grade 8

Students who indicated

their Race/Ethnicity as...

 White 280.7 280.0 0.7

 Black 242.8 242.3 0.5

 Hispanic 250.4 250.3 0.1

 Asian/Pacific Islander 272.0 281.7 -9.7

SOURCE: National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 1996

Mathematics Assessment.

It is important to note that all NAEP results are estimates and are subject to some

degree of sampling variability. If different samples of schools or students had been

obtained, results for some subgroups would be higher than reported here and some would

be lower. In most subgroups, particularly large subgroups or subgroups for which

special sampling procedures are employed, estimates of performance are likely to remain

similar from one sample to another. However, the national population of Asian/Pacific

Islander students is small (about 3 percent of the national population), heterogeneous

with respect to academic achievement, and highly clustered in certain locations and

schools — factors which are associated with large sampling variability in survey results

and reflected in the large standard errors associated with performance estimates for this

subgroup. Furthermore, the sampling plan for the national assessment does not include

explicit stratification procedures designed to mitigate these factors. It was the judgment

of all three organizations (ETS, Westat, and NISS) that investigated these results that the

occurrence of this large, but statistically nonsignificant, change in the grade 8

Asian/Pacific Islander results was a consequence of these three factors: (1) the

heterogeneous nature of the Asian/Pacific Islander population, (2) the current NAEP

sampling design, and, (3) the sample sizes that were assessed.

NCES, working with its current NAEP contractors and other advisory groups, will

continue to investigate cost-effective ways of improving the accuracy and stability of

NAEP results beginning with the 1998 assessment. They will also continue to seek

improvements as part of an ongoing redesign of NAEP for the year 2000 and beyond.

THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS 213
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214 THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS
THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS

This report is the culmination of the efforts of many individuals who contributed their

considerable knowledge, experience, and creativity to the NAEP 1996 mathematics assessment.

The NAEP 1996 mathematics state assessment was a collaborative effort among staff from the

National Center for Education Statistics (NCES), the National Assessment Governing Board

(NAGB), Educational Testing Service (ETS), Westat, Inc., and National Computer Systems

(NCS). In addition, the program benefited from the contributions of hundreds of individuals at

the state and local levels — governors, chief state school officers, state and district test directors,

state coordinators, and district administrators — who provided their wisdom, experience, and

hard work. Most importantly, NAEP is grateful to the over 239,000 students and the teachers and

administrators in over 9,700 schools in 48 jurisdictions who made the assessment possible by

contributing considerable amounts of time and effort.

The NAEP 1996 mathematics state assessment was funded through NCES, in the

Office of Educational Research and Improvement of the U.S. Department of Education. The

Commissioner of Education Statistics, Pascal D. Forgione, Jr., and the NCES staff — Sue

Ahmed, Peggy Carr, Arnold Goldstein, Steven Gorman, Larry Ogle, Gary W. Phillips, Sharif

Shakrani, Maureen Treacy — and Alan Vanneman of the Education Statistics Services Institute,

worked closely and collegially with the authors to produce this report. The authors were also

provided invaluable advice and guidance by the members of the National Assessment Governing

Board and NAGB staff. In particular, the authors are indebted to Arnold Goldstein of NCES for

his daily efforts to coordinate the activities of the many people who contributed to this report.

The NAEP project at ETS is housed in the Center for the Assessment of Educational

Progress under the direction of Paul Williams. The NAEP 1996 assessments were directed by

Stephen Lazer and John Mazzeo. Jeff Haberstroh directed the scoring operations for the 1996

mathematics assessment. Sampling and data collection activities were conducted by Westat

under the direction of Rene Slobasky, Nancy Caldwell, Keith Rust, Debby Vivari, and Dianne

Walsh. Printing, distribution, scoring, and processing activities were conducted by NCS under

the direction of Brad Thayer, Patrick Bourgeacq, Charles Brungardt, Mathilde Kennel, Linda

Reynolds, and Connie Smith.

The complex statistical and psychometric activities necessary to report results for the

NAEP 1996 mathematics assessment were directed by Nancy Allen, John Barone, James

Carlson, and Juliet Shaffer. John Mazzeo and Gene Johnson provided direction on several

ACKNOWLEDGMENTS
THE NAEP 1996 STATE ASSESSMENT IN MATHEMATICS

critical psychometric issues. The analyses presented in this report were led by Frank Jenkins and

Edward Kulick, with assistance from Hua Chang, Steve Wang, Xiaohui Wang, Hong Zhou, Jiahe

Qian, Kate Pashley, David Freund, and Norma Norris.

Laura Jerry was responsible for the development and creation of the computer-generated

reports, with assistance from Xiaohui Wang, Laura Jenkins, Phillip Leung, Inge Novatkoski,

Bruce Kaplan, and Alfred Rogers. A large group of NAEP staff at ETS checked the data, text,

and tables. Debbie Kline coordinated the technical appendices.

Many thanks are due to the comments and critical feedback of numerous reviewers, both

internal and external to NCES and ETS. Important contributions were made by reviewers from

academic institutions and education agencies: Bruce Brombacher of Upper Arlington (Ohio)

Schools; Pasquale DeVito of the Rhode Island Department of Education, John Dossey of Illinois

State University, Thomas Fisher of the Florida Department of Education, Douglas Rindone of the

Connecticut Department of Education, and Irvin Vance of Michigan State University. Valuable

input was given by NAGB staff Mary Lynn Bourque and Lawrence Feinberg, and NCES staff

Susan Ahmed, Peggy Carr (who helped guide the report through several versions), Steven

Gorman, Andrew Kolstad, Mary Frase, Mary Rollefson, Sharif Shakrani, and Shi-Chang Wu.

Cover design and production of the print version was directed by Carol Errickson, with

the assistance of Sharon Davis-Johnson, Alice Kass, and Barbette Tardugno. Karen Damiano

produced tables and text for one state for which the computerized report generating system was

not appropriate. The World Wide Web version of the state reports was produced by Phillip

Leung and Pat O’Reilly with assistance from Debbie Kline, Karen Damiano, Sharon M. DavisJohnson, Craig Pizzuti, Barbette Tardugno, and Christine Zelenak. The NAEP 1996 Mathematics

State Report for all participating jurisdictions is available via http://www.ed.gov/NCES/naep.

NCES 97-974