- 

Advanced Mathematics and Science 

Coursetaking in the Spring High School 

Senior Classes of 1982, 1992, and 2004 

Statistical Analysis Report 

NCES 2007 312 U. S. DEPARTMENT OF EDUCATION 

Advanced Mathematics and Science 

Coursetaking in the Spring High School 

Senior Classes of 1982, 1992, and 2004 

Statistical Analysis Report 

AUGUST 2007 

Ben Dalton 

Steven J. Ingels 

Jane Downing 

Robert Bozick 

RTI International 

Jeffrey Owings 

Project Officer

National Center for Education Statistics 

NCES 2007-312 

U.S. DEPARTMENT OF EDUCATION 
U.S. Department of Education 

Margaret Spellings 

Secretary 

Institute of Education Sciences 

Grover J. Whitehurst 

Director 

National Center for Education Statistics 

Mark Schneider 

Commissioner 

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August 2007 

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Suggested Citation 

Dalton, B., Ingels, S.J., Downing, J., and Bozick, R. (2007). Advanced Mathematics and Science Coursetaking in the Spring High School 

Senior Classes of 1982, 1992, and 2004 (NCES 2007-312). National Center for Education Statistics, Institute of Education 

Sciences, U.S. Department of Education. Washington, DC. 

Content Contact 

Jeffrey Owings 

(202) 502–7423 

jeffrey.owings@ed.gov 
 

 

Executive Summary 

In order to take advantage of rewarding opportunities in college or the world of work, 

high school graduates increasingly require strong quantitative and analytical skills. As 

mathematical and scientific knowledge and abilities grow in value, the amount and quality of 

instruction American high school students receive in mathematics and science become the focus 

of attention. While increased academic requirements for high school graduation have long been 

advocated (National Commission on Excellence in Education 1983; Achieve, Inc. 2005; National 

Governors Association 2005), current research shows a mixed record in mathematics and science 

achievement among American middle and high school students relative to some of their 

international peers (Gonzales et al. 2004; Lemke et al. 2004; Organization for Economic 

Cooperation and Development 2004). 

In response to these concerns and other calls for reform, states have increased the number 

of courses required for a high school diploma (Council of Chief State School Officers 2005).1 

Research using high school transcripts collected by the National Center for Education Statistics 

(NCES) indicates that states have been successful in encouraging students to take more courses 

in science and mathematics before graduation (Legum et al. 1998; Perkins et al. 2004; Shettle et 

al. 2007). However, important questions remain about trends in mathematics and science 

coursetaking. Are more students taking higher level courses in mathematics and science, in 

addition to increasing the number of courses taken? Have upward trends in coursetaking been 

sustained in recent years? And have disparities among student subgroups in coursetaking 

experiences changed over time? 

This report uses in-depth information on the coursetaking patterns of high school 

graduates2

 in 1982, 1992, and 2004 to answer these questions. The analysis employs traditional 

counts of credits earned alongside measures based on the most advanced level of courses a 

student completed in high school in order to examine both the quantity and types of mathematics 

and science courses taken. Coursetaking information was derived from high school transcripts 

collected by NCES during three studies: the High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B), the National Education Longitudinal Study of 1988 (NELS:88), and 

the Education Longitudinal Study of 2002 (ELS:2002).3

 Differences in coursetaking over time or 

across student subgroups are only reported if the comparison met both the criteria of statistical 

significance (using t statistics with an alpha level of .05) and substantive difference (using effect 

sizes that are greater than .20 standard deviations for continuous variables and 5 percentage 

points for categorical variables). All coursetaking information is based on courses where credit 

was earned—meaning that the student received a passing grade according to his or her school’s 

grading system. The major findings are summarized below. 

1

 For example, between 1987 and 2004, the number of states requiring at least 2.5 credits in mathematics more than 

doubled and in science more than tripled (Council of Chief State School Officers 2005). 

2

 High school graduates in this report are defined as spring-term high school seniors who graduated with an honors 

or standard diploma by the end of the summer (August 31) of their senior year. 

3

 More information on these studies can be found on the National Center for Education Statistics (NCES) World 

Wide Web home page at http://nces.ed.gov. 

iii 
 

Executive Summary 

Mathematics Coursetaking Overall 

High school graduates’ completion of mathematics courses clearly increased across the 

three cohorts studied in this report. Graduates came much closer to taking 4 full years of 

academic coursework in mathematics, moving from, on average, 2.7 total credits in mathematics 

in 1982 to 3.6 total credits in 2004. 

In addition, graduates shifted from taking lower level mathematics courses to taking more 

advanced courses.4 For example, the percentage of graduates who persisted through the 

mathematics curriculum into the two most advanced levels—precalculus and calculus—tripled 

between 1982 and 2004 (figure A). Moreover, the upward trend in high-end mathematics 

coursetaking occurred in both time periods—the percentage of graduating seniors completing 

precalculus or calculus increased 11 percentage points between 1982 and 1992 and between 

1992 and 2004. 

Accompanying the increase in advanced-level mathematics coursetaking was a 

significant drop in the percentage finishing high school with one of the two lowest levels of 

mathematics courses completed (no or low academic mathematics, or algebra I/plane geometry). 

In 1982, over half of graduates (56 percent) finished high school with algebra I or less as their 

highest course, while by 2004 only 23 percent of graduates finished at these low levels. 

Figure A. Percentage of high school graduates who completed precalculus or calculus: 1982, 

1992, and 2004 

Percent 

100.0 

80.0 

60.0 

40.0 33.0 

21.7 

20.0 10.7 

0.0 

1982 1992 2004 

Year 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

4

 The mathematics “pipeline” (course level) measure was divided into six categories, moving from least to most 

advanced: (1) no or low (e.g., general math or consumer math) academic mathematics; (2) algebra I/plane geometry; 

(3) algebra II; (4) algebra III/trigonometry/analytic geometry; (5) precalculus; and (6) calculus. 

iv 
 

 

Executive Summary 

Science Coursetaking Overall 

Clear trends were also evident for science coursetaking. The average number of science 

credits increased from 2.2 total credits in 1982 to 3.3 total credits in 2004. Further, graduates 

shifted in significant proportions from taking lower level science courses to taking upper level 

ones.5

 For example, smaller proportions of high school graduates finished high school with 

courses at the two lowest science levels (no or low-level science, or secondary physical science 

and basic biology): 29 percent of graduates finished at these levels in 1982, while only 6 percent 

of graduates finished at these levels in 2004. This was complemented by growth in the upper half 

of science courses (i.e., the top three levels). The percentage of high school graduates who 

completed chemistry (I or II), physics (I or II), or advanced biology about doubled (from 35 

percent to 69 percent) between 1982 and 2004 (figure B). 

Figure B. Percentage of high school graduates who completed chemistry, physics, or advanced 

biology: 1982, 1992, and 2004 

Percent 

100.0 

80.0 

69.2 

60.0 53.6 

35.4 40.0 

20.0 

0.0 

Year 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

Mathematics and Science Coursetaking Among Student Subgroups 

In addition to these overall trends in coursetaking, the number and level of courses taken 

in mathematics and science increased for all student subgroups examined. Across categories of 

sex, race/ethnicity, socioeconomic status6

 (SES) background, educational expectations, and 

1982 1992 2004 

5

 The science “pipeline” (course level) measure was divided into six categories, from least to most advanced: (1) no 

or low-level science; (2) secondary physical science and basic biology; (3) general biology; (4) chemistry I or 

physics I; (5) chemistry I and physics I; and (6) chemistry II, physics II, or advanced biology. 

6

 Each of the three NCES high school cohort studies employed in this report (HS&B, NELS:88; ELS:2002) 

constructed a standardized socioeconomic status (SES) variable based on a composite of parental education, 

occupation, income, and, in HS&B, household items (such as number of books, electric dishwasher, number of cars, 

own room, etc.). The form of the variable used in this report divides the SES distribution into four equally weighted 

quartiles. 

v 
 

 

 

 

Executive Summary 

school sector, graduates in 2004 took more and higher levels of mathematics and science than 

their peers in 1992 and 1982. 

• Sex. Both male and female graduates completed advanced-level coursework in 

mathematics at higher percentages in 2004 than in 1992 and 1982. However, while both 

sexes increased their advanced mathematics coursetaking, they did not differ from each 

other at any of the three points in time: in each of the cohorts, there were no substantive 

differences detected between females and males in the percentage completing advanced 

mathematics courses (precalculus and calculus). 

In science, both males and females completed similar levels of coursework across the 

three cohorts, with the exception of a middle level of science courses, chemistry I or 

physics I. Although the percentages of males and females completing chemistry I or 

physics I showed no detectable differences in 1982, females surpassed males at this 

middle level of science attainment in 2004 (37 percent versus 30 percent completing up 

to chemistry I or physics I, respectively). 

• Race/ethnicity.7

 All racial/ethnic groups increased their participation in higher levels of 

mathematics and science coursework. Between 1982 and 2004, the percentages of 

students completing either precalculus or calculus as their highest mathematics course 

increased from 2 to 13 percent for American Indians, 4 to 19 percent for Blacks, 5 to 22 

percent for Hispanics, 12 to 37 percent for Whites, and 30 to 57 percent for Asians 

(figure C). 

Despite the progress made in advanced-level mathematics coursetaking, disparities 

among racial/ethnic groups persisted across the two decades. White and Asian graduates 

in all three cohorts were more likely than their Black, Hispanic, and American Indian 

peers to persist in the mathematics pipeline through precalculus and calculus (and Asian 

graduates more likely than Whites). For example, the gap between Blacks and Whites in 

advanced mathematics (precalculus and calculus) enrollment persisted at all points in 

time: in 1982, 4 percent of Blacks and 12 percent of Whites had completed advanced 

mathematics, while in 1992 the respective figures were 14 percent and 23 percent, and in 

2004 19 percent and 37 percent. Nevertheless, in terms of average credits earned in 

mathematics, no statistical difference was detected between Blacks and Whites in 2004 

(mean mathematics credits were 3.7 for Blacks and 3.6 for Whites). 

7

 In this report, American Indian includes Alaska Native, Asian includes Native Hawaiian or Other Pacific Islander, 

Black includes African American, and Hispanic includes Latino. Respondents who identified themselves as being of 

Hispanic origin are classified as Hispanic, regardless of race. Choosing more than one race was not permitted in 

HS&B and NELS:88. 

vi 
 

Executive Summary 

Figure C. Percentage of high school graduates who completed precalculus or calculus, by 

race/ethnicity: 1982, 1992, and 2004 

Percent 

100.0 

80.0 

60.0 

40.0 

20.0 

0.0 

2.3 

30.1 

4.0 5.3 

12.2 

3.1 

41.6 

13.6 12.7 

23.0 

12.9 

56.8 

19.0 21.9 

36.7 

American Indian Asian Black Hispanic White 

1982 

1992 

2004 

Race/ethnicity 

NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and 

American Indian includes Alaska Native. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

In science, Asian students in each cohort were more likely than students from all other 

racial/ethnic groups to complete the most advanced level of science courses, and this 

advantage increased over time. In 1982, 24 percent of Asian graduates completed 

chemistry II, physics II, or advanced biology, and 23 percent completed this level in 

1992; in 2004, however, 39 percent of Asian graduates did so. The proportions of nonAsian minority students completing the most advanced level of science remained 

relatively stable from 1982 to 2004, except for Whites, whose completion rates for 

chemistry II, physics II, or advanced biology were relatively stable between 1982 and 

1992 but rose from 16 percent in 1992 to 21 percent in 2004. 

• Socioeconomic status. Students in each of the four SES quartiles increased their 

participation in advanced mathematics courses over time. The percentage of graduates 

completing precalculus or calculus grew over time; students in the lowest quartile, for 

example, increased their calculus and precalculus completion rates from 3 percent in 

1982 to 18 percent in 2004 (figure D). The completion rates in precalculus more than 

doubled from 1982 to 2004 for graduates from each SES quartile. 

In 1982, 1992, and 2004, high SES graduates were consistently more likely than low SES 

graduates to complete advanced-level coursework in mathematics. Disparities between 

the highest and lowest SES quartiles in the percentages of students who completed 

precalculus and calculus not only persisted but increased from 1982 to 2004: the gap 

between the highest and lowest quartiles was 18 percentage points in 1982 but 35 

percentage points in 2004. 

vii 
Executive Summary 

Figure D. Percentage of high school graduates who completed precalculus or calculus, by 

socioeconomic status: 1982, 1992, and 2004 

Percent 

100.0 

80.0 

60.0 

40.0 

20.0 

0.0 

2.7 

6.7 

11.3 

20.5 

8.0 

13.2 

21.9 

38.5 

17.7 

22.7 

34.0 

52.4 

First quartile (lowest) Second quartile Third quartile Fourth quartile (highest) 

1982 

1992 

2004 

Socioeconomic status 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

The percentage of students who completed two of the three highest science course levels 

(chemistry I or physics I, or chemistry I and physics I) also increased for all SES groups, 

with the growth in students completing one standard course in chemistry or physics the 

strongest (figure E). Students in the highest SES quartile also consistently completed the 

most advanced level of science courses at higher rates than their peers in all three cohorts. 

• Educational expectations. Between 1982 and 2004, high school graduates at all levels 

of educational expectations increased their participation in middle and advanced-level 

mathematics courses. Among lower expectation students (expecting less than a college 

degree), most of this growth was in a middle level of mathematics (algebra II), with little 

or no improvement in the percentage completing the most advanced mathematics. In 

contrast, higher expectation students, especially those who expected a graduate or 

professional degree, increased their coursetaking in precalculus and calculus. 

Specifically, over half (53 percent) of those who expected to earn a graduate degree had 

taken calculus or precalculus in 2004, compared with 8 percent of those who expected to 

achieve only some postsecondary education and 33 percent of those who expected to 

attain a baccalaureate degree. For the group with graduate or professional degree 

expectations, precalculus-calculus completion increased from 27 percent in 1982 to 41 

percent in 1992 and 53 percent in 2004. 

viii 
 

Executive Summary 

Figure E. Percentage of high school graduates who completed different levels of science 

courses, by socioeconomic status: 1982, 1992, and 2004 

First quartile 

(lowest) 1982 

1992 

2004 

Second quartile 

1982 

1992 

2004 2.8 

Third quartile 

1982 

1992 2.3 

1.7 2004 

2.8 

Fourth quartile 

(highest) 

1982 

0.5 1992 

3.2 

1.1 2004 

1.4 

16.4 

6.1 11.7 

5.0 5.0 

16.8 17.0 

4.0 9.2 

4.4 

11.4 15.8 

5.5 

6.6 11.6 

13.2 

23.4 

28.4 

23.9 

35.3 

34.7 

30.6 

42.7 

37.6 

35.7 

48.8 

40.8 9.2 

21.2 

33.6 

12.6 

26.1 

34.6 

16.7 

31.2 

35.0 

20.5 

28.5 

31.1 

10.6 

13.3 

6.0 

13.8 

7.9 

4.3 

9.1 

22.7 8.5 

5.4 6.7 

11.6 

11.6 

10.1 

15.5 

22.2 

25.3 

19.5 

18.9 

2.5 

13.9 

12.5 

17.7 

24.9 

27.9 

0.0 20.0 40.0 60.0 80.0 100.0 

Percent 

Secondary physical 

science and basic biology 

Chemistry I or physics I 

Chemistry I and physics I 

No science or lowlevel science 

General biology 

Chemistry II, physics II, 

or advanced biology 

NOTE: Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

In science, students who expected only a high school degree or less grew most in a 

middle level of science courses, chemistry I or physics I (these students moved from 4 

percent to 19 percent completion rates at this level between 1982 and 2004), with no 

improvement in the percentage completing the most advanced science courses. In 2004, 

high school seniors who expected to earn a graduate or professional degree continued to 

be most likely to complete chemistry II or physics II or advanced biology. Nearly 29 

percent of students expecting to earn a graduate or professional degree completed the 

most advanced level of science courses, compared with 16 percent of students expecting 

to earn a baccalaureate degree, 7 percent of students expecting to earn some 

ix 
 

Executive Summary 

postsecondary education, and 8 percent of students expecting to earn no more than a high 

school diploma. 

• School sector. In contrast to the foregoing student-level characteristics, school sector 

represents one aspect of the context in which high school coursetaking occurs. From 

1982 to 2004, increased proportions of students from the public, Catholic, and other 

private school sectors graduated with credits earned in advanced mathematics courses. 

Precalculus completion rates more than doubled between 1982 and 2004 across school 

sectors; calculus rates also rose for students from all sectors. In 1982, 9 percent of public 

school graduates completed one of these advanced mathematics courses, but this 

proportion had reached 31 percent in 2004. Similarly, Catholic school graduates 

increased their completion of precalculus or calculus-level courses from 19 percent to 51 

percent, and other private school graduates increased their rate from 30 percent to 57 

percent. 

In science, the participation rates of public and Catholic high school students in courses 

like chemistry I, physics I, or both more than doubled from 1982 to 2004. However, 

completion rates of the most advanced level of science courses (chemistry II, physics II, 

or advanced biology) remained relatively stable between 1982 and 2004 across school 

sectors. Despite increased completion of advanced-level mathematics and science courses 

by graduates from all school sectors, Catholic and other private school students remained 

more likely than their public school counterparts to complete advanced-level courses in 

mathematics and science. 

These results show that American high school students took an increasing number of 

academic courses between 1982 and 2004 and became more likely to complete advanced-level 

coursework before they graduated from high school. The upward trend in advanced-level 

coursetaking not only occurred among high school graduates nationwide but persisted in all 

subgroups examined in this report, including those identified by sex, race/ethnicity, SES, 

educational expectations, and school sector. Although some disparities remain or have grown, 

the overarching trend for all students is toward completing more demanding mathematics and 

science courses. 

x 
Foreword 

This report presents new time series data on the coursetaking patterns of the high school 

classes of 1982, 1992, and 2004. Using coursetaking pipeline measures developed by University 

of Michigan researchers (Burkam 2003; Burkam and Lee 2003), this report examines both the 

quantity and level of academic coursetaking, with a focus on the highest level of coursework that 

high school graduates completed in mathematics and science. Additionally, the analysis focuses 

on differences in coursetaking patterns among various subgroups defined by sex, race/ethnicity, 

socioeconomic status, educational expectations, and school sector. Coursetaking information was 

derived from high school transcripts collected by the National Center for Education Statistics 

(NCES) from three longitudinal studies: the High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B), the National Education Longitudinal Study of 1988 (NELS:88), and 

the Education Longitudinal Study of 2002 (ELS:2002). 

We hope that the information provided in this report will be useful to a wide range of 

readers, including policymakers and educators interested in improving preparation in 

mathematics and science. Additionally, we hope that the results reported here will encourage 

other researchers to use NCES’s longitudinal datasets to investigate issues that will help enhance 

the functioning of our schools and, consequently, the educational experiences of American 

youth. 

Mark Schneider 

Commissioner 

National Center for Education Statistics 

Jeffrey A. Owings 

Associate Commissioner 

Elementary/Secondary & Libraries Studies 

xi 

 

Acknowledgments 

A number of people contributed to the production of this statistical analysis report, and 

many more to the development of the Education Longitudinal Study of 2002 (ELS:2002). In 

particular, we wish to thank Jeffrey A. Owings, National Center for Education Statistics (NCES) 

Associate Commissioner of Elementary/Secondary & Libraries Studies, in whose division 

ELS:2002 is housed, as was its predecessor study, the National Education Longitudinal Study of 

1988 (NELS:88). 

Other NCES staff who have provided help, support, and assistance include Marilyn 

Seastrom, Kathryn Chandler, Lisa Hudson, Paula Knepper, Edith McArthur, and Peggy Quinn. 

Staff elsewhere in the U.S. Department of Education whose help we gratefully acknowledge are 

Clifford Adelman, Sharon Belli, Jeffery Rodamar, and Marsha Silverberg. We would like to 

thank additional NCES reviewers Janis Brown and Mike Planty, as well as American Institutes 

for Research reviewers Kevin Bromer, Robert Stillwell, and Akemi Kinukawa. We also wish to 

acknowledge our IES Action Editor, Lisa Bridges, and two external reviewers. 

We would like to acknowledge the critical role that Bruce B. Daniel of Kforce 

Government Solutions played in producing results for this report; his statistical analysis and 

programming made the report possible. We also would like to acknowledge the role of the 

ELS:2002 Technical Review Panel, whose members reviewed plans for the ELS:2002 data 

collection, helped refine them, and provided important suggestions to help guide development of 

the instrumentation. The following individuals served as members of the Technical Review 

Panel during the base year and first follow-up: Marco Clark, Richard Duran, Jeremy Finn, 

Thomas B. Hoffer, Sally Kilgore, Richard Lawrence, Samuel R. Lucas, Aaron Pallas, and Andy 

Rogers. 

Daniel J. Pratt of RTI served as the ELS:2002 base-year and first follow-up project 

director. Steven J. Ingels of RTI was principal investigator. Key RTI task leaders for the first 

follow-up transcript component were Tiffany L. Mattox and Robert Bozick. 

This report drew on an earlier unpublished transcript report written by Xianglei Chen and 

John Tuma of MPR Associates, Leslie A. Scott of the American Institutes for Research (AIR), 

and Bruce B. Daniel of Kforce Government Solutions. The contribution of these four individuals 

was particularly valuable to the authors. 

Editorial, document preparation, and graphics support for this statistical analysis report 

were provided by Wallace Campbell, Laura Small, Michelle Myers, Richard Hair, and Sharon 

Powell of RTI. 

xiii 

Contents 

Executive Summary.....................................................................................................................iii 

Foreword....................................................................................................................................... xi 

Acknowledgments ......................................................................................................................xiii 

List of Tables ............................................................................................................................. xvii 

List of Figures............................................................................................................................. xxi 

Chapter 1 Introduction................................................................................................................. 1 

1.1 Credit Measures of Coursetaking..................................................................................... 2 

1.2 Pipeline Measures of Coursetaking ................................................................................. 3 

1.2.1 Construction of the Pipeline Measures ................................................................ 3 

1.2.2 Validity of the Measures...................................................................................... 7 

1.3 Description of the Present Study...................................................................................... 7 

Chapter 2 Trends in Mathematics Coursetaking: 1982–2004 ................................................ 11 

2.1 Overall Trends in Mathematics Coursetaking ............................................................... 11 

2.2 Trends in Mathematics Coursetaking Among Student Subgroups................................ 13 

2.2.1 Sex...................................................................................................................... 13 

2.2.2 Race/Ethnicity.................................................................................................... 16 

2.2.3 Socioeconomic Status ........................................................................................ 20 

2.2.4 Educational Expectations................................................................................... 23 

2.2.5 School Sector ..................................................................................................... 27 

2.3 Mathematics Coursetaking Summary............................................................................ 30 

Chapter 3 Trends in Science Coursetaking: 1982–2004.......................................................... 33 

3.1 Overall Trends in Science Coursetaking........................................................................ 33 

3.2 Trends in Science Coursetaking Among Student Subgroups ........................................ 34 

3.2.1 Sex...................................................................................................................... 34 

3.2.2 Race/Ethnicity.................................................................................................... 36 

3.2.3 Socioeconomic Status ........................................................................................ 39 

3.2.4 Educational Expectations................................................................................... 40 

3.2.5 School Sector ..................................................................................................... 44 

3.3 Science Coursetaking Summary .................................................................................... 46 

Chapter 4 Conclusions................................................................................................................ 49 

References.................................................................................................................................... 51 

Appendix A Technical Notes and Methodology..................................................................... A-1 

A.1 Sources of Data............................................................................................................ A-3 

A.1.1 High School and Beyond ................................................................................. A-3 

A.1.2 National Education Longitudinal Study of 1988 ............................................. A-5 

A.1.3 Education Longitudinal Study of 2002............................................................ A-6 

A.2 Accuracy of Estimates ................................................................................................. A-7 

A.3 Statistical Procedures................................................................................................... A-7 

xv 
Contents 

A.3.1 Testing the Difference between Two Means or Percentages........................... A-8 

A.3.2 Testing the Difference between Differences.................................................... A-8 

A.3.3 Substantive Difference..................................................................................... A-8 

A.4 Bias Analysis ............................................................................................................... A-9 

A.5 Comparability Across HS&B, NELS:88, and ELS:2002 .......................................... A-14 

A.5.1 Cross-Study Bias Analysis............................................................................ A-15 

A.6 Procedures for Selecting the Final Analysis Transcript Samples .............................. A-21 

A.6.1 High School and Beyond (HS&B)................................................................. A-22 

A.6.2 National Education Longitudinal Study of 1988 (NELS:88) ........................ A-22 

A.6.3 Education Longitudinal Study of 2002 (ELS:2002) ...................................... A-23 

A.7 Glossary of Classification and Transcript Variables ................................................. A-23 

 A.7.1 Classification Variables ................................................................................ A-24 

A.7.2 Transcript Variables...................................................................................... A-26 

Appendix B Standard Error Tables........................................................................................ B-1 

Appendix C Sample Size Tables for Select Subgroups ......................................................... C-1 

Appendix D Course-Specific Completion Percentages.......................................................... D-1 

xvi 
 

 

List of Tables 

Appendix A 

Table Page 

A-1. Selected characteristics of all high school graduates versus high school 

graduates with full transcripts: 1982, 1992, and 2004 ........................................... A-11 

A-2. Percentage distribution of selected student characteristics and mean math 

IRT score for freshened versus unfreshened samples (transcript weight) of 

NELS:88 and ELS:2002 seniors: 1992 and 2004 .................................................. A-17 

A-3. Percentage distribution of selected student characteristics and mean math 

score for 1980 senior cohort and 1980 sophomore cohort two years later 

(in 1982) of HS&B: 1980 and 1982....................................................................... A-19 

A-4. Summary of comparisons of coursetaking estimates computed from freshened 

and unfreshened senior samples of NELS:88 and ELS:2002: 1992 and 2004 ...... A-21 

A-5. Elements of the socioeconomic status (SES) composite, HS&B and NELS:88: 

1980 and 1992 ........................................................................................................ A-25 

A-6. Elements of the socioeconomic status (SES) composite, ELS:2002: 2004 ........... A-25 

Appendix B 

B-1. Standard errors for figure 1: Percentage of high school graduates who 

completed different levels of mathematics courses: 1982, 1992, and 2004 ..............B-3 

B-2. Standard errors for figure 2: Mean credits earned in mathematics by high 

school graduates, by sex: 1982, 1992, and 2004........................................................B-3 

B-3. Standard errors for figure 3: Percentage of high school graduates who 

completed different levels of mathematics courses, by sex: 1982, 1992, and 

2004............................................................................................................................B-3 

B-4. Standard errors for figure 5: Mean credits earned in mathematics by high 

school graduates, by race/ethnicity: 1982, 1992, and 2004 .......................................B-4 

B-5. Standard errors for figure 6: Percentage of high school graduates who 

completed different levels of mathematics courses, by race/ethnicity: 1982, 

1992, and 2004...........................................................................................................B-5 

B-6. Standard errors for figure 8: Mean credits earned in mathematics by high 

school graduates, by socioeconomic status: 1982, 1992, and 2004...........................B-6 

B-7. Standard errors for figure 9: Percentage of high school graduates who 

completed different levels of mathematics courses, by socioeconomic status: 

1982, 1992, and 2004.................................................................................................B-7 

B-8. Standard errors for figure 11: Mean credits earned in mathematics by high 

school graduates, by educational expectations: 1982, 1992, and 2004 .....................B-7 

xvii 
 

List of Tables 

B-9. Standard errors for figure 12: Percentage of high school graduates who 

completed different levels of mathematics courses, by educational 

expectations: 1982, 1992, and 2004...........................................................................B-8 

B-10. Standard errors for figure 14: Mean credits earned in mathematics by high 

school graduates, by school sector: 1982, 1992, and 2004........................................B-8 

B-11. Standard errors for figure 15: Percentage of high school graduates who 

completed different levels of mathematics courses, by school sector: 1982, 

1992, and 2004...........................................................................................................B-9 

B-12. Standard errors for figure 17: Percentage of high school graduates who 

completed different levels of science courses: 1982, 1992, and 2004.....................B-10 

B-13. Standard errors for figure 18: Mean credits earned in science by high school 

graduates, by sex: 1982, 1992, and 2004.................................................................B-10 

B-14. Standard errors for figure 19: Percentage of high school graduates who 

completed different levels of science courses, by sex: 1982, 1992, and 2004 ........B-10 

B-15. Standard errors for figure 20: Mean credits earned in science by high school 

graduates, by race/ethnicity: 1982, 1992, and 2004.................................................B-11 

B-16. Standard errors for figure 21: Percentage of high school graduates who 

completed different levels of science, by race/ethnicity: 1982, 1992, and 2004.....B-11 

B-17. Standard errors for figure 22: Mean credits earned in science by high school 

graduates, by socioeconomic status: 1982, 1992, and 2004 ....................................B-12 

B-18. Standard errors for figure 23: Percentage of high school graduates who 

completed different levels of science courses, by socioeconomic status: 1982, 

1992, and 2004.........................................................................................................B-13 

B-19. Standard errors for figure 24: Mean credits earned in science by high school 

graduates, by educational expectations: 1982, 1992, and 2004...............................B-13 

B-20. Standard errors for figure 25: Percentage of high school graduates who 

completed different levels of science courses, by educational expectations: 

1982, 1992, and 2004...............................................................................................B-14 

B-21. Standard errors for figure 26: Mean credits earned in science by high school 

graduates, by school sector: 1982, 1992, and 2004 .................................................B-14 

B-22. Standard errors for figure 27: Percentage of high school graduates who 

completed different levels of science courses, by school sector: 1982, 1992, 

and 2004...................................................................................................................B-15 

B-23. Standard errors for appendix table A-2: Percentage distribution of selected 

student characteristics and mean math IRT score for freshened versus 

unfreshened samples (transcript weight) of NELS:88 and ELS:2002 seniors: 

1992 and 2004 ........................................................................................................ B-16 

B-24. Standard errors for appendix table A-3: Percentage of selected student 

characteristics and mean math score for 1980 senior cohort and 1980 

sophomore cohort two years later (in 1982) of HS&B: 1980 and 1982 ................ B-17 

xviii 
List of Tables 

Appendix C 

C-1. Sample sizes of select subgroups for each level of the mathematics pipeline: 

1982, 1992, and 2004.................................................................................................C-4 

C-2. Sample sizes of select subgroups for each level of the science pipeline: 1982, 

1992, and 2004...........................................................................................................C-5 

Appendix D 

D-1. Percentage and standard errors of graduating seniors who received credit in 

mathematics courses, by pipeline level: 1982........................................................... D-4 

D-2. Percentage and standard errors of graduating seniors who received credit in 

science courses, by pipeline level: 1982................................................................... D-6 

D-3. Percentage and standard errors of graduating seniors who received credit in 

mathematics courses, by pipeline level: 1992........................................................... D-9 

D-4. Percentage and standard errors of graduating seniors who received credit in 

science courses, by pipeline level: 1992................................................................. D-11 

D-5. Percentage and standard errors of graduating seniors who received credit in 

mathematics courses, by pipeline level: 2004......................................................... D-14 

D-6. Percentage and standard errors of graduating seniors who received credit in 

science courses, by pipeline level: 2004................................................................. D-16 

xix 

List of Figures 

Executive Summary 

Figure Page 

A. Percentage of high school graduates who completed precalculus or calculus: 

1982, 1992, and 2004................................................................................................... iv 

B. Percentage of high school graduates who completed chemistry, physics, or 

advanced biology: 1982, 1992, and 2004 ......................................................................v 

C. Percentage of high school graduates who completed precalculus or calculus, 

by race/ethnicity: 1982, 1992, and 2004.................................................................... viii 

D. Percentage of high school graduates who completed precalculus or calculus, 

by socioeconomic status: 1982, 1992, and 2004........................................................ viii 

E. Percentage of high school graduates who completed different levels of science 

courses, by socioeconomic status: 1982, 1992, and 2004............................................ ix 

Text 

1. Percentage of high school graduates who completed different levels of 

mathematics courses: 1982, 1992, and 2004 ...............................................................13 

2. Mean credits earned in mathematics by high school graduates, by sex: 1982, 

1992, and 2004.............................................................................................................14 

3. Percentage of high school graduates who completed different levels of 

mathematics courses, by sex: 1982, 1992, and 2004 ...................................................15 

4. Percentage of high school graduates who completed precalculus or calculus, 

by sex: 1982, 1992, and 2004 ......................................................................................16 

5. Mean credits earned in mathematics by high school graduates, by 

race/ethnicity: 1982, 1992, and 2004...........................................................................17 

6. Percentage of high school graduates who completed different levels of 

mathematics courses, by race/ethnicity: 1982, 1992, and 2004...................................18 

7. Percentage of high school graduates who completed precalculus or calculus, 

by race/ethnicity: 1982, 1992, and 2004......................................................................20 

8. Mean credits earned in mathematics by high school graduates, by 

socioeconomic status: 1982, 1992, and 2004...............................................................21 

9. Percentage of high school graduates who completed different levels of 

mathematics courses, by socioeconomic status: 1982, 1992, and 2004 ......................22 

10. Percentage of high school graduates who completed precalculus or calculus, 

by socioeconomic status: 1982, 1992, and 2004..........................................................23 

11. Mean credits earned in mathematics by high school graduates, by educational 

expectations: 1982, 1992, and 2004.............................................................................24 

xxi 
List of Figures 

12. Percentage of high school graduates who completed different levels of 

mathematics courses, by educational expectations: 1982, 1992, and 2004.................26 

13. Percentage of high school graduates who completed precalculus or calculus, 

by educational expectations: 1982, 1992, and 2004 ....................................................27 

14. Mean credits earned in mathematics by high school graduates, by school 

sector: 1982, 1992, and 2004 .......................................................................................28 

15. Percentage of high school graduates who completed different levels of 

mathematics courses, by school sector: 1982, 1992, and 2004 ...................................29 

16. Percentage of high school graduates who completed precalculus or calculus, 

by school sector: 1982, 1992, and 2004.......................................................................30 

17. Percentage of high school graduates who completed different levels of science 

courses: 1982, 1992, and 2004.....................................................................................34 

18. Mean credits earned in science by high school graduates, by sex: 1982, 1992, 

and 2004.......................................................................................................................35 

19. Percentage of high school graduates who completed different levels of science 

courses, by sex: 1982, 1992, and 2004 ........................................................................36 

20. Mean credits earned in science by high school graduates, by race/ethnicity: 

1982, 1992, and 2004...................................................................................................37 

21. Percentage of high school graduates who completed different levels of science 

courses, by race/ethnicity: 1982, 1992, and 2004........................................................38 

22. Mean credits earned in science by high school graduates, by socioeconomic 

status: 1982, 1992, and 2004........................................................................................39 

23. Percentage of high school graduates who completed different levels of science 

courses, by socioeconomic status: 1982, 1992, and 2004............................................41 

24. Mean credits earned in science by high school graduates, by educational 

expectations: 1982, 1992, and 2004.............................................................................42 

25. Percentage of high school graduates who completed different levels of science 

courses, by educational expectations: 1982, 1992, and 2004 ......................................43 

26. Mean credits earned in science by high school graduates, by school sector: 

1982, 1992, and 2004...................................................................................................44 

27. Percentage of high school graduates who completed different levels of science 

courses, by school sector: 1982, 1992, and 2004.........................................................46 

xxii 
 

Chapter 1 

Introduction 

Strong quantitative and analytical skills are increasingly important for youth who will be 

working in an economy that is technical in nature and global in scope. Yet cross-national 

research on mathematics and science achievement indicates that American youth in middle or 

high school grades are not faring as well as some of their international peers. For example, the 

2003 Program for International Student Assessment (PISA) finds that 15-year-old students in the 

United States rank 24th of 29 nations in problem solving and mathematics literacy (Lemke et al. 

2004). In science, while research indicates that U.S. middle school students are above the 

international achievement average (tied for 9th out of 44 nations) and have been gaining in recent 

years (Gonzales et al. 2004), some U.S. policymakers continue to express concern about the 

achievement and long-term competitiveness of its students in science (National Science Board 

2006). 

In response to concerns that students leave high school underprepared in mathematics and 

science, many states have increased their requirements for graduation. For example, between 

1987 and 2004, the number of states requiring at least 2.5 credits in mathematics grew from 12 to 

26, and the number of states requiring at least 2.5 credits in science grew from 6 to 23 (Council 

of Chief State School Officers [CCSSO] 2005). In 2004, 17 states required specific courses in 

math and 23 states required specific courses in science to graduate. These requirements appear 

to be reflected in high school student coursetaking (CCSSO 2005). Research using high school 

transcript data collected by the National Center for Education Statistics (NCES) shows that high 

school students have been taking a greater number of academic courses over the past 15 years 

(Legum et al. 1998; Levesque et al. 2000; National Commission on Excellence in Education 

1983; Perkins et al. 2004; U.S. Department of Education 2000). 

However, important questions remain about the mathematics and science coursetaking of 

American high school students. First, have documented increases in course credits in math and 

science continued in recent years? Second, have increases in course credits in math and science 

been accompanied by increases in advanced coursetaking in subjects such as calculus and 

physics? Third, have coursetaking differences between students from different backgrounds 

changed in conjunction with rising academic requirements? This report answers these questions 

by examining both the number of credits and the types of courses taken in mathematics and 

science by the high school graduating classes of 1982, 1992, and 2004—over two decades of 

coursetaking patterns. 

Earlier research focused on the number of credits earned by students, regardless of the 

type or content of the courses. For example, if two students both earned three credits in 

mathematics, with one taking mostly basic courses and the other taking honors and Advanced 

Placement (AP) courses, the consequences for their learning might be quite different. To better 

understand the qualitative aspect of curricular experiences, researchers at the University of 

Michigan recently took a different approach to measuring coursetaking (Burkam 2003; Burkam 

and Lee 2003). Instead of following the number of course credits accumulated by students, this 

alternative approach focuses on the most advanced level of courses a student completed in high 

school or how far the student progressed along an academic-subject-area “pipeline.” Thus far, 

coursetaking pipelines have been created for mathematics, science, English, and foreign 

1 
 

 

Chapter 1. Introduction 

language. While pipeline measures do not measure the quality of courses, they create an 

opportunity to examine students’ coursetaking behaviors from the perspective of course progress. 

The analysis reported here focuses on differences in credits and courses among various 

subgroups defined by sex, race/ethnicity, socioeconomic status,1 educational expectations, and 

school sector, with a brief discussion of coursetaking trends overall. Coursetaking information 

for graduating seniors was derived from high school transcripts collected by NCES from three 

longitudinal studies: the High School and Beyond Longitudinal Study of 1980 Sophomores 

(HS&B), the National Education Longitudinal Study of 1988 (NELS:88), and the Education 

Longitudinal Study of 2002 (ELS:2002). All coursetaking information is based on courses where 

credit was earned—meaning that the student received a passing grade according to his or her 

school’s grading system. (See appendix A for details on the datasets used in this report.) 

1.1 Credit Measures of Coursetaking 

Previous studies on student coursetaking have focused primarily on the number of 

courses taken or Carnegie units earned. A Carnegie unit is a standard of measurement used for 

secondary education that represents the completion of a course that meets one period per day for 

1 year. The number of units (or credits) accumulated in a subject is a good indicator of the total 

amount of instruction in that subject received and is a proxy measure for the continuity of that 

instruction. In a standard 9th-12th grade high school, four credits of math or science corresponds 

to a typical pattern of one unit each year—particularly in mathematics, where following specific 

course sequences may be typical and “doubling up” two courses in the same subject is more 

difficult. Credit counts thus provide a general overview of student involvement in specific 

subjects. 

However, researchers and policymakers have pointed to some limitations of credit 

measures for investigating and understanding high school coursetaking experiences and the 

linkages between those experiences and a variety of outcomes of interest, such as student 

achievement and preparedness for college. The Congressional Budget Office (1987) offered 

student coursework trends as a possible explanation for the decline in achievement scores during 

the 1960s and 1970s but stressed that course content rather than completed credits should be 

analyzed to achieve a thorough analysis. Likewise, Schmidt (1983) found in his analysis of the 

National Longitudinal Study of the High School Class of 1972 (NLS-72) that more academic 

coursetaking was generally associated with higher performance on standardized assessments. 

However, Schmidt indicated that the NLS-72 data were limited because credit measures were 

less desirable than content measures for assessing educational experiences. 

More recent research has used transcript data to better classify the content of courses and 

to assess the relation between curricular intensity and achievement (Chaney, Burgdorf, and Atash 

1997; Cool and Keith 1991; Perkins et al. 2004; Rock and Pollack 1995; Shettle et al. 2007). For 

example, Meyer (1999) analyzed HS&B data using a qualitative measure (e.g., advanced 

mathematics versus nonadvanced mathematics) rather than a quantitative one (e.g., number of 

1

 Each of the three NCES studies used in this report—High School and Beyond Longitudinal Study of 1980 

Sophomores (HS&B), National Education Longitudinal Study of 1988 (NELS:88), and Education Longitudinal 

Study of 2002 (ELS:2002)—used a standardized socioeconomic status variable based on a composite of education, 

income, and occupation and, in HS&B, household items. Household items (e.g., appliances, books) were sometimes 

used in NELS:88 when parent-reported income was missing. Household items were not used in ELS:2002. Instead, 

for this study, an imputation strategy was adopted for all missing elements. 

2 
Chapter 1. Introduction 

mathematics courses taken or credits earned) and found that advanced mathematics courses were 

associated with achievement gains for both college and non-college-bound students and for 

students with low to high mathematics skills. Furthermore, his analysis indicated that low-level 

courses such as basic and general mathematics were not statistically significantly associated with 

students’ development of mathematics skills in high school. These findings suggest that 

understanding curricular experiences requires measures that better capture the breadth and depth 

of course content. Credit counts provide some of the breadth needed to assess patterns of student 

coursetaking, and therefore remain useful alongside measures of specific courses taken. 

1.2 Pipeline Measures of Coursetaking 

In response to the desire to provide additional information about the course experiences 

of high school students, David Burkam and Valerie Lee from the University of Michigan 

developed a series of coursetaking measures called “pipeline” measures (Burkam 2003; Burkam 

and Lee 2003). The measures represent an initial attempt to capture students’ coursetaking 

experiences in terms of course content. Using 1992 transcript data from NELS:88, they 

developed pipeline measures in four subject areas: mathematics, science, English, and foreign 

language. Although the measures vary by subject area, they share important characteristics: (1) 

the categories on the scale are ordinal, distinguishing lower, middle, and upper level courses; and 

(2) each measure indicates the highest level of courses that a student completed in a particular 

subject during high school. Since they are based on course labels indicated on transcripts, the 

pipeline measures do not represent differences in content or academic challenge of the courses 

taken by individual students. They may also not account for differences in coursetaking 

availability for students in some schools, or for self-selection into courses. Nevertheless, they 

permit an examination of student coursetaking patterns beyond credit counts. 

1.2.1 Construction of the Pipeline Measures 

The pipeline measures are built on the assumption that students who complete advancedlevel coursework have mastered the skills of lower level courses and gained experience with 

more complex and advanced subject matter. In turn, these students should have a greater 

understanding of the subject area than their peers who reach only lower levels of the pipeline. 

Structured this way, the pipeline measures are better able to distinguish the degree of academic 

preparation and are hypothesized to be better predictors of student achievement than credit or 

Carnegie unit counts alone. 

The pipeline measures quantify the purported difficulty or content of courses, 

operationally defined as the course label. That is, the measures distinguish between lower level 

courses, which are assumed to be less difficult, and upper level courses in the same academic 

area, which are assumed to be more challenging. The four pipeline measures in the academic 

subject areas of mathematics, science, English, and foreign language were constructed by 

Burkam and Lee (2003; Burkam 2003) using high school transcript data from NELS:88 (Ingels 

et al. 1995). The high school courses taken by members of the NELS:88 sample, as they appear 

on the transcript file, were coded using high school or district course catalogs in accordance with 

the Classification Scheme of Secondary School Courses (CSSC), updated for the 1990 National 

3 
 

 

 

Chapter 1. Introduction 

Assessment of Educational Progress (NAEP) High School Transcript Study (Ingels et al. 1995).2 

Thus, the various levels of the pipeline measures were developed from the courses the NELS:88 

students took in high school during 1989 through 1992, and these constructed pipeline 

frameworks were used to classify the coursetaking behaviors of high school graduates in HS&B 

and ELS:2002. 

The purpose of the mathematics pipeline measure is to capture the nature of the most 

advanced-level mathematics course completed. To create this measure, Burkam and Lee 

examined the high school transcript component of NELS:88. They used the CSSC to identify all 

courses considered to be mathematics. In their analyses of these courses, they found that the 

mathematics curriculum in most schools followed a sequence of courses that increased in 

difficulty. Moreover, the mathematics curriculum was relatively homogenous: nearly 75 percent 

of NELS:88 sample members fit into one of five mathematics coursetaking patterns, with 

students who took more than one mathematics course taking sequentially more difficult and 

advanced-level courses than the preceding courses (e.g., algebra I only [a pattern taken by about 

12 percent of the NELS:88 sample] versus algebra I, geometry, and algebra II [a pattern taken by 

approximately 21 percent of the NELS:88 sample]) (Burkam and Lee 2003). 

For the mathematics pipeline measure, 47 high school courses (with nonzero enrollment) 

were initially assigned to one of four levels using their CSSC codes and a description of course 

content: nonacademic mathematics courses, low academic mathematics courses, middle 

academic mathematics courses, and advanced academic mathematics.3

 This initial four-level 

measure was expanded by Burkam and Lee (2003) to create a more detailed eight-level measure. 

The analysis presented in this report uses a condensed version of Burkam and Lee’s eight-level 

measure where the lowest categories are combined to yield sufficient cell sizes for statistical 

estimation. This approach does not alter the distributions of the advanced course levels, which 

are of most concern to educators and policymakers. Additionally, the category titles differ from 

the original ones used by Burkam and Lee; these were changed so that clearer interpretations can 

be drawn from the analyses:4 

• The no mathematics or low academic mathematics course level included 

− 1 = no mathematics or low academic mathematics (other general mathematics, 

mathematics 7, accelerated mathematics 7, mathematics 8, accelerated 

mathematics 8, general mathematics 1, general mathematics 2, science 

mathematics, mathematics in the arts, vocational mathematics, technical 

mathematics, mathematics review, mathematics tutoring, consumer mathematics, 

other actuarial sciences, other applied mathematics, basic mathematics 1, basic 

2

 The CSSC is designed to describe course offerings in secondary education and to provide a coherent means for 

classifying these courses. Each CSSC code comprises six digits, with an associated course title, alternate titles, and a 

course description. The first two digits identify the main program area (e.g., mathematics), the second set of two 

digits represents a subcategory of courses within the main program area (e.g., pure mathematics), and the last two 

digits are associated with the specific courses in each of the main and subcategories (e.g., trigonometry). 

3

 The number of mathematics courses included in the time series analysis in this report was expanded to 62 courses 

to accommodate additional courses identified in a review of transcripts from earlier (1982) and later (1998) years. 

New courses in the mathematics curriculum, as identified by the recent ELS:2002 transcript collection, have been 

assigned appropriate levels in the pipeline. 

4

 For example, Burkam and Lee (2003) used middle academic mathematics I, middle academic mathematics II, 

advanced mathematics I, advanced mathematics II, and advanced mathematics III as the category titles for levels 2 

through 6 presented here. 

4 
 

 

Chapter 1. Introduction 

mathematics 2, basic mathematics 3, basic mathematics 4, pre-algebra, algebra I– 

part 1, algebra I–part 2, or informal geometry). 

• Middle academic mathematics course levels included 

− 2 = algebra I/plane geometry (other pure mathematics, algebra I, plane geometry, 

solid geometry, unified mathematics 1, unified mathematics 2, geometry–part 1, 

geometry–part 2, unified mathematics 1–part 1, unified mathematics 1–part 2, 

pre-International Baccalaureate [IB] geometry, IB mathematics methods 1, IB 

mathematics studies 1, discrete mathematics, finite mathematics, algebra and 

geometry, or other mathematics); 

− 3 = algebra II (algebra II, unified mathematics III, or pre-IB algebra II/ 

trigonometry); and 

− 4 = algebra III/trigonometry/analytic geometry (algebra III, trigonometry, analytic 

geometry, trigonometry and solid geometry, algebra and trigonometry, algebra 

and analytic geometry, linear algebra, independent study, statistics, probability, 

probability and statistics, or Advanced Placement [AP] statistics). 

• Advanced academic mathematics course levels included 

− 5 = precalculus (introductory analysis or IB mathematics studies 2); and 

− 6 = calculus (calculus and analytic geometry, calculus, AP calculus, IB 

mathematics studies/calculus, or AP calculus CD). 

The percentages of graduates completing each individual course comprising the math 

pipeline measure is presented in appendix D—Course-Specific Completion Percentages 

(tables D-1, D-3, and D-5). The courses are arranged according to pipeline level. 

The science pipeline measure was developed using an examination of the science 

coursetaking patterns of the NELS:88 students. Because high school science coursetaking 

typically occurs across different strands or disciplines of science—life science (e.g., biology), 

chemistry, physics, and physical science (e.g., earth science, geology)—capturing highest 

science course completed along a single continuum of difficulty is less straightforward than it is 

with mathematics. For example, it is not completely clear that a 12th-grade advanced biology 

course, after 3 years of lower level, but sequentially more difficult, life science courses, is less 

difficult than a 12th-grade physics course after a year of biology and a year of chemistry. Initial 

analyses of the NELS:88 transcript data, however, revealed that science coursetaking in U.S. 

high schools appears to follow a pattern. Among the 30 different science courses taken by 

NELS:88 students, only 7 courses were ever completed by 10 percent or more of students 

(Burkam and Lee 2003, p. 31).5 

To develop the science pipeline measure, Burkam and Lee (2003) evaluated science 

courses using four criteria: (1) the subject matter of the course; (2) when the course was taken 

(e.g., freshman year, sophomore year, etc.); (3) whether the course was taken in conjunction with 

another science course; and (4) the complexity of the material likely taught in the course. Using 

5

 The seven courses that 10 percent or more of students ever completed were general biology 1 (68 percent), 

chemistry 1 (41 percent), physical science (39 percent), earth science (18 percent), unified science (15 percent), and 

basic biology 1 (10 percent) (unweighted percentages). 

5 
 

 

 

Chapter 1. Introduction 

these criteria, they created a seven-level science pipeline measure to capture the breadth and 

depth of students’ coursetaking histories. The continuum reflects the order of the most common 

science curriculum used in schools where students take general science courses first, followed by 

biology, chemistry, physics, and advanced biology. The analysis in this report uses a modified 

six-level version that combines “no science” with the most basic science: “primary physical 

science.” These categories are combined to yield sufficient cell sizes for statistical estimation. 

This method does not alter the distributions of the advanced course levels, which are of most 

concern to educators and policymakers. The categories are as follows: 

• 1 = no science6

 or low academic science (unified science, physical science, applied 

physical science, other geological sciences, earth science, college preparatory earth 

science, or miscellaneous physical sciences); 

• 2 = secondary physical science and basic biology (basic biology 1, basic biology 2, 

other biological and physical sciences, independent science study, outdoor education, 

other systems science, futuristics, environmental science, IB environmental studies, 

energy and environment, astronomy, other astronomy, other astrophysics, 

atmospheric sciences and meteorology, meteorology, introductory chemistry, 

chemistry in the community, organic biochemistry, physical chemistry, consumer 

chemistry, chemistry independent study, other chemistry, AP environmental science, 

geology, geology–field studies, mineralogy, oceanography, general physics, other 

physics, electricity and electronics science, acoustics, other planetary science, other 

rocketry and space science, or aerospace science); 

• 3 = general biology (general biology 1, general biology 2, honors biology 1, other 

biology, pre-IB biology, ecology, marine biology, advanced marine biology, zoology, 

other zoology, vertebrate zoology, invertebrate zoology, animal behavior, human 

physiology, advanced physiology, pathology, comparative embryology, or other life 

sciences); 

• 4 = chemistry I or physics I (chemistry 1, pre-IB chemistry, or physics 1); 

• 5 = chemistry I and physics I (highest completed courses include one level I 

chemistry course [see above] and one level I physics course [see above]); and 

• 6 = chemistry II or physics II or advanced biology (chemistry 2, IB chemistry 2, IB 

chemistry 3, AP chemistry, physics 2, IB physics, AP physics B, AP physics C: 

mechanics, AP physics C: electricity/magnetism, physics 2 without calculus, 

advanced biology, field biology, genetics, biopsychology, biology seminar, 

biochemistry and biophysics, biochemistry, botany, other botany, cell and molecular 

biology, cell biology, microbiology, microbiology other, other life sciences 

specialized areas, anatomy, IB biology 2, IB biology 3, or AP biology). 

The percentages of graduates completing each individual course comprising the science 

pipeline measure is presented in appendix D—Course-Specific Completion Percentages 

(tables D-2, D-4, and D-6). The courses are arranged according to pipeline level. 

6

 This category includes graduates who did not complete any courses in science or who completed only remediallevel science. It is possible for a graduate to have taken one or more courses in science but to be placed in the “no 

science” level. 

6 
 

 

 

 

 

Chapter 1. Introduction 

1.2.2 Validity of the Measures 

The pipeline measures were developed to measure the breadth and depth of preparation in 

key subject areas. The face validity of the measures depends on the proper classification of 

courses as described in the previous section—combining information about the timing, 

sequencing, and likely subject matter of math and science courses yields measures exhibiting 

strong face validity. In addition, these measures should have good predictive validity—that is, 

they should yield a strong association with academic achievement in their respective subject 

matters. Initial evaluations revealed that both pipeline measures meet these criteria. 

Burkam and Lee (2003) showed that the mathematics pipeline variable correlated .74 

with achievement on the NELS:88 twelfth-grade mathematics assessment (stronger than the .47 

correlation between math credits and math achievement). Further, the mathematics pipeline 

measure continued to demonstrate a significant relationship with math achievement once 

background characteristics were held constant. The science pipeline variable was positively 

correlated with the number of science items answered correctly on the NELS:88 tenth- and 

twelfth-grade assessments (correlations ranging from .42 to .52).7

 The somewhat weaker science 

correlations are not surprising given that mathematics courses follow a hierarchical sequence 

more closely than do science courses. See Burkam and Lee (2003) and Burkam (2003) for more 

information. 

1.3 Description of the Present Study 

This report presents data on the quantity and level of mathematics and science courses 

taken by three groups of graduating high school seniors: the class of 1982, the class of 1992, and 

the class of 2004. This work complements earlier studies that looked at trends in the number of 

courses taken up to the year 2000 (Perkins et al. 2004; Tuma and Burns 1996) and updates the 

data using transcript information from a recent graduating class. Unlike earlier trend studies that 

primarily looked at participation in vocational education (Tuma and Burns 1996), this work 

examines trends in academic coursetaking with a special focus on advanced-level coursetaking in 

high school. Specifically, the following questions are examined in this report: 

• Did the number of mathematics and science courses taken by graduating high school 

seniors change between 1982, 1992, and 2004? In other words, are recent high school 

graduates taking more, fewer, or about the same number of courses as their peers 

22 years earlier? 

• Did the level of mathematics and science courses taken by graduating high school 

seniors change between 1982, 1992, and 2004? In other words, apart from the number 

of courses taken, are recent high school graduates taking more advanced courses than 

their peers 22 years earlier? 

• Were there any differences within and across various subgroups (race/ethnicity, sex, 

socioeconomic status, educational expectations, and school sector) in terms of 

advanced-level coursetaking? If so, how did the differences change over the years? 

7

 Burkam and Lee did not correlate science credits with science achievement (for comparison to the science pipeline 

correlation with science achievement) in their analysis or conduct multivariate science coursetaking analyses as in 

the case of mathematics coursetaking. 

7 
 

 

 

 

Chapter 1. Introduction 

For example, were differences between Blacks8 and Whites in advanced-level 

coursetaking greater in 2004 than in 1982 or 1992? 

• Did the number and level of mathematics and science courses taken by graduating 

high school seniors with high educational expectations change between 1982, 1992, 

and 2004? 

The first two questions address general trends in coursetaking and demonstrate whether, 

on average, training in mathematics and science has changed over the past two decades. The 

third question assesses whether well-documented differences in educational experiences have 

increased, decreased, or persisted into the 21st century. The final question addresses the growing 

concern among researchers and policymakers that students who leave high school with lofty 

educational plans do not have the academic preparation to achieve them. 

The data for this report come from surveys conducted by NCES between 1982 and 2004. 

These surveys are (1) the High School and Beyond Longitudinal Study of 1980 Sophomores 

(HS&B), (2) the National Education Longitudinal Study of 1988 (NELS:88), and (3) the 

Education Longitudinal Study of 2002 (ELS:2002). The report focuses on three cohorts: the high 

school graduating class of 1982 (surveyed by HS&B), the high school graduating class of 1992 

(surveyed by NELS:88), and the high school graduating class of 2004 (surveyed by ELS:2002). 

Only those graduates who had complete high school transcripts available in their respective 

dataset were included in the analysis. It is important to note that by including only high school 

graduates in this analysis, it is possible that the findings reflect the coursetaking histories of 

higher achieving students, since dropouts are more likely to be less academically proficient. The 

sample of graduates may exclude some of those who were most likely to take the lowest level 

courses (as well as some students, such as early graduates, who may have taken relatively more 

advanced courses). However, because comparison of the cohort dropout rates from sophomore to 

senior year for the three studies shows that the dropout rate declined from 1982 to 1992 and then 

remained relatively stable from 1992 to 2004, it is unlikely that reported trends simply are an 

artifact of school dropout rates.9

 Moreover, an analysis of NELS:88 found that increased course 

requirements were not associated with higher dropout rates (Hoffer 1997). Appendix A section 

A.4 includes a bias analysis of the samples used in this report. 

Some caution in interpreting the report’s findings should be considered because of 

differences in data collection methodology across the studies. Differences in the sampling 

frames, eligibility requirements, and transcript collection methodologies could possibly account 

for increases or decreases in the proportion of students taking advanced-level academic courses. 

Both NELS:88 and ELS:2002 high school transcript studies are based on a 12th-grade cohort; 

HS&B, however, is based on a 1980 sophomore cohort two years later (in 1982). HS&B 

excluded students with severe mental, physical, or linguistic barriers from its transcript 

collection, while NELS:88 included some of these students; ELS:2002, however, pursued 

8

 In this report, Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or 

Other Pacific Islander, and American Indian includes Alaska Native. Respondents who identified themselves as 

being of Hispanic origin are classified as Hispanic, regardless of race. Choosing more than one race was not 

permitted in HS&B and NELS:88. 

9 The spring sophomore to spring senior cohort dropout rate was 11.4 percent in 1982 (HS&B), 6.2 percent in 1992 

(NELS:88), and 6.9 percent in 2004 (ELS:2002) (Kaufman, McMillen, and Sweet 1996; Ingels, Planty, and Bozick 

2005). Event dropout rates based on Current Population Survey data show a similar trend of long-term decline but 

rough stability from about 1990 (Laird et al. 2006). 

8 
Chapter 1. Introduction 

transcripts for all students eligible for its student questionnaire. Finally, both HS&B and 

NELS:88 collected transcripts from the last school attended by the students (which normally but 

not invariably included the full cumulative record), while ELS:2002 collected transcripts from 

the students’ base-year school (i.e., the school from which they were originally sampled) and 

their final school if they transferred out of their base-year school. All of these issues are 

discussed in detail in section A.5 of appendix A. 

Comparisons drawn in the text of this report have been tested for statistical significance 

at the .05 level using t statistics to ensure that the differences are larger than those that might be 

expected because of sampling variation. Given the large sample sizes for each of the three 

studies used in this report, some comparisons of relatively small differences are likely to meet 

this criterion of statistical significance. In order to focus the discussion, effect sizes are employed 

as a second criterion. In comparing means, the effect size is the standardized difference, which is 

expressed in terms of standard deviation units. A standardized difference of 0.2 (or one-fifth of a 

standard deviation) or larger was selected as the criterion for determining which statistically 

significant differences would be reported. For comparisons of proportions, a 5 percentage point 

or greater difference between estimates was established as the criterion for determining which 

statistically significant differences would be reported. Differences were reported in the text only 

if the comparison met the criteria of both statistical significance and substantive difference. See 

appendix A for further discussion of these criteria; see appendix B for the standard errors of the 

estimates used in these calculations. 

Readers interested in learning more about trends in high school coursetaking should read 

the recently released publication The High School Transcript Study: A Decade of Change in 

Curricula and Achievement, 1990–2000 (Perkins et al. 2004). A Decade of Change builds upon 

earlier NAEP High School Transcript Study trend reports (Roey et al. 2001) by extending the 

trend line to an examination of the coursetaking patterns of high school graduates as of 2000. It 

includes information about coursetaking patterns in 1990, 1994, 1998, and 2000, and may be 

used alongside of the current report’s findings to examine the timing of coursetaking changes. 

However, because of differences in the purposes and designs of the longitudinal studies (HS&B, 

NELS:88, and ELS:2002) and NAEP, the current study and the NAEP-based studies report 

slightly different analyses. For example, the present analysis examines patterns in coursetaking 

by socioeconomic status and educational expectations—information not collected in NAEP. 

However, the most salient difference between the current analysis and the NAEP-based studies is 

the foci of the reports. A Decade of Change examines trends over time in the number of credits 

students earned in various subject areas, whereas the present report investigates the number of 

credits earned and changes over time in the level of courses taken by students, focusing primarily 

on changes in advanced-level coursetaking. For more recent studies that examine coursetaking, 

see America’s High School Graduates: Results from the 2005 High School Transcript Study 

(Shettle et al. 2007) and High School Coursetaking: Findings from The Condition of Education 

2007 (Planty, Provasnik, and Daniel 2007). It should be pointed out that the Condition of 

Education report uses a wider range of graduation dates (September 1 of prior year to August 31 

of graduation year) as compared to the spring-term senior definition of this report (January 1 to 

August 31 of graduating year). This results in slight differences in some estimates for the two 

studies. 

9 
Chapter 1. Introduction 

Every effort has been made to make all variables used in this report as comparable as 

possible across the three studies. For both transcript variables (course credits and pipeline) and 

classification variables (e.g., sex, race/ethnicity), similar measures and procedures were used to 

ensure the maximum amount of cross-study comparability. Some subtle differences exist for 

some variables, however, in particular for the construction of socioeconomic status quartile. A 

glossary of variables is provided in section A.7 of appendix A. 

Four appendixes are included in the report. Appendix A includes technical notes and 

documentation of methodology, including an account of the sources of the data, statistical 

procedures, and a bias analysis. Appendix B contains standard errors for all estimates, as well as 

standard deviations and rounded sample sizes for all means. Appendix C supplies rounded 

sample sizes for select subgroups. Finally, appendix D presents the percentage distribution of 

individual mathematics and science courses in which the three cohorts of graduating seniors 

earned credits. 

10 
 

 

Chapter 2 

Trends in Mathematics Coursetaking: 1982–2004 

This chapter examines changes in mathematics coursetaking in terms of accumulated 

credits in math and the level of math courses taken. Credits earned indicate both the total amount 

of mathematics preparation received in high school and the continuity of that instruction: four 

credits of math in high school equates to a full-year math course each year between 9th and 12th 

grade, and it represents a common ceiling on total possible math instruction in high school given 

other academic requirements and the sequential structure of most mathematics courses. Earlier 

recommendations for increased curriculum standards called for a minimum threshold of three 

credits in math required for graduation (National Committee on Excellence in Education 1983; 

Council of Chief State School Officers 2005). Inasmuch as states and districts have established 

credit minima consistent with these recommendations, but have not required or advocated four 

credits of math for high school graduation, credit counts may reflect relatively small variation 

between the three-credit floor and the four-credit ceiling. 

In addition, as noted in chapter 1, credit counts say little about the content or difficulty of 

the courses taken, nor can they indicate if a student began high school later in the mathematics 

pipeline (with, for example, algebra I already completed). The mathematics coursetaking 

pipeline measure used here is an ordered, sequential measure moving from no or low academic 

coursework to middle-level courses (such as algebra I, plane geometry, algebra II, or algebra III) 

to advanced courses (such as precalculus or calculus). A graduate’s assignment to a level 

represents the highest level of high school mathematics coursework he or she completed at the 

point on the curriculum continuum where the student exited the pipeline (i.e., precluding 

completion of mathematics courses at higher levels while in high school).10 

The findings for mathematics are first reported overall and then by student subgroups 

(sex, race/ethnicity, socioeconomic status, educational expectations, and school sector). The 

principal findings of this chapter are consistent: from 1982 to 2004, graduates increased the 

number of math credits they accumulated, stopped much less often with lower level math 

courses, and repeatedly increased their involvement in higher level math courses. 

2.1 Overall Trends in Mathematics Coursetaking 

Overall, high school graduates earned more credits in mathematics in 2004 than in either 

1992 or 1982; the average number of credits in mathematics students earned by the time of 

graduation rose from 2.7 credits in 1982 to 3.6 credits in 2004. This represents nearly one full 

academic year of additional mathematics by graduates, on average. Growth in number of credits 

earned by graduates, however, was greater between 1982 and 1992 (an increase of 0.6 credits) 

than between 1992 and 2004 (an increase of 0.3 credits), perhaps representing a ceiling effect. 

10 Although it is logical to assume that a student exiting the pipeline at the middle or advanced level completed all 

earlier courses in the pipeline, this is not necessarily the case. For example, when students reach the advanced level, 

it means that they have completed at least one advanced-level course (precalculus or calculus) and may or may not 

have completed courses at levels below the advanced level. However, given the sequential nature of the high school 

mathematics curriculum, it is implied that students who have reached a certain level have an understanding of the 

mathematical concepts taught at lower levels. 

11 
Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

In addition to overall increases in credits earned, graduates’ coursetaking patterns 

increasingly included more upper-level courses. Figure 1 shows the distribution of the 

mathematics pipeline across the three studies. The overall pattern is a 33 percentage point growth 

from 1982 to 2004 in the top four mathematics course levels completed (from about 45 percent 

to 77 percent), with a corresponding drop in the two lowest math levels over that time period (56 

to 23 percent). The largest percentage point decrease—20 points from 1982 to 2004—occurred 

for graduates taking no math or low academic math courses. Among the advanced courses, the 

largest shift occurred in precalculus: in 2004, 19 percent of graduates’ highest course was 

precalculus, compared with 5 percent in 1982—a 14 percentage point increase. 

Although growth in aggregate mathematics credits earned was higher between 1982 and 

1992 than between 1992 and 2004, the increase in advanced coursetaking was comparable 

between the two time periods. For example, the percentage of seniors graduating high school 

with precalculus or calculus as their highest class grew by 11 percentage points between 1982 

and 1992 and between 1992 and 2004. However, the decline in low-level mathematics courses 

(no or low math courses and algebra I/plane geometry) was greater in the first period (20 

percentage points) than in the second (12 percentage points). 

Although student coursetaking patterns shifted from 1982 to 2004 to include more 

challenging mathematics courses, the percentage of graduates who stopped taking mathematics 

at the level of algebra I or algebra II remained relatively high in 2004. The combined percentage 

of students completing either algebra I or algebra II was 49 percent in 1982, 49 percent in 1992, 

and 44 percent in 2004. Yet, whereas in 1982, a greater percentage of graduates left high school 

with algebra I (31 percent) than algebra II (18 percent) as their highest course, by 2004, this 

pattern was reversed; the percentage of students completing algebra II (26 percent) was higher 

than the percentage of students completing algebra I (18 percent). Thus, while the total 

percentage of students completing these two course levels declined by only 5 percent from 1982 

to 2004, closer inspection of coursetaking at the middle level shows a shift toward more 

challenging courses. 

12 
Figure 1. Percentage of high school graduates who completed different levels of mathematics 

courses: 1982, 1992, and 2004 

Year 

1982 24.9 30.6 18.2 15.6 4.8 5.9 

1992 12.9 22.6 26.4 16.4 11.0 10.7 

2004 5.2 18.1 25.7 18.0 18.9 14.1 

Algebra I/plane 

geometry 

Algebra III/trigonometry/ 

analytic geometry 

Precalculus 

No math or low 

academic math 

Algebra II 

Calculus 

0.0 20.0 40.0 60.0 80.0 100.0 

 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Percent 

NOTE: Detail may not sum to totals because of rounding. See appendix table B-1 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

2.2 Trends in Mathematics Coursetaking Among Student Subgroups 

2.2.1 Sex 

Figure 2 shows the distribution of mathematics credits by sex, and figure 3 shows the 

distribution of the mathematics pipeline by sex. Changes in mathematics coursetaking for males 

and females parallel the overall trend. The mean number of credits earned in mathematics by 

both groups increased from 1982 to 2004, with a larger increase between 1982 and 1992 than 

between 1992 and 2004. In all years, no differences were detected in the average math credits 

earned by females and those earned by males. 

13 
 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Figure 2. Mean credits earned in mathematics by high school graduates, by sex: 1982, 1992, and 

2004 

2.8 2.6 

3.3 3.3 

3.6 3.6 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0

1982 

1992 

2004 

Mean credits 

 Male Female 

Gender 

NOTE: See appendix table B-2 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

In the math pipeline, males and females maintained growth in advanced-level 

mathematics courses (figure 3). Between 1982 and 2004, males and females both were more 

likely to take algebra II, precalculus, or calculus and less likely to finish high school with only no 

or low academic math courses or algebra I/geometry. The largest increases for both males and 

females were in precalculus-level coursetaking (from 5 percent to 18 percent for males, and 5 to 

20 percent for females), and the largest decreases were in the proportion taking no math or low 

academic math courses (from 26 to 6 percent for males, and 24 to 4 percent for females). In each 

of the cohorts, no differences were detected between females and males in the combined 

percentage completing advanced mathematics courses (figure 4). Thus, the coursetaking patterns 

for males and females are similar across all three cohorts. 

14 
 

Figure 3. Percentage of high school graduates who completed different levels of mathematics 

courses, by sex: 1982, 1992, and 2004 

Male 

1982 26.1 28.1 17.7 16.4 5.1 6.6 

1992 14.8 23.1 24.4 16.1 10.5 11.2 

2004 6.1 19.6 25.2 16.7 17.6 14.7 

Female 

1982 23.8 32.9 18.6 14.9 4.5 5.3 

1992 11.1 22.2 28.4 16.6 11.4 10.3 

2004 4.3 16.6 26.2 19.3 20.1 13.5 

Algebra I/plane 

geometry 

Algebra III/trigonometry/ 

analytic geometry 

Precalculus 

No math or low 

academic math 

Algebra II 

Calculus 

 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

0.0 20.0 40.0 60.0 80.0 100.0 

Percent 

NOTE: Detail may not sum to totals because of rounding. See appendix table B-3 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

15 
 

 

 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Figure 4. Percentage of high school graduates who completed precalculus or calculus, by sex: 

1982, 1992, and 2004 

Percent 

100.0 

80.0 

60.0 

40.0 

20.0 

0.0 

11.7 9.8 

21.6 21.7 

32.4 33.6 

Male Female 

Gender 

NOTE: See appendix table B-3 for standard errors of these estimates. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

2.2.2 Race/Ethnicity 

Figure 5 shows the distribution of mathematics credits by race/ethnicity, and figure 6 

shows the distribution of the mathematics pipeline by race/ethnicity. Between 1982 and 2004, 

and in each time period (1982–1992 and 1992–2004), the mean number of credits earned by 

graduates from all racial/ethnic groups increased, except that the mean number of credits earned 

by Hispanic graduates did not show a measurable difference in the latter period of 1992 to 2004. 

The largest increase in the number of credits earned occurred among Blacks and Hispanics, 

whose mean credits grew from 2.4 to 3.7 credits for Blacks and from 2.8 to 3.4 credits for 

Hispanics between 1982 and 2004. In 1982, Asian students earned, on average, more credits in 

math than students in all other race/ethnic groups; by 2004, however, Asian students earned more 

credits than Hispanic or White students only. In addition, the credit gap between Asians and their 

White peers decreased between 1982 and 2004.11 

1982 

1992 

2004 

11 Since, as noted earlier in this report, cohort dropout rates have declined (since 1982) or held relatively steady 

(between 1992 and 2004), the overall trend of increased coursetaking in mathematics and science or higher level 

course enrollment in these subjects would not seem, in part or whole, to be an artifact of trends in early school 

leaving. However, in comparing one group to another at any of the three points in time, it is of note that dropout 

rates may differ substantially by subgroup, so that the proportion of the original cohort completing the high school 

curriculum is different for various race/ethnicity and sex groups. For example, in terms of a cohort dropout rate, 11 

percent of NELS:88 1988 8th-graders were classified as dropouts 4 years later (spring term 1992), but proportions 

differed by race/ethnicity group: 18 percent of Hispanics were dropouts, as were 13 percent of Blacks, 9 percent of 

Whites, and 5 percent of Asians (McMillen, Kaufman, and Klein 1997). 

16 
 

 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Figure 5. Mean credits earned in mathematics by high school graduates, by race/ethnicity: 1982, 

1992, and 2004 

2.4 

3.2 

2.4 

2.8 2.6 

3.0 

3.5 3.3 3.2 3.3 3.3 

3.8 3.7 

3.4 3.6 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0 

1982 

1992 

2004 

Mean credits 

American Indian Asian Black Hispanic White 

Race/ethnicity 

NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and 

American Indian includes Alaska Native. See appendix table B-4 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

Across all racial/ethnic groups, high school senior coursetaking patterns in each of the 

three studies increasingly included higher level mathematics classes (figure 6). Between 1982 

and 2004, the percentage of seniors taking no mathematics or low academic mathematics courses 

for all racial/ethnic groups decreased. The most dramatic declines in the percentages of students 

taking no or low academic mathematics courses were seen among non-Asian minority groups: 

for American Indians, the decline was from 48 percent in 1982 to 13 percent in 2004; for Blacks, 

the decline was from 41 percent in 1982 to 7 percent in 2004; and for Hispanics, the decline was 

from 39 to 6 percent across the same period. For Blacks and Hispanics, these declines were 

greater between 1982 and 1992 than between 1992 and 2004. 

17 
Figure 6. Percentage of high school graduates who completed different levels of mathematics 

courses, by race/ethnicity: 1982, 1992, and 2004 

American Indian 

# 

1982 48.0 27.8 13.4 8.6 2.3 

2.1 

1992 28.9 28.5 28.0 11.6 1.0 

2004 13.3 23.7 40.8 9.3 7.5 5.4 

Asian 

1982 10.6 17.2 19.1 23.0 14.6 15.4 

1992 9.2 12.5 23.9 12.9 19.5 22.1 

2004 2.1 11.1 17.5 12.5 23.0 33.8 

Black 

2.0 1982 40.6 27.7 18.5 9.2 2.0 

1992 18.9 32.0 23.5 12.0 6.7 6.9 

2004 6.6 18.7 31.5 24.1 14.2 4.9 

Hispanic 

2.7 1982 39.1 33.1 13.8 8.6 2.6 

1992 14.1 30.9 26.3 16.1 7.8 5.0 

2004 6.4 26.5 31.9 13.2 14.9 7.0 

White 

1982 20.5 30.9 18.9 17.5 5.4 6.8 

1992 11.9 20.8 26.9 17.3 11.6 11.5 

2004 4.6 16.4 23.8 18.5 20.6 16.2 

0.0 20.0 40.0 60.0 80.0 100.0 

Percent 

Algebra I/plane 

geometry 

Algebra III/ 

trigonometry/analytic 

geometry 

Precalculus 

No math or low 

academic math 

Algebra II 

Calculus 

 

 

 

 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

# Rounds to zero. 

NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and 

American Indian includes Alaska Native. Detail may not sum to totals because of rounding. See appendix table B-5 for standard 

errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

At the middle coursetaking level of algebra II, American Indian, Black, and Hispanic 

students made gains between 1982 and 2004. Whereas 13 percent of American Indian graduates 

left high school with algebra II as their highest course in 1982, 41 percent did so in 2004, a gain 

of 27 percentage points. Similarly, 31 percent of Black graduates completed algebra II as their 

highest course in 2004, compared with 19 percent in 1982. While 14 percent of Hispanic 

graduates completed algebra II as their highest course in 1982, 32 percent did so in 2004, an 

18 
 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

increase of 18 percentage points. Black graduates also completed algebra III/trigonometry/ 

analytic geometry at higher levels in 2004 than in 1982 (24 percent compared with 9 percent). 

At the advanced levels of math coursetaking, all groups completed precalculus at a higher 

rate in 2004 than in 1982. Among non-Asian groups, in 1982, almost no American Indians, 2 

percent of Blacks, 3 percent of Hispanics, and 5 percent of Whites graduated from high school 

with precalculus as their highest course, whereas in 2004, 8 percent of American Indians, 14 

percent of Blacks, 15 percent of Hispanics, and 21 percent of Whites did so. In addition, Whites 

completed calculus at higher rates in 2004 than in 1982 (16 percent compared with 7 percent). 

Compared to all groups except Whites, Asian graduates had higher percentages of 

students completing precalculus and calculus in all cohorts. In 1982, 15 percent of Asian 

graduates completed precalculus and 15 percent completed calculus as their highest level 

courses. By 2004, 23 percent of Asian students completed precalculus and 34 percent completed 

calculus. Compared to Whites, Asians also participated in precalculus and calculus at higher 

levels in 1982 and 1992. However, while Asians continued to complete calculus at higher levels 

than Whites in 2004 (34 percent compared with 16 percent), the rates of completion for 

precalculus for Asians and Whites were not significantly different in 2004 (23 and 21 percent, 

respectively). In contrast, only 7 percent of Hispanics, 5 percent of Blacks, and 5 percent of 

American Indians completed calculus in 2004. It is worth noting that in addition to completing 

calculus at higher levels than all other racial/ethnic groups, Asian graduates made the greatest 

gains in the percentage of students completing calculus between 1982 and 2004. 

Despite the progress made by Black, Hispanic, and American Indian graduates in taking 

precalculus or calculus between 1982 and 2004, disparities remained across all three cohorts 

when comparing these students with their Asian and White counterparts. For example, in 2004, 

fully 57 percent of Asian graduates completed precalculus or calculus and 37 percent of Whites 

(a statistically lower percentage than that of Asians) completed one of these high-level courses 

(figure 7). In comparison, only 22 percent of Hispanics, 19 percent of Blacks, and 13 percent of 

American Indians completed either precalculus or calculus in 2004. 

19 
 

 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Figure 7. Percentage of high school graduates who completed precalculus or calculus, by 

race/ethnicity: 1982, 1992, and 2004 

Percent 

100.0 

80.0 

60.0 

40.0 

20.0 

0.0 

2.3 

30.1 

4.0 5.3 

12.2 

3.1 

41.6 

13.6 12.7 

23.0 

12.9 

56.8 

19.0 21.9 

36.7 

American Indian Asian Black Hispanic White 

1982 

1992 

2004 

Race/ethnicity 

NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and 

American Indian includes Alaska Native. See appendix table B-5 for standard errors for these estimates. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

2.2.3 Socioeconomic Status 

Figure 8 shows the distribution of mathematics credits by socioeconomic status (SES), 

and figure 9 shows the distribution of the mathematics pipeline by SES (see appendix A, section 

A.7.1, for discussion of the construction of SES quartiles across the three studies). The mean 

number of credits earned by graduates across SES levels increased between 1982 and 2004. 

Students in the highest SES quartile earned, on average, the most number of credits in 

mathematics in 1982, 1992, and 2004 (3.1 credits, 3.6 credits, and 3.8 credits, respectively). 

Nevertheless, marked increases in credits earned occurred between 1982 and 2004 for students in 

the lowest two quartiles, rising from 2.4 in 1982 to 3.4 credits in 2004 for students in the first 

quartile and from 2.5 to 3.5 credits for students in the second quartile. Furthermore, by 2004, the 

gap between credits earned by students in the highest versus the lowest quartile declined from 

0.8 credits in 1982 to 0.3 credits in 2004. 

20 
 

 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Figure 8. Mean credits earned in mathematics by high school graduates, by socioeconomic 

status: 1982, 1992, and 2004 

2.4 2.5 

2.8 

3.0 3.1 3.1 

3.3 

3.6 3.4 3.5 3.6 3.8 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0

1982 

1992 

2004 

Mean credits 

 First quartile (lowest) Second quartile Third quartile Fourth quartile (highest) 

Socioeconomic status 

NOTE: See appendix table B-6 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

As with the overall trends, students in all SES subgroups increasingly finished high 

school with upper level math courses and less often finished with only lower level math courses 

(figure 9). Smaller proportions of students completed only algebra I, low academic, or no 

mathematics courses in high school in 2004 than in 1982. In particular, the percentages of 

students in the lowest and second quartiles graduating without taking mathematics courses or 

taking only low academic courses dropped considerably from 1982 to 1992, and then again from 

1992 to 2004. In 1982, 43 percent of students in the lowest quartile and 29 percent of students in 

the second quartile completed no or low academic mathematics courses. By 2004, these 

proportions had dropped to 11 percent and 6 percent, respectively. 

At the middle level of math coursetaking, a greater proportion of students in the first 

(lowest), second, and third SES quartiles finished high school with algebra II-level courses; for 

example, the percentage of students in the first quartile exiting the pipeline at algebra II more 

than doubled from 1982 to 2004, increasing from 14 to 29 percent. In addition, a greater 

proportion of graduates from the first SES quartile also took algebra III-level courses. At the top 

SES quartile, however, a smaller proportion of students took algebra III-level courses in 2004 

(19 percent) than in 1982 (24 percent), while no differences were detected over that period in the 

proportions of top SES quartile students taking algebra II as their highest course. 

Instead, gains for the highest SES students occurred at the advanced mathematics levels 

(precalculus and calculus). The highest SES graduates completed calculus at a 15 percentage 

point higher rate over time, increasing from 12 percent in 1982 to 27 percent in 2004. Although 

students in all SES groups completed courses in precalculus and calculus at a greater rate in 2004 

than in 1982, the percentages of graduates from quartiles below the fourth (highest) SES quartile 

completing calculus were much lower (e.g., 6 percent of first quartile graduates completed 

calculus in 2004) than those in the fourth SES quartile. In addition, fourth SES quartile students 

21 
 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

also increasingly outpaced their closest peers in the third SES quartile: the gap between the 

percentage of highest quartile and third quartile students completing calculus grew from a 7 

percentage point gap to 14 percentage points between 1982 and 2004. Students in the highest 

SES quartile also made greater absolute gains in completing precalculus than did their peers in 

the first and second quartiles. For example, while the percentage of highest quartile students who 

left high school with precalculus as their highest course increased from 8 percent in 1982 to 26 

percent in 2004, the lowest SES quartile students grew from 1 percent in 1982 to only 11 percent 

by 2004. 

Figure 9. Percentage of high school graduates who completed different levels of mathematics 

courses, by socioeconomic status: 1982, 1992, and 2004 

First quartile 1.1 (lowest) 1982 1.6 

4.7 

1992 3.4 

2004 

Second quartile 

3.1 

1982 3.6 

1992 

2004 

Third quartile 

1982 

1992 

2004 

Fourth quartile 

(highest) 

1982 

1992 

2004 1.7 

42.6 32.9 

24.4 31.6 

10.5 27.7 

28.6 32.2 

16.0 29.7 

5.8 25.3 

19.2 32.7 

9.5 21.5 

3.8 

10.2 25.8 

4.4 11.6 

7.4 19.1 

24.4 

19.3 

27.4 

29.6 

19.8 

28.8 

25.9 

19.7 

29.2 

26.2 

14.0 7.9 

9.7 

15.0 

12.8 

15.3 

17.4 

17.0 

17.5 

19.5 

24.2 

21.1 

19.4 

8.3 

11.5 

6.0 

15.0 

8.1 

11.3 6.4 

5.1 

5.4 

15.3 

12.1 

21.3 

17.7 

7.7 

10.4 

12.7 

20.7 

25.9 26.6 

No math or low 

academic math 

Algebra I/plane 

geometry 

Algebra II 

Algebra III/ 

trigonometry/ analytic 

geometry 

Precalculus 

Calculus 

0.0 20.0 40.0 60.0 80.0 100.0 

Percent 

NOTE: Detail may not sum to totals because of rounding. See appendix table B-7 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

22 
Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Figure 10. Percentage of high school graduates who completed precalculus or calculus, by 

socioeconomic status: 1982, 1992, and 2004 

Percent 

100.0 

80.0 

60.0 

40.0 

20.0 

0.0 

 

2.7 

6.7 

11.3 

20.5 

8.0 

13.2 

21.9 

38.5 

17.7 

22.7 

34.0 

52.4 

First quartile (lowest) Second quartile Third quartile Fourth quartile (highest) 

1982 

1992 

2004 

Socioeconomic status 

NOTE: See appendix table B-7 for standard errors for these estimates. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

2.2.4 Educational Expectations 

Figure 11 shows the distribution of mathematics credits by educational expectations, and 

figure 12 shows the distribution of the mathematics pipeline by educational expectations. Not 

surprisingly, the number of credits earned is related to students’ expectations for their future 

education. In 1982, 1992, and 2004, students with the highest educational expectations earned 

more credits in mathematics than their peers with less ambitious expectations. However, from 

1982 to 2004, the mean number of credits earned by graduating seniors across all levels of 

educational expectations increased. In addition, students expecting to earn no more than a high 

school diploma or General Educational Development (GED) certificate showed the greatest gain 

in credits earned, increasing from 2.1 credits in 1982 to 3.2 credits in 2004, a gain of 1.1 credits. 

This gain is associated with a smaller gap compared with graduates expecting to earn a graduate 

degree. For example, the difference in average credits between the two student groups (those 

who expected no more than a high school diploma versus those who expected a graduate degree) 

declined from 1.3 in 1982 to 0.6 credits in 2004. This decrease in disparity suggests that youth 

with different educational expectations are more uniformly exposed to mathematics content 

today than 22 years earlier. 

23 
 

 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Figure 11. Mean credits earned in mathematics by high school graduates, by educational 

expectations: 1982, 1992, and 2004 

2.1 

2.4 

3.1 

3.4 

2.3 2.4 

3.1 

3.4 3.2 3.2 

3.6 

3.8 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0 

1982 

1992 

2004 

Mean credits 

High school diploma/ Some postsecondary Baccalaureate degree Graduate degree 

GED or less education 

Educational expectations 

NOTE: See appendix table B-8 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

The pipeline results show that shifts in coursetaking from 1982 and 2004 are somewhat 

uneven for students with different educational expectations (figure 12). For students of all levels 

of educational expectations, there was a decrease in the proportions graduating without or with 

low academic math courses. For example, among graduates who expected a baccalaureate 

degree, the proportions completing high school with no or low academic math courses declined 

from 9 percent in 1982 to 2 percent in 2004. For all students except those expecting a high 

school diploma or less, there were declines between 1982 and 2004 in the proportions finishing 

with just algebra I/plane geometry. 

Further up the pipeline, students expecting a high school diploma or less increased their 

enrollment—for example, moving from 10 percent finishing with algebra II in 1982 to 22 

percent in 2004. Students with the highest expectations, however, finished high school with 

algebra II or algebra III-level courses less often, with increases more prominent in the advanced 

math courses. For example, among students expecting a graduate degree, algebra III-level-only 

completion declined from 27 percent in 1982 to 19 percent in 2004. At advanced mathematics 

levels, however, proportions of these students taking precalculus increased from 12 percent in 

1982 to 26 percent in 2004. By contrast, there were no detectable differences between 1982 and 

2004 in the proportions of students attaining calculus for students who expected no more than a 

high school diploma or only some postsecondary education. Thus, the pattern across expectation 

levels is a decline over time in the lowest level math courses, an increase in the highest level 

only for students expecting at least a college degree, and mixed results for courses in between. 

In terms of differences over time between students with varying expectations, the results 

indicate that gaps in preparation persisted over time and in some cases grew. With each 

graduating class, graduates at the lowest two levels of educational expectations were more likely 

to exit the mathematics pipeline at the level of algebra I than their peers with higher educational 

24 
 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

expectations. In 2004, 40 percent of students expecting to obtain a high school diploma, GED, or 

less and 36 percent of students expecting to obtain some postsecondary education left high 

school with algebra I as their highest mathematics course, compared with 15 percent of students 

expecting to earn a baccalaureate degree and 7 percent of students expecting to earn a graduate 

degree. For the two lowest levels of math courses, this represents a slightly smaller gap (by 6 

percentage points) than observed in 1982 between graduates expecting a high school diploma or 

less and those expecting a graduate degree. 

By contrast, in all three cohorts, graduates who expected to earn a baccalaureate degree 

or graduate degree were more likely than their peers with lower educational expectations to 

complete precalculus or calculus (figure 13). Fifty-three percent of those expecting to earn a 

graduate degree completed precalculus or calculus in high school, and 33 percent of those 

expecting only a bachelor’s degree did so. But only 8 percent of graduates expecting some 

postsecondary education only, and only 2 percent of graduates expecting a high school diploma 

or less, completed precalculus or calculus courses. These disparities persisted and grew much 

wider from 1982 to 2004: at these two highest course levels, the gap was about 27 percentage 

points in 1982 between those expecting, at most, a high school diploma and those expecting a 

graduate degree; in 2004, this gap was 51 percentage points. 

25 
Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Figure 12. Percentage of high school graduates who completed different levels of mathematics 

courses, by educational expectations: 1982, 1992, and 2004 

High school 

diploma/ 

GED or 1982 less 

1992 

2004 

Some 

postsecondary 

education 1982 

1992 

2004 

Baccalaureate 

degree 

1982 

1992 

2004 

Graduate degree 

1982 

1992 

2004 

 

4.4 

49.9 35.2 9.7 

38.8 33.4 22.3 

24.5 40.1 21.9 11.4 

29.1 40.2 16.8 10.3 

26.1 37.6 25.0 9.1 

11.0 36.1 32.6 12.6 6.6 

8.9 26.2 25.3 23.6 7.6 8.3 

18.0 31.5 21.6 14.0 10.0 

14.5 29.1 21.3 21.7 11.1 

6.4 16.9 22.9 26.5 11.6 15.7 

11.3 22.6 20.4 18.2 23.1 

7.3 19.0 19.2 26.1 26.8 

0.2 

0.6 

2.9 

1.3 

1.3 

1.8 

0.4 

1.7 

1.8 

1.9 

0.4 

1.1 

4.9 

2.3 

4.4 

1.6 

No math or low 

academic math 

Algebra I/plane 

geometry 

Algebra II 

Algebra III/ 

trigonometry/analytic 

geometry 

Precalculus 

Calculus 

0.0 20.0 40.0 60.0 80.0 100.0 

Percent 

NOTE: Detail may not sum to totals because of rounding. See appendix table B-9 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

26 
 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Figure 13. Percentage of high school graduates who completed precalculus or calculus, by 

educational expectations: 1982, 1992, and 2004 

0.7 3.5 

15.9 

27.3 

2.6 2.3 

23.9 

41.3 

2.2 

7.7 

32.8 

52.9 

0.0 

20.0 

40.0 

60.0 

80.0 

100.0 1982 

1992 

2004 

Percent 

High school diploma/ Some postsecondary Baccalaureate degree Graduate degree 

GED or less education 

Educational expectations 

NOTE: See appendix table B-9 for standard errors for these estimates. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

2.2.5 School Sector 

Compared to student characteristics and expectations, school sector represents one aspect 

of the context in which coursetaking occurs. Students attending schools in separate sectors may 

be systematically exposed to different curricular opportunities and varying peer influences 

related to selecting courses. Some graduates may also have attended schools in different sectors 

over their high school career. The following results thus represent the profile of school sector 

graduates and not the curriculum of the schools themselves; the results should be interpreted with 

care. 

Figure 14 shows the distribution of mathematics credits by sector, and figure 15 shows 

the distribution of the mathematics pipeline by sector. Between 1982 and 2004, students (on 

average) in each sector increased the number of mathematics credits earned by the end of high 

school (average credits showed no detectable differences for Catholic and other private school 

students between 1992 and 2004, however). In all three cohorts, public high school students 

earned fewer math credits than their Catholic or other private high school peers. No differences 

were detected in average math credits between Catholic and other private high school students in 

any year. 

27 
Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Figure 14. Mean credits earned in mathematics by high school graduates, by school sector: 1982, 

1992, and 2004 

2.6 

3.2 3.3 3.2 

3.7 

4.1 

3.6 

3.8 3.8 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0

1982 

1992 

2004 

Mean credits 

 Public Catholic Other private 

School sector 

NOTE: See appendix table B-10 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

In terms of the levels of courses completed by students from different school sectors, all 

groups saw a shift over time toward finishing high school with higher level courses (such as 

precalculus) and away from the two lowest levels of courses (no or low academic math or 

algebra I/plane geometry) (figure 15). All sectors saw significant decreases in the students 

exiting with only no math/low academic math and algebra I-level courses, and saw increases in 

precalculus and calculus coursetaking. 

However, depending on the sector, the middle-level courses of algebra II and algebra IIIlevel courses either increased, decreased, or remained stable. For example, among public school 

graduates, the proportions of students finishing high school with algebra II or algebra III-level 

courses increased between 1982 and 2004 (from 18 to 26 percent and from 15 to 18 percent, 

respectively). In contrast, Catholic and other private school students saw no detectable 

differences in the two middle categories of math coursetaking between 1982 and 2004. Overall, 

by 2004, public school graduates were more likely than their peers in Catholic or other private 

schools to exit the mathematics pipeline at algebra I and algebra II-level courses. 

Across all school sectors, the greatest shift in advanced-level math coursetaking between 

1982 and 2004 was in the percentage of students reaching precalculus as their highest course. In 

1982, 4 percent of public school students graduated from high school with precalculus as their 

highest course, while in 2004, 18 percent did so. The percentage of Catholic school students 

graduating from high school with precalculus as their highest course was 11 percent in 1982 and 

29 percent in 2004; the percentage of other private school students completing precalculus as 

their highest course was 7 percent in 1982 and 26 percent in 2004. At the lowest levels of 

coursetaking, the decline in the percentage of students taking no or low academic mathematics 

courses was greatest for the public school sector, falling from 27 percent in 1982 to 6 percent in 

2004. The declines between 1982 and 2004 for Catholic and other private school graduates were 

28 
 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

greatest in algebra I/plane geometry (from 26 to 4 percent for Catholic school graduates and 

from 24 to 7 percent for other private school graduates), partly because no and low academic 

math coursetaking in 1982 was already very low for these groups. 

Figure 15. Percentage of high school graduates who completed different levels of mathematics 

courses, by school sector: 1982, 1992, and 2004 

Public 

No math or low 

academic math 1982 27.1 31.4 17.7 14.7 4.2 5.0 

Algebra I/plane 

geometry 

1992 14.2 24.1 26.7 15.5 10.0 9.6 

Algebra II 

2004 Algebra III/ 5.7 19.2 26.4 17.6 18.1 13.0 

trigonometry/ analytic 

geometry 

Precalculus Catholic 

Calculus 1982 6.9 25.6 24.4 23.7 10.9 8.5 

1992 0.6 9.3 25.3 23.0 24.0 17.8 

2004 0.4 4.1 20.7 23.9 28.5 22.4 

Other private 

1982 

7.9 23.5 16.5 22.1 7.1 22.9 

1992 1.4 

7.5 18.8 28.9 14.4 28.9 

2004 0.4 

6.9 16.4 19.5 26.2 30.7 

0.0 20.0 40.0 60.0 80.0 100.0 

Percent 

NOTE: Detail may not sum to totals because of rounding. See appendix table B-11 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

Despite the growth in precalculus and calculus coursetaking among public school 

graduates, differences in levels of enrollment in calculus between this group and their private 

school (Catholic and other private school) peers persisted. In addition, by 2004, graduates of 

other private schools were more likely to complete precalculus than their public school peers; 

this gap did not exist in either 1982 or 1992. In 1982, 30 percent of graduates of other private 

29 
Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

schools completed precalculus or calculus, compared with 19 percent of graduates of Catholic 

schools and 9 percent of graduates of public schools (figure 16). By 2004, the percentage of 

other private school graduates completing precalculus or calculus was 57 percent, compared with 

51 percent of Catholic school graduates and 31 percent of public school graduates. 

Figure 16. Percentage of high school graduates who completed precalculus or calculus, by 

school sector: 1982, 1992, and 2004 

Percent 

100.0 

80.0 

60.0 

40.0 

20.0 

0.0 

 

9.1 

19.1 

30.0 

19.5 

41.7 43.3 

31.1 

50.9 

56.8 

Public Catholic Other private 

1982 

1992 

2004 

School sector 

NOTE: See appendix table B-11 for standard errors for these estimates. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

2.3 Mathematics Coursetaking Summary 

Across the graduating high school classes of 1982, 1992, and 2004, students increased 

their math coursetaking overall, coming closer to 4 full years of academic work in math in high 

school. In addition, higher proportions of graduates took advanced coursework over time: the 

percentage of graduates exiting the pipeline at precalculus increased nearly fourfold, and the 

percentage of graduates completing calculus more than doubled. By 2004, about a third (33 

percent) of graduates took one of these two most advanced levels of mathematics (figure 1). This 

shift to advanced math coursetaking came at the expense of the lowest math course levels: the 

proportion of students completing only algebra I or lower dropped in half in the 22 years from 

1982 to 2004. 

This general pattern held for all student subgroups: males, females, every racial and 

ethnic group, students from different socioeconomic backgrounds, students attending different 

school sectors, and even students only expecting to finish high school all took lower level 

mathematics courses at substantially lower rates and, for the most part, advanced math courses at 

higher rates. Although the gaps between certain student subgroups tell a more varied story, with 

some gaps narrowing and others increasing over time, there is an overall shift to more 

mathematics courses and more courses completed at advanced math levels. 

30 
 

Chapter 2. Trends in Mathematics Coursetaking: 1982–2004 

Some groups’ mathematics attainment in high school remains fairly low, however, 

despite similar credit counts. For example, although there was no detectable difference between 

the number of credits earned in 2004 by Black and White high school graduates, 37 percent of 

White graduates in 2003 took precalculus and calculus while 19 percent of Black students did so 

(figure 6). In addition, some gaps among students from different backgrounds or with different 

educational expectations showed no decline or even grew. A growing gap between 1982 and 

2004 occurred among graduates of different SES levels: those from the highest SES quartile 

made greater gains in completing precalculus or calculus than students from all other SES 

quartiles (figure 10), and a similar growing advantage held for students who expected a graduate 

degree versus those who expected a high school diploma or less (figure 13). Majorities of 

students who expect to attend postsecondary education institutions, even for obtaining bachelor’s 

degrees, do not complete advanced mathematics courses. Finally, private school (Catholic and 

other private school) graduates had a higher completion rate of precalculus or calculus than did 

their public school peers in that cohort (figure 16). 

Despite aggregate increases in coursetaking and advanced coursetaking (and, conversely, 

decreases in students taking no math or low-level math), several of these shifts took place 

between 1982 and 1992. For example, growth in number of credits earned by graduates was 

greater between 1982 and 1992 than between 1992 and 2004. It is possible that this reflects 

initial adoption of three credits as a minimum requirement in mathematics for high school 

graduation (for example, as advocated by the National Committee on Educational Excellence 

1983) and less momentum in the latter period toward requiring more mathematics credits. It may 

also be the case that students are reaching the ceiling in terms of the number and level of courses 

they can take. Most high school students have the opportunity to take only four math courses, 

and thus, it is not possible for large increases once mean credits earned moves closer to four. 

However, as the pipeline measures showed (figure 1), the types of courses taken and when 

students stop taking them still show extensive variation in academic preparation in mathematics 

by the end of high school. 

31 

 

 

Chapter 3 

Trends in Science Coursetaking: 1982–2004 

This chapter discusses science coursetaking over three cohorts of high school graduates, 

with respect to both their overall number of science credits and the types of science courses 

taken. As with mathematics, the number of science credits students attain represents the total 

amount of science instruction received and the extent to which science courses are a regular 

feature of the high school experience. Four credits may be a typical upper ceiling on science 

coursetaking in high school, assuming one science course each year in grades 9 through 12, 

while three credits is consistent with curriculum standards advocated by policymakers (National 

Committee on Excellence in Education 1983; Achieve, Inc. 2005; National Governors 

Association 2005). 

The science pipeline measure complements the credit counts by indicating how far along 

typical science course pathways a student progressed by the end of high school. This measure 

describes the point at which students exited the science coursetaking pipeline, completing no 

higher level science classes while in high school. Again, it does not necessarily mean that 

students took all lower level courses before exiting the pipeline, especially because scientific 

courses are not as strongly sequential as mathematics pipelines (Burkam and Lee 2003). 

In general, the results from this chapter mirror the findings for mathematics: a clear, 

consistent growth in science coursetaking overall and for most subgroups, more graduates 

finishing with advanced courses, and far fewer finishing with low-level courses. However, at the 

most advanced level of science coursetaking, growth was stagnant or only occurred among 

already advantaged groups. 

3.1 Overall Trends in Science Coursetaking 

The average number of credits in science students earned by the time of graduation rose 

across the two decades, increasing from 2.2 credits in 1982 to 2.9 credits in 1992 and 3.3 credits 

in 2004. This represents about one additional academic year of science instruction being taken by 

high school graduates, on average. Like mathematics, which saw a rapid rise in credits earned 

between 1982 and 1992, increases in science credits earned were higher in the first period than in 

the second. 

A marked change occurred in the distribution of science coursetaking among high school 

graduates between 1982 and 2004: across the 22 years, the distribution shifted to the upper end 

of the pipeline (figure 17). The percentage of graduates who either did not complete any science 

courses or completed only low-level science courses dropped from 14 percent in 1982 to 3 

percent in 1992. Declines were also observed for the secondary physical science and basic 

biology level (from 15 percent in 1982 to 3 percent of graduates in 2004 completing only that 

level) and the general biology level (from 35 to 25 percent). 

In the top three levels of science coursetaking, graduates increased their participation. 

The largest growth occurred for the proportion of graduates exiting the pipeline at chemistry I or 

physics I, which grew from 15 percent in 1982 to 33 percent in 2004. The corresponding 

percentages for those exiting the pipeline with both chemistry I and physics I moved from 6 

percent to 17 percent. By contrast, at the most advanced level of science courses—chemistry II, 

33 
Figure 17. Percentage of high school graduates who completed different levels of science 

courses: 1982, 1992, and 2004 

Year 

1982 

1992 

2004 

14.4 15.0 35.2 14.9 5.9 14.6 

7.0 36.4 27.1 12.2 14.3 

25.0 33.4 17.4 18.4 

Secondary physical 

science and basic 

bi l 

Chemistry I or physics I 

Chemistry I and physics 

No science or lowlevel science 

General biology 

3.1 Chemistry II, physics II, 

or advance biology 

2.6 

3.3 

0.0 20.0 40.0 60.0 80.0 100.0 

Percent 

 

Chapter 3. Trends in Science Coursetaking: 1982–2004 

physics II, or advanced biology—there was no substantive difference in participation between 

1982 and 2004. Overall, the top three science coursetaking levels saw a doubling from 35 

percent of graduates completing one of them in 1982 to 70 percent completing one of them in 

2004. 

NOTE: Detail may not sum to totals because of rounding. See appendix table B-12 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

3.2 Trends in Science Coursetaking Among Student Subgroups 

3.2.1 Sex 

Figure 18 shows the distribution of science credits by sex, and figure 19 shows the 

distribution of the science pipeline by sex. The mean number of credits earned in science by both 

males and females increased from 1982 to 2004. Males earned 3.3 credits in science in 2004, 

compared with 2.3 credits in 1982; females also earned 3.3 credits in science in 2004, compared 

with 2.2 credits in 1982. There were no detectable differences between males and females in the 

number of credits earned in science in the 1982, 1992, and 2004 cohorts. 

34 
 

 

Chapter 3. Trends in Science Coursetaking: 1982–2004 

Figure 18. Mean credits earned in science by high school graduates, by sex: 1982, 1992, and 2004 

2.3 2.2 

2.9 2.9 

3.3 3.3 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0

1982 

1992 

2004 

Mean credits 

 Male Female Gender 

NOTE: See appendix table B-13 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

Changes in science coursetaking for males and females mirrored the overall trend. 

Between 1982 and 2004, students of both sexes became more likely to complete courses at the 

top three levels of science coursetaking, and they became less likely to exit the science 

coursetaking pipeline at the bottom three levels (figure 19). At the lowest end, the percentage of 

males taking no science or low-level science courses decreased from 14 percent in 1982 to 

3 percent in 2004, while the percentage of females doing so dropped from 15 percent in 1982 to 

2 percent in 2004. 

In 1992 and 2004, there were no measurable differences between male and female 

participation rates in the top two most advanced levels of science courses (i.e., chemistry I and 

physics I; and chemistry II, physics II, or advanced biology), with 35 percent of females and 36 

percent of males completing courses at this level in 2004. In the next lowest level of science 

coursetaking, chemistry I or physics I, 15 percent of males and females exited the pipeline in 

1982, but by 1992, the rate of participation for females surpassed that of males, which remained 

true in 2004 as well: in the latest cohort, 37 percent of females completed either of these courses, 

compared with 30 percent of males.12 

12 This female advantage derives from an advantage in chemistry I, with more females than males completing it 

overall (66 percent of females versus 59 percent of males complete chemistry I at some point in high school—results 

not shown); in contrast, there is no substantive difference in the percentage of males and females completing 

physics I. 

35 
Chapter 3. Trends in Science Coursetaking: 1982–2004 

Figure 19. Percentage of high school graduates who completed different levels of science 

courses, by sex: 1982, 1992, and 2004 

Male 

1982 

1992 

2004 

Female 

1982 

1992 

2004 

 

14.7 

3.7 

14.1 

5.1 

14.7 

8.8 

23.1 

36.6 

36.4 

27.0 

36.2 

34.0 

36.8 

29.8 

15.1 

29.8 

24.3 

14.7 

16.6 

12.0 

4.4 

18.2 

12.5 

7.6 

18.8 

14.1 

14.9 

18.0 

14.5 

14.3 

3.3 

2.5 

1.9 

3.7 

2.8 

15.4 

0.0 20.0 40.0 60.0 80.0 100.0 

Percent 

Secondary physical 

science and basic 

biology 

Chemistry I or physics I 

Chemistry I and 

physics I 

No science or lowlevel science 

General biology 

Chemistry II, physics II, 

or advance biology 

NOTE: Detail may not sum to totals because of rounding. See appendix table B-14 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

3.2.2 Race/Ethnicity 

Figure 20 shows the distribution of science credits by race/ethnicity, and figure 21 shows 

the distribution of the science pipeline by race/ethnicity. Between 1982 and 2004, the mean 

number of credits earned in science increased for all racial/ethnic groups. Asians earned the most 

number of credits across the 22-year period. In 2004, in addition to Asian graduates earning 

more credits on average (3.7) than other groups, Black and White graduates earned more credits 

than Hispanic graduates (3.2 and 3.3 compared to 2.9, respectively). Nevertheless, by 2004, all 

graduates earned, on average, 2.9 credits or more in science. 

36 
 

 

Chapter 3. Trends in Science Coursetaking: 1982–2004 

Figure 20. Mean credits earned in science by high school graduates, by race/ethnicity: 1982, 

1992, and 2004 

2.1 

2.7 

2.1 

1.8 

2.3 

2.5 

3.2 

2.8 2.7 

3.0 3.1 

3.7 

3.2 

2.9 

3.3 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0 

1982 

1992 

2004 

Mean credits 

American Indian Asian Black Hispanic White 

Race/ethnicity 

NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and 

American Indian includes Alaska Native. See appendix table B-15 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

In terms of science coursetaking levels, each racial/ethnic group finished high school 

having completed higher science courses in 2004 than in 1982 (figure 21). Across all 

racial/ethnic groups except American Indians (where apparent differences were not statistically 

significant), smaller proportions of students completed only the two lowest levels (no or lowlevel science, and secondary physical science or basic biology). At the level of general biology, 

all groups except American Indians saw declines in completion rates. For example, the 

percentages of Hispanic students completing only the general biology level fell from 39 percent 

in 1982 to 30 percent in 2004. 

In higher level science courses, greater proportions of students in all racial/ethnic 

categories, except for Asians, finished high school with chemistry I or physics I. Additionally, 

greater proportions of Blacks, Whites, and Hispanics completed the chemistry I and physics I 

level of coursetaking. For example, the percentages of Whites completing chemistry I and 

physics I rose from 6 percent in 1982 to 19 percent in 2004. However, at the most advanced 

course level (chemistry II, physics II, or advanced biology), only Asian and White students 

completed this level at higher rates in 2004 than in 1982. One of the most notable changes in 

advanced science coursetaking from 1982 to 2004 occurred among the percentages of Asian 

students completing chemistry II, physics II, or advanced biology. In 1982, nearly 24 percent of 

Asian graduates exited the science pipeline at this highest level. However, by 2004, the 

percentage increased to 39 percent—a 15 percentage point increase in an already high 

participation rate. 

37 
 

 

Chapter 3. Trends in Science Coursetaking: 1982–2004 

Figure 21. Percentage of high school graduates who completed different levels of science 

courses, by race/ethnicity: 1982, 1992, and 2004 

American Indian 

1982 

1992 

2004 2.9 

Asian 

1982 

1992 2.1 

1.9 2004 

1.2 

Black 

1982 

1992 2.9 

2.3 2004 2.5 

Hispanic 

1982 

1992 3.3 

2004 3.9 

White 

1982 

1992 3.1 

2.3 2004 

2.9 

8.9 16.8 

4.8 

11.1 

5.6 

11.0 

14.3 

13.1 14.0 

5.4 

23.7 

35.4 

34.6 

29.9 

39.0 

38.6 

31.1 

43.7 

38.8 

12.8 

29.5 

22.7 

43.1 

43.3 

33.9 13.6 

12.7 

29.3 

22.5 

20.6 

26.2 

13.7 

23.0 

40.3 

9.3 

27.3 

36.9 

15.9 

28.2 

32.0 

6.5 

8.3 

3.3 

12.9 

10.6 

3.4 

19.0 

19.4 

14.1 

12.9 

8.3 

14.0 23.2 4.0 11.4 

10.0 

7.1 

6.0 23.6 

22.9 

38.9 

16.8 16.2 11.1 

8.8 

21.9 19.2 7.7 

4.8 

16.0 

18.6 

12.5 

11.0 

7.8 

15.3 9.3 

15.5 

20.6 

No science or lowlevel science 

Secondary physical 

science and basic 

biology 

General biology 

Chemistry I or physics I 

Chemistry I and 

physics I 

Chemistry II, physics II, 

or advanced biology 

0.0 20.0 40.0 60.0 80.0 100.0 

Percent 

NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and 

American Indian includes Alaska Native. Detail may not sum to totals because of rounding. See appendix table B-16 for standard 

errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

Racial/ethnic differences in graduates’ rates of enrollment in more challenging science 

courses persisted or grew across the 22-year period. For example, in 1982, Asians completed the 

most advanced level of science courses (i.e., chemistry II or physics II or advanced biology) at a 

higher rate than all other racial ethnic groups (24 percent of Asians compared with 8 percent of 

Hispanics, 11 percent of Blacks, 11 percent of American Indians, and 16 percent of Whites). 

These gaps between Asian and all other racial/ethnic groups increased overall between 1982 and 

2004. By 2004, 9 percent of Hispanics, 11 percent of Blacks, 7 percent of American Indians, and 

21 percent of Whites completed chemistry II, physics II, or advanced biology, compared with 

38 
Chapter 3. Trends in Science Coursetaking: 1982–2004 

39 percent of Asians. In addition, although White graduates continued to lag behind their Asian 

peers in completing this most advanced level of science courses in 2004, their participation rate 

was nevertheless higher than those of their non-Asian minority peers. 

3.2.3 Socioeconomic Status 

Figure 22 shows the distribution of science credits by socioeconomic status (SES), and 

figure 23 shows the distribution of the science pipeline by SES (see appendix A, section A.7.1, 

for discussion of the construction of SES quartiles across the three studies). Between 1982 and 

1992 and between 1992 and 2004, the mean number of credits earned in science increased for 

students from all SES quartiles. As with the overall trend, increases were comparable for all SES 

groups over time. Graduates from the highest SES quartile earned the most number of credits 

relative to graduates from all other SES quartiles in 1982, 1992, and 2004. Graduates from each 

of the lowest two quartiles earned the least number of credits relative to graduates from each of 

the highest two SES quartiles in 1982 and 1992. These gaps persisted in 2004, except that the 

discrepancy in credits earned between second and third quartile students had closed. 

Nevertheless, by 2004 graduates from all SES quartiles earned, on average, 3.0 or more credits in 

science. 

Figure 22. Mean credits earned in science by high school graduates, by socioeconomic status: 

1982, 1992, and 2004 

1.9 2.1 

2.3 

2.6 2.7 2.6 

3.0 

3.3 

3.0 3.1 3.3 

3.6 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0

1982 

1992 

2004 

Mean credits 

 First quartile (lowest) Second quartile Third quartile Fourth quartile (highest) 

Socioeconomic status 

NOTE: See appendix table B-17 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

As with the overall trends in levels of science courses taken, smaller proportions of high 

school graduates in all SES quartiles exited the science pipeline at the three lowest levels of 

coursetaking (no or low-level science, secondary physical science and basic biology, and general 

biology) in 2004 than in 1982 (figure 23). In the first three SES quartiles, the three lowest level 

courses dropped from being a majority among students to a minority (for the highest SES 

quartile students, the first point of comparison in 1982 began with a minority proportion 

graduating high school with these courses). The largest percentage point drop within the lowest 

39 
 

 

Chapter 3. Trends in Science Coursetaking: 1982–2004 

three science course levels occurred among the first (lowest) SES quartile group, where the 

percentage of graduates exiting high school with no or low-level science dropped from 23 

percent in 1982 to 5 percent in 2004, an 18 point decline. 

At two upper science course levels—chemistry I or physics I, and chemistry I and 

physics I—the percentages of students completing them increased over time for all SES groups. 

The largest increase among SES quartiles was again observed for the first (lowest) group 

compared to the third and fourth (highest) groups: among first SES quartile students, the 

percentages completing high school with chemistry I or physics I grew from 9 percent in 1982 to 

34 percent in 2004. Graduates in the second and third SES quartiles also made greater gains at 

this level (chemistry I or physics I) than the fourth (highest) SES quartile students (from 13 to 35 

percent for second SES quartile students, and from 17 to 35 percent for third SES quartile 

students, from 1982 to 2004). However, at the highest level (chemistry II, physics II, or advanced 

biology), only the highest SES quartile increased participation from 1982 to 2004, moving from 

22 percent to 28 percent completing high school with at least one of these most advanced science 

courses. 

Variations in science coursetaking patterns across SES quartiles persisted across the 

decades. In all three cohorts, students from the highest SES quartile were more likely than those 

from the lowest, second, and third quartiles to complete science courses at the two most 

advanced levels, that is, chemistry I and physics I, and chemistry II, physics II, or advanced 

biology. For example, in 2004, 28 percent of students from the highest SES quartile completed 

chemistry II, physics II, or advanced biology, compared with 18 percent of students from the 

third SES quartile, 14 percent of students from the second SES quartile, and 12 percent of 

students from the lowest SES quartile. Similarly, 25 percent of the highest SES quartile 

graduates exited the pipeline at chemistry I and physics I, compared with 19 percent of third SES 

quartile, 14 percent of second SES quartile, and 9 percent of first (lowest) SES quartile 

graduates. 

3.2.4 Educational Expectations 

Figure 24 shows the distribution of science credits by educational expectations, and 

figure 25 shows the distribution of the science pipeline by educational expectations. The mean 

number of credits earned in science by graduating seniors at all levels of educational 

expectations increased from 1982 to 2004. Although nearly all of the gaps in credits earned 

between students at different levels of educational expectations decreased from 1982 to 2004, 

students expecting to earn no more than a high school diploma or no more than some 

postsecondary education continued to earn fewer credits in science than their peers who expected 

to earn a college or graduate degree. In 2004, graduates at the two lowest levels of educational 

expectations earned 2.7 and 2.8 credits, respectively, while graduates at the two higher levels of 

educational expectations earned 3.3 and 3.6 credits, respectively. 

40 
Chapter 3. Trends in Science Coursetaking: 1982–2004 

Figure 23. Percentage of high school graduates who completed different levels of science 

courses, by socioeconomic status: 1982, 1992, and 2004 

First quartile 

(lowest) 1982 

1992 

2004 

Second quartile 

1982 

1992 

2004 2.8 

Third quartile 

1982 

1992 2.3 

1.7 2004 

2.8 

Fourth quartile 

(highest) 

1982 

0.5 1992 

3.2 

1.1 2004 

1.4 

 

16.4 

6.1 11.7 

5.0 5.0 

16.8 17.0 

4.0 9.2 

4.4 

11.4 15.8 

5.5 

6.6 11.6 

13.2 

23.4 

28.4 

23.9 

35.3 

34.7 

30.6 

42.7 

37.6 

35.7 

48.8 

40.8 9.2 

21.2 

33.6 

12.6 

26.1 

34.6 

16.7 

31.2 

35.0 

20.5 

28.5 

31.1 

10.6 

13.3 

6.0 

13.8 

7.9 

4.3 

9.1 

22.7 8.5 

5.4 6.7 

11.6 

11.6 

10.1 

15.5 

22.2 

25.3 

19.5 

18.9 

2.5 

13.9 

12.5 

17.7 

24.9 

27.9 

0.0 20.0 40.0 60.0 80.0 100.0 

Percent 

Secondary physical 

science and basic biology 

Chemistry I or physics I 

Chemistry I and physics I 

No science or lowlevel science 

General biology 

Chemistry II, physics II, 

or advanced biology 

NOTE: Detail may not sum to totals because of rounding. See appendix table B-18 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

41 
Chapter 3. Trends in Science Coursetaking: 1982–2004 

Figure 24. Mean credits earned in science by high school graduates, by educational 

expectations: 1982, 1992, and 2004 

1.7 

1.9 

2.6 

3.0 

2.4 2.4 

3.1 

3.4 

2.7 2.8 

3.3 

3.6 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0 

1982 

1992 

2004 

Mean credits 

High school diploma/ Some postsecondary Baccalaureate degree Graduate degree 

GED or less education 

Educational expectations 

NOTE: See appendix table B-19 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

Changes in science coursetaking for graduating high school students at all levels of 

educational expectations reflect the overall trend in science coursetaking patterns (figure 25). 

Between 1982 and 2004, graduating seniors across educational expectation levels became less 

likely to exit the science coursetaking pipeline having taken no or only low-level science courses 

and more likely to leave high school with chemistry I or physics I as their highest course level. 

Students expecting to earn a college or graduate degree were also more likely to complete 

chemistry I and physics I as their highest course in 2004 than in 1982. At the highest level of 

science courses—chemistry II, physics II, or advanced biology—there was little or no 

improvement for students at any level of educational expectations. 

While the pattern of changes in science coursetaking within each group were largely 

similar, differences in levels of participation based on educational expectations persisted across 

the decades. In 1982 and 2004, students at the lowest level of educational expectations were 

more likely than students at all other levels of educational expectations to exit the science 

coursetaking pipeline having taken no or only low-level science courses. In 1982, 27 percent of 

students expecting to obtain a high school degree, GED, or less exited the pipeline at the level of 

no or low-level science courses. By 2004, this percentage had decreased to 13 percent. In 

comparison, in 2004, 5 percent of students expecting to obtain only some postsecondary 

education exited at this level, as did about 1 percent each of graduates expecting to earn a 

baccalaureate degree and graduates expecting to earn a graduate degree. 

42 
 

 

Chapter 3. Trends in Science Coursetaking: 1982–2004 

Figure 25. Percentage of high school graduates who completed different levels of science 

courses, by educational expectations: 1982, 1992, and 2004 

High school 

diploma/ 1982 GED or less 

1992 

2004 

Some 

postsecondary 

education 1982 

1992 

2004 

Baccalaureate 

degree 

1982 

1992 

2004 

Graduate degree 

1982 

1992 

2004 

6.9 44.6 32.0 

27.4 18.6 

7.7 14.9 

13.4 10.6 

16.3 19.1 

5.9 11.9 

4.5 7.5 

6.1 12.2 

7.9 21.5 

22.3 

12.3 

44.3 4.3 

56.5 17.5 

46.6 19.4 

42.5 11.2 

55.7 19.3 

29.3 23.5 

29.7 37.2 

23.0 37.3 

23.1 

15.7 

4.8 

8.0 

8.4 

4.9 

8.6 20.2 

26.5 

33.0 

13.6 

20.3 

19.6 

0.6 

12.5 

15.8 

29.7 

27.1 

24.0 28.8 

0.0 20.0 40.0 60.0 80.0 100.0 

Percent 

2.4 

1.0 

2.1 

2.5 

2.4 

4.5 

1.4 

3.5 

1.4 

2.3 

4.2 

1.3 

3.2 

0.8 

1.1 

No science or lowlevel science 

Secondary physical 

science and basic 

biology 

General biology 

Chemistry I or physics I 

Chemistry I and 

physics I 

Chemistry II, physics II, 

or advanced biology 

NOTE: Detail may not sum to totals because of rounding. See appendix table B-20 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

Additionally, in all three cohorts, students expecting to obtain a baccalaureate or graduate 

degree were more likely than students with lower educational expectations to complete science 

courses at the highest level. High school seniors who expected to earn a graduate degree 

continued to be most likely to complete chemistry II or physics II or advanced biology. Nearly 

29 percent of students expecting to earn a graduate degree completed the most advanced level of 

science courses, compared with 16 percent of students expecting to earn a baccalaureate degree, 

7 percent of students expecting to earn some postsecondary education, and 8 percent of students 

expecting to earn no more than a high school diploma or General Educational Development 

(GED) certificate. 

43 
Chapter 3. Trends in Science Coursetaking: 1982–2004 

3.2.5 School Sector 

Compared to direct measures of student characteristics and expectations, school sector 

represents one aspect of the context in which coursetaking occurs. Not only may the 

characteristics and expectations of students in different sectors differ, but students attending 

schools in separate sectors may be systematically exposed to different curricular opportunities 

and varying peer influences related to selecting courses. Some graduates may also have attended 

schools in different sectors over their high school career. The following results thus represent the 

profile of school sector graduates and not the schools themselves; reasons for differences across 

students from different school sectors are not explored, and the results should be interpreted with 

caution. 

Figure 26 shows the distribution of science credits by school sector, and figure 27 shows 

the distribution of the science pipeline by school sector. The mean number of credits earned in 

science by graduates of all school sectors increased from 1982 to 2004; in 2004, students in all 

school sectors earned, on average, more than 3.0 credits in science. However, differences in 

credits earned by public school graduates compared with Catholic and other private school 

graduates persisted across the two decades: in each of the three cohorts, private school students 

earned more credits in science than did their public school peers (in 2004, other private school 

graduates earned 3.6 credits and Catholic school students earned 3.5 credits in science, on 

average, while public school graduates earned 3.3 credits on average). 

Figure 26. Mean credits earned in science by high school graduates, by school sector: 1982, 

1992, and 2004 

2.2 

2.5 

2.8 2.9 

3.1 3.3 3.3 

3.5 3.6 

0.0 

1.0 

2.0 

3.0 

4.0 

5.0 

1982 

1992 

2004 

Mean credits 

Public Catholic Other private 

School sector 

NOTE: See appendix table B-21 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

As with the overall trend, graduates of schools in different sectors finished high school 

taking more upper level and fewer lower level science courses in 2004 than in 1982 (figure 27). 

At the low end of science courses, all groups decreased their participation in the bottom three 

course levels (no or low-level science, secondary physical science or basic biology, and general 

44 
 

 

 

Chapter 3. Trends in Science Coursetaking: 1982–2004 

biology), except for no or low-level science participation by other private school graduates 

(whose completion rates at that level were already low). For example, the largest drop observed 

here was among other private school graduates, whose percentage completing general biology 

declined from 39 percent in 1982 to 11 percent in 2004, a 29 (28.6) percentage point drop. At the 

upper level of science coursetaking, all groups increased their participation in two of the three 

levels: chemistry I or physics I, and chemistry I and physics I. Thirty-four percent of public 

school graduates, for example, finished high school with chemistry I or physics I in 2004, 

compared with 14 percent in 1982. However, at the highest level (chemistry II, physics II, or 

advanced biology), no differences of 5 percentage points or greater were observed over time in 

the participation rates of students in any school sector. 

Despite the similar changes in coursetaking patterns over time, differences in completion 

rates persisted from 1982 to 2004 among school sector types. Graduates of other private high 

schools were more likely than their public high school counterparts to progress through the 

science pipeline into the highest level: in 2004, 28 percent of other private school students 

completed chemistry II, physics II, or advanced biology before leaving high school, compared 

with 18 percent of public school graduates. Graduates of Catholic and other private schools were 

also more likely than graduates of public schools to complete chemistry I and physics I in 2004. 

Similarly, Catholic and other private school graduates were less likely than their public school 

peers to exit the science pipeline at the level of general biology (15 percent and 11 percent, 

respectively, compared with 26 percent). 

45 
Chapter 3. Trends in Science Coursetaking: 1982–2004 

Figure 27. Percentage of high school graduates who completed different levels of science 

courses, by school sector: 1982, 1992, and 2004 

Public 

1982 

1992 3.4 

2.8 

2004 3.5 

Catholic 

1982 

0.5 

1992 2.3 

0.6 

2004 

1.5 

Other private 

1982 1.2 

0.4 

1992 2.6 

# 

2004 

0.6 

 

 

15.8 15.3 

7.4 

15.4 

6.9 

10.7 

17.3 

39.2 

14.9 

23.6 

31.9 

26.1 

38.0 

35.4 14.4 

26.7 

33.5 

20.0 

26.1 

30.7 

15.5 

37.2 

32.9 27.9 

12.7 

14.2 

30.5 

25.0 

9.2 

16.3 

11.4 

5.3 13.8 

13.1 

17.9 

4.1 19.4 

22.5 

21.7 

23.0 

29.8 

27.9 

0.0 20.0 40.0 60.0 80.0 100.0 

Secondary physical 

science and basic 

biology 

Chemistry I or 

physics I 

Chemistry I and 

physics I 

No science or lowlevel science 

General biology 

Chemistry II, physics II, 

or advanced biology 

Percent 

# Rounds to zero. 

NOTE: Detail may not sum to totals because of rounding. See appendix table B-22 for standard errors for this figure. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), 

“Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School 

Transcript Study, 2004.” 

3.3 Science Coursetaking Summary 

In 2004, high school graduates earned more science credits than in previous years— 

nearly a full year’s worth, on average, compared with the graduating cohort of 1982. Most 

student subgroups accumulated 3.0 credits or more of science courses by 2004, bringing them in 

line with curriculum recommendations such as those established as the “New Basics” (National 

Commission on Excellence in Education 1983) or touted by other groups (Achieve, Inc. 2005; 

National Governors Association 2005). 

46 
 

 

Chapter 3. Trends in Science Coursetaking: 1982–2004 

In addition, graduates moved away from concentrating on low-level science coursework 

toward completing higher level science courses. However, unlike the trends in mathematics 

coursetaking, most of this shift occurred toward the middle science course levels of general 

biology or chemistry I or physics I. The course level with the greatest gain in proportions of 

students completing it was chemistry I or physics I, which rose from 15 percent to 33 percent 

from 1982 to 2004 (figure 17). This came at the expense of the two lowest course levels, which 

saw their combined percentages drop from 29 percent in 1982 to 6 percent in 2004. Changes 

were far more muted at the most advanced course levels and in particular at the highest level of 

chemistry II, physics II, or advanced biology, which saw no change of 5 percentage points or 

greater over time. 

The general increase in science coursetaking was shared by all students examined in this 

study, regardless of sex, race/ethnicity, socioeconomic status, educational expectations, or school 

sector. In some student subgroups, however, the most advanced course level saw significant 

increases. For example, 39 percent of Asian graduates completed chemistry II, physics II, or 

advanced biology in 2004, an increase from a relatively high 24 percent in 1982 (figure 21).13 

White and Asian graduates each completed chemistry II, physics II, or advanced biology at 

higher rates than Black, Hispanic, and American Indian graduates. 

Other disparities among various student subgroups persisted into 2004. There were no 

detectable differences between males and females completing the two highest levels of advanced 

science courses in 1982, 1992, and 2004 (figure 19). However, in 2004, females were more 

likely than males to finish high school with the chemistry I or physics I level of coursetaking. 

Also in 2004, males were more likely than females (34 percent for males versus 28 percent for 

females) to have completed only one of the three lowest levels of science as their highest course 

taken (no or low-level science, secondary physical science and basic biology, or general 

biology). 

Completion rates for some of the most advanced course levels were also higher among 

graduates from private schools (Catholic and other private schools) and high SES backgrounds 

than among those from public schools or low SES backgrounds (figures 23 and 27, respectively). 

Finally, though students with educational expectations lower than a baccalaureate degree 

increased their participation in the middle level of chemistry I or physics I, those expecting at 

least a college degree continued to take courses at the two top levels at a higher rate, as much as 

or more than twice the rates of their lower expectation peers. Still, 64 percent of those expecting 

a baccalaureate degree fail to take both a standard chemistry and physics course by the end of 

high school (figure 25). 

13 Indeed, Asian graduates in 1982 outranked all other racial/ethnic groups from any year in the percentage taking 

the highest level science courses. 

47 

 

 

Chapter 4 

Conclusions 

Between 1982 and 2004, American high school students took an increasing number of 

academic courses in mathematics and science and were increasingly likely to complete advanced 

academic coursework in these subjects before they graduated from high school. This trend was 

most consistent over time at all levels of mathematics coursetaking and among middle-level 

science courses. The upward movement in coursetaking occurred not only among high school 

graduates nationwide but also in all student subgroups examined in this report, including those 

identified by sex, race/ethnicity, socioeconomic status (SES), and school sector. This bodes well 

for American youth in the aggregate—as the demand for quantitative and analytical skills 

increases, there is evidence that students are taking more advanced mathematics and science 

instruction. 

In addition to this shift toward higher level courses, some preexisting gaps in 

mathematics and science preparation closed over time or even reversed themselves. For example, 

although Asian graduates continued to earn more credits in mathematics (figure 5) and science 

(figure 20) than graduates in most other racial/ethnic groups, the math credit gaps between this 

group and Whites and Hispanics narrowed between 1982 and 2004. Also, the gap in credits 

earned in mathematics between Whites and Blacks in 1982 (favoring Whites) showed no 

substantive difference in 2004, where Blacks earned, on average, 3.7 credits, and Whites earned 

3.6 credits (figure 5). (However, as discussed below, the Black-White gap in advanced math 

course levels did not close.) 

Despite some narrowing differences, other disparities remained among student subgroups 

and occasionally widened over time. Although patterns among males and females in advanced 

science coursetaking generally remained the same from 1982 to 2004, a gap in favor of females 

over males in completing chemistry I or physics I developed over time (figure 19). In 1982, 15 

percent each of males and females exited the pipeline at chemistry I or physics I. Yet by 2004, 37 

percent of females were taking chemistry I or physics I prior to graduating from high school, but 

only 30 percent of males were doing so. However, no differences were detected in the 

completion rates for the two most advanced levels of science courses (chemistry I and physics I, 

and chemistry II, physics II, or advanced biology). 

In addition, White and Asian graduates were more likely to enroll in advanced 

mathematics (figure 6) and science (figure 21) courses than their Black, Hispanic, and American 

Indian peers, and Asian graduates in particular extended their advantage over all other groups in 

taking precalculus; calculus; and chemistry II, physics II, or advanced biology. Further, students 

from high-SES backgrounds completed advanced courses in mathematics (figure 9) and science 

(figure 22) at higher rates than did those from low-SES backgrounds. The highest SES group 

substantially widened its advantage over other groups in completing precalculus and calculus; 

chemistry I and physics I; and chemistry II, physics II, or advanced biology. Students expecting a 

baccalaureate or graduate degree were more likely than their peers with lower educational 

expectations to complete precalculus or calculus (figure 14) or to complete chemistry II, physics 

II, or advanced biology (figure 25). Finally, Catholic school and other private school graduates 

were more likely than their public school peers to persist in the coursetaking pipeline longer and 

to complete advanced courses in mathematics (figure 16) and science (figure 27). 

49 
Chapter 4. Conclusions 

This study shows that, on average, American youth are taking more mathematics and 

science courses, as well as more advanced mathematics and science courses. Future research will 

be needed to assess the extent to which these advanced courses present challenging material and 

translate into proficiency in mathematics and science, as well as to address the persistent gaps in 

coursetaking demonstrated in this study. 

50 
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for Education Statistics. 

54 
Appendix A 

Technical Notes and Methodology 

 

 

Appendix A. Technical Notes and Methodology 

A.1 Sources of Data 

The data for this report came from three surveys begun by the National Center for 

Education Statistics (NCES) between 1982 and 2004. These surveys are the High School and 

Beyond Longitudinal Study of 1980 Sophomores (HS&B), the National Education Longitudinal 

Study of 1988 (NELS:88), and the Education Longitudinal Study of 2002 (ELS:2002). 

For all transcripts and samples used in this report, a course identification code number, 

based on the Classification of Secondary School Courses (CSSC), was assigned to each course 

taken by a student. A report by Bradby and Hoachlander (1999), 1998 Revision of the Secondary 

School Taxonomy, further classified these CSSC codes into subject (e.g., mathematics) and 

program (e.g., academic) areas. This taxonomy served to standardize all transcript data included 

in the analysis. 

The analysis sample from each survey was restricted to a subset of sample members who 

were high school graduates and had a complete set of transcripts. High school graduates were 

defined as spring term senior cohort members1

 who graduated with an honors or standard 

diploma by the end of the summer (August 31) of their graduating year (1982 for HS&B, 1992 

for NELS:88, and 2004 for ELS:2002 graduates). A complete transcript was defined as one that 

recorded 16 or more Carnegie units (a Carnegie unit is equivalent to a course taken every day, 

one period per day, for a full school year), with a positive, nonzero number of credits completed 

in English. These criteria for defining the analysis samples also served to make them comparable 

across the different years and studies. According to Hoachlander (1991) and Ingels and Taylor 

(1995), one solution for making transcript samples comparable is to select graduating seniors 

with 16 to 32 credit hours. This methodology acts to exclude the more extremely disabled and 

language minority students from the more eligibility-liberal ELS:2002, bringing HS&B and 

NELS:88 into line with ELS:2002. (ELS:2002 has a comparatively low rate of survey exclusion 

and, additionally, systematically collects the transcripts of students with disabilities and students 

who are not proficient in English). The comparability of the samples is examined and discussed 

in section A.4 of this appendix. The sections immediately following provide a brief description 

of each survey. 

A.1.1 High School and Beyond 

The HS&B longitudinal survey was first administered in 1980 to a stratified, nationally 

representative sample of approximately 30,000 high school sophomores and 28,000 high school 

seniors from more than 1,000 high schools. Follow-up surveys were administered in 1982, 1984, 

1986, and 1992. This report used the 1980 sophomore cohort sample. As part of the first followup study, conducted in 1982, high school transcripts were collected for a probability subsample 

of 18,500 members of the 1980 sophomore cohort. For this report, the demographic 

characteristics of the 1982 graduates were drawn from the first follow-up data file, and their 

coursetaking information was drawn from the transcript data file. The analysis sample included 

approximately 11,200 sophomores who graduated in 1982 and had complete transcripts. 

1

 Spring term of the cohort’s respective graduating year. A small number of early graduates (not enrolled in the 

spring term of the typical graduating year) are excluded on this basis. A slightly different convention may be used 

for basic reporting in which all early graduates are explicitly accounted for; however, the current report follows the 

spring term definition in order to provide coursetaking results for 4-year on-time high school graduates. 

A-3 
 

Appendix A. Technical Notes and Methodology 

Excluded students were those who dropped out of school or were still working for their diploma 

or those who did not have complete transcript data. More information on the first follow-up and 

transcript data files can be found in High School and Beyond, 1980 Sophomore Cohort, First 

Follow-up (1982), Data File User’s Manual (Jones et al. 1983) and High School and Beyond 

Transcripts Survey (1982), Data File User’s Manual (Jones et al. 1984). 

High school transcripts for HS&B were collected in the first follow-up (1982) for 

members of the 1980 sophomore cohort only, when the majority of sophomore cohort members 

were seniors. (Transcripts were collected in September following their senior year.) According to 

NCES Statistical Standards (Seastrom 2003), in an analysis using data from only the first followup student questionnaire and transcript surveys, the overall unit response rate is a function of the 

base-year school unit response rate (first stage of selection for the study) and the unit response 

rate for sample members eligible for both the first follow-up student survey and the high school 

transcript survey. In the base year, of the 1,122 schools initially selected to participate in the 

study, 811 schools agreed to do so, for a school cooperation rate (not school questionnaire 

response rate) of 72 percent (the base year student questionnaire response rate was 84 percent, 

unweighted). In the first follow-up, of the subsample of 18,500 sophomores for whom transcript 

data were requested in 1980 (and who were eligible for the first follow-up student survey), 

transcripts were received for 16,200 students, for a unit response rate of 88 percent (the first 

follow-up student questionnaire response rate was 95 percent, unweighted). This translates into 

an overall unit response rate of 64 percent (0.723 x 0.880 = 0.636). Because the classification 

variables used in this report could be drawn from either base year or first follow-up data, we also 

provide the response rates for questionnaire completion in both these rounds. In the base year, 84 

percent of sample members completed the student questionnaire; in the first follow-up, 95 

percent completed a questionnaire. Based on questionnaire completion, the unweighted twostage response rates for the study are 61 percent for the base year (0.841 x 0.723 = 0.608) and 68 

percent for the first follow-up (0.945 x 0.723 = 0.683). 

The overall unit response rate of 64 percent, resulting in an overall unit nonresponse rate 

of 36 percent, does not mean that the magnitude of nonresponse bias for the analysis sample used 

in this report is large. Nonresponse bias will be small if the nonrespondent strata constitute only 

a small portion of the survey population or if the differences between respondents and 

nonrespondents are small. With a school response rate of 72 percent, the biggest contributor to 

possible nonresponse bias is nonresponse on the part of schools in the base year. However, 

nonresponse analyses conducted in the first follow-up of HS&B found that nonresponse had little 

effect on base-year and first follow-up estimates. The results of these nonresponse analyses 

showed that the school-level component of the bias affected base-year and first follow-up 

estimates by 2 percent or less (Tourangeau et al. 1983; Zahs et al. 1995).2 

For this analysis, item response rates ranged from a low of 96 percent for incomplete 

transcripts to a high of 100 percent. Only two demographic items registered less than 100 percent 

item response: race/ethnicity, with a 99 percent item response rate, and socioeconomic status, 

with a 97 percent item response rate. 

2 Neither HS&B publication specified whether the response rates presented were weighted or unweighted. 

A-4 
 

Appendix A. Technical Notes and Methodology 

A.1.2 National Education Longitudinal Study of 1988 

NELS:88 is another major longitudinal study sponsored by NCES. The base-year survey 

was administered in 1988 to about 24,000 8th-graders in more than 1,000 schools. The first and 

second follow-ups revisited the same sample of students in 1990 and 1992, when most of the 

1988 8th-graders were in the 10th grade and 12th grade; then for the third and fourth times in 

1994 and 2000, which were 2 and 8 years after their scheduled graduation from high school. 

Unlike HS&B, for each in-school follow-up (i.e., 1990 and 1992), the student sample was 

“freshened” to obtain a representative, cross-sectional grade-cohort (i.e., 10th-graders in 1990 

and 12th-graders in 1992). In addition, as a part of the second follow-up, high school transcripts 

were collected for all students attending a subset of second follow-up schools selected for the 

transcript study, all dropouts and dropouts attending alternative programs who had attended high 

school for a minimum of one term, all early graduates, and sample members with disabilities that 

precluded them from completing a student questionnaire and cognitive test battery in the base 

year and the first and second follow-ups. For this report, the demographic characteristics of 1992 

high school graduates came from the NELS:88 second follow-up data file, and their coursetaking 

information from the survey’s transcript data file. The analysis sample was drawn from the 

transcript sample. Of the approximately 17,300 students in the transcript file, about 13,500 were 

identified as high school graduates with complete transcripts. For more information on the 

NELS:88 second follow-up transcript study, see NELS:88 Second Follow-up: Transcript 

Component Data File User’s Manual (Ingels et al. 1995). 

The overall unit response rate for the NELS:88 analysis sample used in this report is 

derived as it was for the HS&B analysis sample—as a function of the base-year school unit 

response rate (first stage of selection for the study) and the unit response rate for sample 

members eligible for both the second follow-up student survey and the high school transcript 

survey (the NELS:88 analysis sample used for this report is a freshened senior cohort). In the 

base year of NELS:88, of the 1,002 schools initially selected (and eligible) to participate in the 

study, 698 schools agreed to do so, for a school cooperation rate (not school questionnaire 

response rate) of 70 percent. In the second follow-up, of the subsample of 19,320 students for 

whom transcript data were requested (and who were eligible for the second follow-up student 

survey), transcripts were received for 17,285 students, for a weighted unit response rate of 88 

percent or an unweighted unit response rate of 90 percent (Ingels et al. 1995). This translates into 

an overall unit response rate of 61 percent (0.697 x 0.878 = 0.6119). Because the classification 

variables used in this report could be drawn from the base year, first follow-up, or second followup, we also provide the response rates for student questionnaire completion in each of those 

rounds. In the base year, 93 percent of sample members completed the student questionnaire; in 

the first follow-up, 94 percent completed a questionnaire; and in the second follow-up, 93 

percent completed a questionnaire. Based on questionnaire completion, the unweighted twostage response rates for the study are 65 percent for the base year (0.931 x 0.697 = 64.9 percent), 

66 percent for the first follow-up (0.942 x 0.697 = 65.7 percent), and 65 percent for the second 

follow-up (0.925 x 0.697 = 64.5 percent). 

A unit nonresponse bias analysis similar to that conducted for HS&B was conducted for 

NELS:88. The analysis found a magnitude of bias of 5 percent (Spencer et al. 1990). For 

analyses in this report, item response rates ranged from a low of 97 percent for socioeconomic 

status to a high of 100 percent. Ninety-nine percent of transcripts were complete. No other 

NELS:88 items used in this analysis registered less than a 100 percent item response. 

A-5 
 

 

 

 

 

Appendix A. Technical Notes and Methodology 

A.1.3 Education Longitudinal Study of 2002 

ELS:2002 began with a national probability sample of high school sophomores in 2002. 

Individual students are expected to be followed until about age 30; the base-year schools have 

been surveyed twice (they were surveyed in 2002 and again in 2004). A second follow-up was 

completed in the summer of 2006. In the high school years, ELS:2002 is an integrated, multilevel 

study involving multiple respondent populations, including students, their parents, their teachers, 

and their schools (from which data are collected at three levels: from the principal, the librarian, 

and on a facilities checklist). This multilevel focus supplies researchers with a comprehensive 

picture of the home, community, and school environments that provide context for understanding 

student educational processes and outcomes. The ELS:2002 base-year study was carried out in a 

national probability sample of 752 public, Catholic, and other private schools in the spring term 

of the 2001–02 school year. Of 17,591 eligible selected sophomores, 15,362 completed a baseyear questionnaire, as did 13,486 parents, 7,135 teachers, 743 principals, and 718 librarians. The 

unweighted response rate at the school level was 62 percent and at the sophomore baseline level 

was 87 percent. Data weights were adjusted for nonresponse at each level. 

The overall unit response rate for the ELS:2002 sample used in this report is derived as a 

function of the base-year school response rate (first stage of selection for the study) and the unit 

response rate for sample members eligible for the high school transcript survey (transcript 

eligibility was normally3

 conditioned on questionnaire completion in the ELS:2002 base year, or 

first follow-up, or both; the ELS:2002 analysis sample used for this report was a freshened senior 

cohort). In the base year of ELS:2002, of the 976 eligible schools initially selected to participate 

in the study, 631 schools agreed to do so, for an unweighted school cooperation rate of 65 

percent. In the first follow-up, of the approximately 16,400 students for whom transcript data 

were requested, transcripts were received for about 14,290 students, or an unweighted 87 percent 

of the total transcript sample. [For the senior cohort used in this report, 93 percent (13,424) had 

transcripts (Bozick et al. 2006, Table 5)]. This translates into an overall unit response rate of 56 

percent (0.647 x 0.871 = 0.564).4 Because the classification variables used in this report could be 

drawn from either base year or first follow-up data, we also provide the response rates for 

questionnaire completion in both the 2002 and the 2004 rounds. In the base year, 88 percent of 

sample members completed the student questionnaire; in the first follow-up, 91 percent 

completed a questionnaire. Based on questionnaire completion, the two-stage unweighted 

3

 While for questionnaire-eligible sample members, transcript eligibility was based on participation (completing at 

least the student questionnaire) in either or both rounds, transcripts were also collected for questionnaire-ineligible 

sample members (i.e. the small number of individuals who could not be surveyed because of severe disability or 

language barrier, and who appear only on restricted use files). 

4

 Calculation of overall unit response for the three studies is constrained by the limitations in the documentation of 

HS&B and NELS:88. Alternative calculations are possible for ELS:2002, because of its greater richness of 

documented information. For example, instead of basing the school response rate on the subset of participating 

schools that were part of the original pool, one can calculate the response rate based on the total pool of schools 

(including replacements) used in achieving the final sample. Likewise, instead of basing calculations on unweighted 

rates, one can employ the design weight to generate a weighted response rate. The weighted completion rate for 

ELS:2002, based on all schools drawn into the sample and contacted is, weighted, 67.8 percent. The weighted 

transcript response rate is 90.7 percent. Thus the two-stage response becomes, not 56.4 percent, but 61.5 percent 

(0.678 x 0.907 = .615). Also, if restricted to simply the senior cohort, the transcript response rate (weighted) goes up 

to 93.1 percent (0.678 x 0.931 = 63.1 percent). Readers may see different ELS:2002 response rate information than 

is reported in trend analyses, in reports based solely on the one study. 

A-6 
 

 

 

Appendix A. Technical Notes and Methodology 

response rates for the study are 57 percent for the base year and 59 percent for the first follow-up 

(0.647 x 0.877=56.7 percent; 0.647 x 0.908= 58.7 percent). 

A.2 Accuracy of Estimates 

The estimates in this report are derived from a sample and are subject to two broad 

classes of error: nonsampling and sampling errors. Nonsampling errors occur not only in sample 

surveys but also in complete censuses of entire populations. Nonsampling errors can be 

attributed to a number of factors: inability to obtain complete information about all students in all 

institutions in the sample (some students or institutions refused to participate, or students 

participated but answered only certain items); ambiguous definitions; differences in interpreting 

questions; inability or unwillingness to give correct information; mistakes in recording or coding 

data; and other errors of collecting, processing, sampling, and imputing missing data. Although 

nonsampling errors due to questionnaire and item nonresponse can be reduced somewhat by 

adjusting sample weights and imputation procedures, correcting all the forms of nonsampling 

errors that may be operating, or gauging the effects of these errors, is usually difficult. 

Sampling errors occur because observations are made only on samples of students, not on 

entire populations. Surveys of population universes are not subject to sampling errors. Estimates 

based on a sample will differ somewhat from those that would have been obtained by a complete 

census of the relevant population using the same survey instruments, instructions, and 

procedures. The standard error is a measure of the variability due to sampling when estimating 

statistics. Standard errors can be used as a measure of the precision expected from a particular 

sample. If all possible samples were surveyed under similar conditions, intervals of 1.96 standard 

errors below to 1.96 standard errors above a particular statistic would include the true population 

parameter being estimated in about 95 percent of the samples. In addition, the standard errors for 

two sample statistics can be used to estimate the precision of the difference between the two 

statistics and to help determine whether the difference based on the sample is large enough to 

represent the population difference. 

Because HS&B, NELS:88, and ELS:2002 data were collected using a complex sampling 

design, the sampling errors of the estimates from these surveys are typically larger than would be 

expected if the sample were a simple random sample and the observations were independent and 

identically distributed random variables. Not taking the complex sample design into account can 

lead to an underestimate of the sampling variance associated with an estimate. To generate 

accurate standard errors for the statistics reported in this study, the Taylor series approximation 

method was used. In particular, standard errors of estimates from the HS&B, NELS:88, and 

ELS:2002 data were computed using the Taylor series approximation. For more information 

about these methods, see Wolter (1985). SUDAAN (Research Triangle Institute) and AM 

(American Institutes for Research) were the statistical software packages used to generate 

estimates and standard errors. 

A.3 Statistical Procedures 

Two types of statistical tests were used in this report. First, t tests ensured that reported 

differences (e.g., difference between two means/percentages and difference between differences) 

are larger than those that might be expected because of sampling variance. Second, effect sizes 

were calculated and only those differences large enough to meet preset criteria were discussed. 

A-7 
 

 

 

Appendix A. Technical Notes and Methodology 

Differences were reported in the text only if the comparison met the criteria of both statistical 

significance and substantive difference. These procedures are discussed in this section. 

A.3.1 Testing the Difference between Two Means or Percentages 

The student’s t statistic was used to test the likelihood that the differences between two 

independent means or percentages were larger than would be expected because of sampling 

error. The Student’s t values can be computed for comparisons using the estimates in the report’s 

tables with the following formula: 

E1 − E

t = 2 

(se 2 + se 2 

1 2 )

where E1 and E2 are the estimates to be compared, and se1 and se2 are their corresponding standard 

errors. Generally, whether a difference is considered statistically significant is determined by 

comparing this t value or “test statistic” with published tables of t values or “critical values” and 

their corresponding alpha levels. The alpha level is an a priori statement of the probability of 

inferring that a difference exists when in fact, it does not. The alpha level used in this report is 

.05; differences discussed in the text have been tested and found significant at this level. Twotailed tests were performed. 

A.3.2 Testing the Difference between Differences 

Another statistical test used in this report assessed the difference between two difference 

estimates. For example, to test whether the gender gap in a specific year (e.g., 1982) differed 

significantly from the gender gap in another year (e.g., 2004), a test of differences between 

differences was performed using the following formula: 

(E11 − E21 ) − (E12 − E22 ) t = 2

( 2 

2 2 2 2 

se 11 + se 21 ) + ( se 12 + se 22 )

where E11 and E21 are the estimates for the two comparison groups at time 1 (i.e., E11 – E21 is the 

difference between males and females at time 1), E12 and E22 are the estimates for the two 

comparison groups at time 2 (i.e., E12– E22 is the difference between males and females at time 2), 

and se11, se21, se12 , and se22 are their corresponding standard errors. After the t value was obtained, 

it was compared with the alpha level to determine whether the differences between the 

comparison groups changed significantly between the two time points. 

A.3.3 Substantive Difference 

With large samples, such as ELS:2002, even very small differences may be statistically 

significant. Therefore, differences that met our criterion for statistical significance were also 

examined using effect size calculations. 

For differences between means (in this report, credits earned in mathematics or science), 

effect sizes (or standardized mean difference, expressed as Cohen’s d [Cohen 1988]) were 

calculated. The effect size is interpreted as the number of standard deviations separating the 

means of the two groups. Effect sizes were calculated as the difference in mean numbers of 

A-8 
 

 

Appendix A. Technical Notes and Methodology 

credits divided by the pooled standard deviation. The formula for computing the pooled standard 

deviation was 

(n1 – 1) σ1

2 + (n2 – 1) σ22

n1 + n2 – 2

(n1 – 1) σ1 

2 + (n2 – 1) σ2 2 

n1 + n2 –2 . 

Whether an effect size is small, moderate, or large depends on the variables being studied 

and the research context. Cohen (1988) provided some general guidelines for the behavioral 

sciences, suggesting that “...when no better basis for estimating the ES index is available” (p. 

25), effect sizes of .2 or less could be considered small, those around .5 medium, and those of .8 

or greater could be considered large. Based on these guidelines, an effect size of .2 was selected 

as a cut-point for determining which mean differences would be discussed in this report.5 While 

tables of effect sizes are not provided in the report, standard deviations are reported for mean 

credits earned, should readers wish to calculate an effect size. Because some readers may choose 

the pooled standard deviation approach, sample sizes (rounded to protect confidentiality) are 

reported in appendix D. 

For proportions, this report has adopted a simple convention of considering differences 

that are 5 percentage points or greater as being substantively different. Though such differences 

may be differentially meaningful depending on the initial percentage (a 5 to 10 percent growth 

may be substantively different from a 55 to 60 percent growth), this rule limits discussion of very 

small group differences. 

A.4 Bias Analysis 

This analysis report investigated the mathematics and science coursetaking patterns of 

high school students who graduated in 1982, 1992, and 2004. A graduate was defined as a 

student who had received either a standard or an honors diploma. Additionally, only the 

coursetaking histories of graduates for whom complete transcripts were available were analyzed. 

A full or complete transcript was defined as a transcript that reported at least 16 credit hours for 

the graduate, with some of the 16 credit hours including credit hours in English. The 

Classification of Secondary School Courses (CSSC) and the 1998 Revision of the Secondary 

Schools Taxonomy (SST) (Bradby and Hoachlander 1999) were used to code transcripts and 

identify credit hours, called Carnegie units. 

Because of the need to apply the additional criterion—only graduates for whom complete 

transcripts were available—a bias analysis was undertaken to determine the extent to which the 

final analysis samples from HS&B, NELS:88, and ELS:2002 differed from, and thus may not 

generalize to, the target population of American high school graduates. To do this, all student 

sociodemographic characteristics examined in this report—gender, race/ethnicity, school sector, 

socioeconomic status, and educational expectations—were compared for all 12th-grade 

graduates (the full sample for the target population) and 12th-grade graduates with complete 

transcripts (the analytic sample). If the distribution of student characteristics was different 

between these groups, the generalizability of the estimates presented here could be compromised. 

Estimates are considered different if the difference exceeds 5 percentage points—the effect size 

5

 For more information about these cutoffs and effect sizes, see Cohen (1988), Murphy and Myers (2004), and 

Seastrom (2003). 

A-9 
 

Appendix A. Technical Notes and Methodology 

criterion used in this report to assess substantive difference. The variables used to identify each 

final analysis sample and the analysis weights used are described at the end of this appendix. 

The results of this bias analysis are shown in Table A-1. The table displays the three high 

school transcript samples and selected sociodemographic characteristics (row variables) by the 

full target population sample and the analytic sample (sample size figures have been rounded to 

protect confidentiality). Not surprisingly, the analysis reveals no within-sample bias. None of the 

differences in estimates exceed the five percentage point criterion. This is likely because very 

few graduating seniors were excluded from the analysis. 

As an analysis note, this bias analysis is not an analysis of survey nonresponse for the 

population of graduating seniors. That is, it does not investigate the possibility of bias owing to 

the fact that there may be systematic differences between responding seniors and nonresponding 

seniors. For an analysis of nonresponse bias, readers should consult the data file user’s manuals 

of the studies used in this report. The analysis conducted here evaluated the possibility of biased 

analytic samples resulting from the exclusion of seniors who otherwise participated in the studies 

but for whom transcripts were either missing or did not meet the criteria for inclusion in the 

analysis samples (i.e., transcripts reported at least 16 credit hours for each senior, of which some 

were credit hours in English). For the bias analysis reported here, weights that correct for 

nonresponse bias were used.6 

Additionally, some bias in coursetaking trends may result from differences in subgroup 

graduation rates over time. This report describes the coursetaking of spring-term graduating high 

school seniors and does not include very late graduates (i.e., beyond August 31 of their 

graduating year), those who obtained alternative credentials other than a high school diploma, or 

dropouts. Differences in dropout rates over time, or by subgroup, may qualify the conclusions of 

reports based on seniors. For example, if dropout rates were increasing over time, this might 

artificially augment a seeming trend in increases in the proportion of students taking advanced 

courses (presuming that the remaining non-dropouts are more likely to take advanced courses in 

each cohort). The fact that sophomore cohort dropout rates were considerably higher in 1982 (11 

percent; Kaufman, McMillen, and Sweet 1996) than in 1992 (6 percent; Kaufman, McMillen, 

and Sweet 1996) or 2004 (7 percent; Ingels, Planty, and Bozick 2005) offers some reassurance 

that observed trends of increase in advanced math and science coursetaking are not an artifact of 

changing dropout rates. 

6

 Though nonresponse-adjusted weights are used, bias remains a possibility because the weights do not adjust for the 

subsettings invoked to create the analysis sample. Some cases have been removed from the target population 

(seniors) owing to incomplete transcripts or transcripts that do not meet the criteria for inclusion (e.g., zero credit 

hours in English; receipt of a certificate of attendance, special education diploma, or no diploma; and lack of a 

minimum of 16 earned Carnegie units). 

A-10 
Table A-1. Selected characteristics of all high school graduates versus high school graduates with full transcript

2004 

12th-grade graduates 12-grade graduates with full transcripts 

(full target population sample) (analysis sample) 

Weighted Weighted 

estimate Standard estimate Standa

Characteristic Sampled (percent) error Sampled (percent) err

HS&B 

Total 11,700 100.0 † 11,200 100.0 

Gender 

Male 5,600 47.9 0.60 5,300 47.3 0.6

Female 6,100 52.1 0.60 5,800 52.7 0.6

Race/ethnicity 

Americ Ian ndian 160 1.1 0.20 150 1.1 0.2Asian 320 1.4 0.15 310 1.4 0.Black 1,500 10.6 0.61 1,500 10.3 0.6

Hispanic 2,300 11.1 0.41 2,200 10.9 0.4

White 7,200 74.9 0.81 7,000 75.2 0.8

School sector 

Public 8,900 89.1 0.66 8,400 88.8 0.6

Catholic 2,100 7.1 0.35 2,100 7.5 0.3

Ot priher vate 750 3.8 0.60 730 3.8 0.5

Socioeconomi stc atus 

Lowest quartile 3,000 23.3 0.71 2,800 23.1 0.7

Middl twe o quartiles 5,200 50.1 0.79 5,000 49.7 0.8Highest quartile 3,100 26.7 0.84 3,000 27.2 0.8

Educati eonal xpectations 

Hi scgh dihool ploma/GED lesor s 2,000 21.6 0.64 1,800 20.9 0.6

pSome ostsecondary education 3,300 33.0 0.64 3,100 32.9 0.6

Baccalaureat dee gree 2,800 25.4 0.63 2,700 26.0 0.6Graduat de egree 2,500 19.9 0.58 2,400 20.2 0.6

See notes at end of table. 

A-11 
Table A-1. Selected characteristics of all high school graduates versus high school graduates with full transcript

2004—Continued 

12th-grade graduates 12-grade graduates with full transcripts 

(full target population sample) (analysis sample) 

Weighted Weighted 

estimate Standard estimate Standard 

Characteristic Sampled (percent) error Sampled (percent) erro

NELS:88 

Total 13,600 100.0 † 13,500 100.0 

Gender 

Male 6,800 50.1 0.91 6,700 50.0 0.9

Female 6,900 50.0 0.91 6,800 50.0 0.9

Race/ethnicity 

American Indian 130 0.9 0.16 130 0.9 0.1

Asian 1,000 4.4 0.34 1,000 4.3 0.3Black 1,100 11.0 0.83 1,100 11.0 0.8Hispanic 1,400 9.1 0.75 1,400 9.0 0.7White 9,900 74.3 1.17 9,800 74.3 1.1

School sector 

Public 11,600 90.5 0.96 11,500 90.6 0.9

Catholic 780 5.7 0.52 780 5.7 0.5

Other private 1,200 3.8 0.69 1,200 3.7 0.6

Socioeconomic status 

Lowest quartile 2,300 17.6 0.76 2,300 17.5 0.7

Middle two quartiles 6,400 52.1 1.06 6,400 52.1 1.0

Highest quartile 4,500 30.4 1.20 4,400 30.4 1.2

Educational expectations 

High school diploma/GED or less 530 4.7 0.37 520 4.7 0.3

Some postsecondary education 2,800 25.4 0.89 2,800 25.5 0.8

Baccalaureate degree 4,300 36.6 1.00 4,300 36.6 1.0Graduate degree 4,500 33.2 1.05 4,500 33.1 1.0

See notes at end of table. 

A-12 
Table A-1. Selected characteristics of all high school graduates versus high school graduates with full transcript

2004—Continued 

12th-grade graduates 12-grade graduates with full transcripts 

(full target population sample) (analysis sample) 

Weighted Weighted 

estimate Standard estimate Standard 

Characteristic Sampled (percent) error Sampled (percent) erro

ELS:2002 

Total 10,900 100.0 † 10,800 100.0 † 

Gender 

Male 5,300 49.0 0.61 5,300 48.9 0.60 

Female 5,600 51.0 0.61 5,500 51.1 0.60 

Race/ethnicity 

American Indian 80 0.8 0.20 80 0.8 0.20 

Asian 1,200 4.6 0.32 1,100 4.6 0.31 

Black 1,200 12.1 0.68 1,200 12.1 0.68 Hispanic 1,400 14.0 0.83 1,400 14.0 0.84 White 6,600 64.5 1.05 6,600 64.6 1.06 

School sector 

Public 8,300 91.4 0.41 8,300 91.5 0.41 

Catholic 1,600 4.9 0.26 1,600 4.9 0.26 

Other private 1,000 3.6 0.33 1,000 3.6 0.33 

Socioeconomic status 

Lowest quartile 2,100 20.8 0.69 2,100 20.8 0.69 

Middle two quartiles 5,200 50.5 0.72 5,200 50.5 0.72 

Highest quartile 3,500 28.7 0.84 3,500 28.7 0.84 

Educational expectations 

High school diploma/GED or less 410 4.5 0.28 400 4.5 0.28 

Some postsecondary education 1,600 18.6 0.58 1,600 18.5 0.57 

Baccalaureate degree 3,800 37.7 0.61 3,800 37.8 0.61 

Graduate degree 4,300 39.1 0.69 4,300 39.1 0.69 

† Not applicable. # Rounds to zero. 

NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and American Indian include

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophomores (HSTranscript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudin“First Follow-up, High School Transcript Study, 2004.” 

A-13 
 

Appendix A. Technical Notes and Methodology 

While subgroup generalizations based on graduating seniors provide a valid trend line, 

they may also blunt or mask differences between groups. Cohort dropout rates in HS&B, 

between 10th and 12th grade, were 10 percent for Whites and 19 percent for Hispanics. In 

NELS:88 ten years later, the Hispanic rate had dropped to 12 percent while the White rate was 5 

percent. Event dropout rates show considerable variability not only by race but also by family 

income (Laird et al. 2006) (indeed, race differences diminish as SES is controlled for). A deeper 

accounting of subgroup differences in coursetaking might take into account not only overall 

change in dropout rates over time but also change in relative position of subgroups. 

A.5 Comparability Across HS&B, NELS:88, and ELS:2002 

Though the within-cohort bias is negligible, readers should keep in mind that there are 

key differences among the studies that could potentially influence the interpretations of the 

trends presented in this report. Differences in the sampling frames, eligibility requirements, and 

transcript collection methodologies could possibly account for increases or decreases in the 

proportion of students taking advanced-level academic courses. Each of these are discussed in 

turn. 

Both the National Education Longitudinal Study of 1988 (NELS:88) and the Education 

Longitudinal Study of 2002 (ELS:2002) include a nationally representative sample of 12thgraders, of which a subset is 12th-grade graduates that constitute a naturally occurring nationally 

representative sample of 12th-grade graduates. High School and Beyond (HS&B), on the other 

hand, is a nationally representative sample of 1980 sophomores, and of the 1980 sophomore 

cohort 2 years later (1982) when the HS&B transcript study was conducted. HS&B imperfectly 

represents the nation’s 1982 graduating seniors primarily because 1982 seniors who were not 

sophomores in 1980 are not included in the sample. The potential bias arising from comparing 

full senior samples from NELS:88 and ELS:2002 to a longitudinal senior sample of HS&B 

sophomores is explored in section A.5.1 below. 

In addition to differences in sampling the target populations, study eligibility 

requirements could influence the results of this analysis. HS&B and NELS:88 excluded students 

with severe mental, physical, or linguistic barriers to completing survey forms, at a rate ranging 

from approximately 3 to perhaps 6 percent. In NELS:88, exclusion was primarily in the 8thgrade base year (5 percent of the 8th-grade sample) but a subsample of excluded 8th-graders was 

followed to high school and incorporated into the study when their status had changed (e.g., if an 

excluded student had since become proficient in English). Thus, about 3 percent of the NELS:88 

high school sample was excluded for eligibility reasons. In ELS:2002, no students were formally 

excluded from the study, but some students with physical, mental, or linguistic barriers to 

participation were classified as “questionnaire-ineligible.” For these students, basic demographic 

information, contextual and records information (parent questionnaire, school administrator 

questionnaire, high school transcript) were collected, but the student was not administered a 

questionnaire. 

HS&B did not collect transcripts for students excluded from the questionnaire and test 

components of the study. NELS:88 collected transcripts for a probability subsample of its 

cohorts, which included 8th-grade ineligible students whose eligibility had changed by high 

school and a special methodological sample of “triple ineligibles”; it did not otherwise include 

the ineligible sample in the transcript collection. ELS:2002, however, pursued transcripts both 

for questionnaire-eligible and questionnaire-ineligible sample members. Thus, all three samples 

A-14 
 

 

 

 

Appendix A. Technical Notes and Methodology 

fall short of representing American high school 12th-graders by the small amount (from less than 

1 percent to possibly as much as 6 percent) of excluded students during the years in focus, and 

for HS&B and NELS:88 (but not ELS:2002) this undercoverage affects the transcript studies. 

However, the studies underrepresent graduating 12th-graders to a lesser degree, since only a 

portion of excluded students were seniors who graduated on time.7 

Procedures for collecting transcripts differed very slightly across studies. Both HS&B 

and NELS:88 collected transcripts from the last school attended by the student (which normally 

but not invariably included the full cumulative record), while ELS:2002 collected transcripts 

from the student’s base-year school (i.e. the school from which they were originally sampled) 

and their final school if they transferred out of their base-year school. 

Readers interested in a more extensive discussion of comparability across NCES 

transcript studies should see either the National Center for Education Statistics (NCES) Working 

Paper, National Education Longitudinal Study of 1988: Conducting Cross-Cohort Comparisons 

Using HS&B, NAEP, and NELS:88 Academic Transcript Data (Ingels and Taylor 1995) or 

appendix A in the Education Longitudinal Study of 2002: First Follow-up Transcript Component 

Data File Documentation (Bozick et al. 2006). 

A.5.1 Cross-study Bias Analysis 

The lack of a freshened senior cohort in HS&B’s 1982 follow-up survey to the 1980 

sophomore survey may introduce bias with respect to cross-study comparisons of HS&B to 

NELS:88 and ELS:2002. To assess the presence and extent of bias arising from the different 

cohort definitions, this section presents results from an analysis of the differences between 

freshened and unfreshened samples in NELS:88 and ELS:2002, differences between the HS&B 

senior and sophomore cohorts, and an analysis of the differences in substantive results when 

using freshened and unfreshened analysis samples in NELS:88 and ELS:2002.8 

There are two complementary approaches that may be used for assessing the impact of 

freshening. The first approach is to look at differences in student characteristics between 

freshened and unfreshened senior samples (for NELS:88 and ELS:2002) and differences in 

student characteristics between the 1980 and 1982 senior samples (of HS&B). Since HS&B’s 

1980 sophomore survey does not have a freshened senior cohort sample for 1982, but there is a 

1980 senior survey, they may be compared profitably. Both survey samples are nationally 

representative (in 1980) and were drawn from the same schools, heightening the prospect that the 

true 1982 senior cohort and the observed 1982 senior cohort (measured as 1980 sophomores two 

years later) are similar. With the (relatively strong) assumption that the 1980 senior and 

sophomore cohorts were similarly composed with respect to student demographics, a finding of 

few differences between the 1980 senior cohort and the 1980 sophomore cohort in 1982 would 

suggest that the 1982 seniors fairly represent the population of seniors at that time. The 

assumption of cohort similarities limits the ability to draw positive conclusions, but the findings 

7

 For the longitudinal studies—HS&B, and NELS:88, and ELS 2002—“on time” means graduated by August 31 of 

their respective graduating years. 

8

 An additional question of interest, but not explored here, is the effect of sample definitions that filter cases based 

on curricular minima and graduation requirements, and which have been used to compare longitudinal study results 

to NAEP results. The hypothetical effect of such filters would be to make freshened and unfreshened samples more 

similar, given the known characteristics (typically high school grade repeaters) of the freshened samples. 

A-15 
Appendix A. Technical Notes and Methodology 

may be used alongside the other approaches in this section to provide an overall picture of 

potential bias. 

For NELS:88 and ELS:2002 within-study comparisons, the analyses are more 

straightforward. Here we compare (for each study) the freshened senior sample, the longitudinal 

sample of seniors, and the combination of the two. Few differences in student characteristics 

between the different sample definitions in these studies would suggest, by analogy, that the lack 

of freshening as present in HS&B does not substantially distort HS&B estimates. The main 

difference between NELS:88 and ELS:2002 is the fact that key item statistical imputation was 

performed for the latter. 

The second approach is to look at the impact of the sample differences on actual 

estimates and their standard errors. For this approach, a selection of NELS:88 and ELS:2002 

transcript estimates are reported with the freshened students removed and compared to the results 

from the main parts of this report. The impact is examined in terms of both the statistical 

significance of the difference between with- and without-freshened estimates, as well as the 

systematic direction of any bias. 

Characteristics of freshened versus unfreshened senior samples in NELS:88 and 

ELS:2002. Table A-2 shows selected student characteristics from both the full (freshened) senior 

samples and the longitudinal (unfreshened) samples of seniors who were sophomores two years 

earlier (using the transcript weight). The latter samples are analogous to the HS&B 1980 

sophomore cohort two years later, in terms of selection into the sample. The NELS:88 

sophomores were surveyed in 1990 and are a nationally representative sample of sophomores in 

that year; the NELS:88 seniors were surveyed in 1992 and include both sophomores surveyed in 

the previous wave (in 1990) and an additional supplement of seniors that together are a 

nationally representative sample of seniors in 1992. Similarly, ELS:2002 sophomores are 

nationally representative of high school sophomores in 2002, when they were surveyed, and the 

ELS:2002 senior cohort includes both sophomores surveyed in the previous study wave as well 

as additional seniors in 2004. 

For NELS:88, no statistically significant differences were observed between the 

alternatively defined senior cohorts in terms of student characteristics of sex, race/ethnicity, 

socioeconomic status (SES) quartile, school sector, region, or senior year math test score. For 

ELS:2002, only one statistically significant difference was observed: a two percentage-point 

difference in the percentage of seniors who were non-Hispanic White. Sixty-four percent of 

sophomores who were seniors two years later were White in 2004, while 62 percent of all seniors 

were White in 2004. 

A-16 
 

 

Appendix A. Technical Notes and Methodology 

Table A-2. Percentage distribution of selected student characteristics and mean math IRT score 

for freshened versus unfreshened samples (transcript weight) of NELS:88 and 

ELS:2002 seniors: 1992 and 2004 

NELS:88: 1992 ELS:2002: 2004 

Seniors who Seniors who 

were Full senior were Full senior 

sophomores cohort sophomores cohort 

two years (freshened two years (freshened 

Characteristic earlier sample) earlier sample) 

Sex 

Male 50.3 50.3 49.6 49.9

Female 49.7 49.7 50.4 50.1

Race/ethnicity 

Asian 4.1 4.3 4.2 4.5

Hispanic 9.8 10.0 14.1 15.0

Black 12.0 12.0 13.1 13.3

White 72.9 72.1 63.7 62.2 *

American Indian 1.1 1.2 0.9 0.9 

More than one race — — 4.1 4.1 

SES 

1st (low) quartile 18.6 18.8 22.2 22.3 

Middle 2 quartiles 52.2 52.0 50.8 50.7 

4th (high) quartile 29.2 29.2 27.0 27.0 

School control 

Public 90.4 91.0 91.8 91.9

Catholic 5.7 5.2 4.7 4.5

 

NAIS private 1.6 1.5 — — 

Other private 2.3 2.2 3.6 3.6 

Region 

Northwest 20.2 20.4 18.7 18.7

Midwest 25.9 25.6 24.9 24.5

South 35.0 34.4 34.4 34.0

West 18.9 19.6 22.1 22.7

Math test (mean IRT score) 48.9 48.7 48.8 48.5 

— Not available. 

* Statistically significantly different from sample based on seniors who were sophomores two years earlier (p<.05). 

NOTE: IRT = item response theory. SES = socioeconomic status. NAIS = National Association of Independent Schools. Black 

includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and American Indian 

includes Alaska Native. NELS:88 did collect “more than one race” information. For NELS:88, F2TRSCWT was the transcript weight 

used. For ELS:2002, F1TRSCWT was the transcript weight used. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88/92), "Second Follow-up, 1992"; and Education Longitudinal Study of 2002 (ELS:2002), "First Follow-up, 2004." 

To the extent that the difference observed in ELS:2002 might apply to the differences 

between a hypothetical HS&B full (freshened) senior cohort in 1982 versus the actual 1980 

HS&B sophomore cohort two years later, this suggests that the HS&B survey could have a small 

overrepresentation of Whites. Since White seniors in HS&B were more likely to have completed 

more and higher levels of math and science coursetaking than students overall, this could have 

inflated overall estimates of coursetaking in the HS&B sample used for the current report, 

making the actual growth in coursetaking between 1982 and 2004 somewhat greater. However, 

A-17 
 

 

 

Appendix A. Technical Notes and Methodology 

the lack of any other differences either in ELS:2002 or NELS:88 suggests that a sophomore 

cohort two years later is a good approximation for a fully representative senior cohort.9 

Characteristics of HS&B sophomore cohort as seniors (in 1982) versus senior cohort 

(in 1980). Another way of examining the potential bias in using the 1980 HS&B sophomore 

cohort two years later as an approximation of 1982 seniors is to compare this senior sample to 

the nationally representative senior cohort surveyed in 1980. Table A-3 presents selected student 

and school characteristics from these two senior samples.10 

In contrast to the NELS:88 and ELS:2002 results, comparison of the two temporally close 

HS&B samples shows that the longitudinal sample of seniors (who were sophomores in 1980) 

may somewhat underestimate, in particular, the percentage of White and low socioeconomic 

status (SES) students, and somewhat overestimate the percentage of seniors in the middle SES 

quartiles: there were 4 percentage points fewer Whites, 5 percentage points more Hispanics, 3 

percentage points fewer low-SES seniors, and 2 percentage points more middle-SES seniors 

among the longitudinal sample of 1982 seniors than the cross-sectional 1980 senior sample. An 

additional but smaller difference was observed in the mean number of math test items answered 

correctly (about one-half a test question less [0.4] in the longitudinal sample; an examination of 

the distribution of correct answers shows that about a half-percentage point fewer seniors in the 

longitudinal sample scored in the middle and upper quartile of items answered correctly). 

The smaller proportions of Whites and low-SES seniors, and the higher percentage of 

Hispanics, in the longitudinal sample may be attributable to cohort differences between the two 

groups of seniors measured two years apart. Indeed, the shifts are consistent with the overall 

decline in the proportion of Whites, the increase in Hispanics, and the shifts in SES from the 

1980 HS&B to the 1992 senior cohort of NELS:88 (see table A-2). However, differences due to 

the sampling procedure (a longitudinal versus full cross-sectional cohort) cannot be ruled out. 

With respect to the trend analysis presented in the current report, these underestimates may have 

balanced each other, as Whites were more likely, and lower SES students and Hispanics less 

likely, to take some higher level courses in 1982. 

9

 A similar analysis for both NELS:88 and ELS:2002 was conducted using the full sample weights appropriate to 

each wave. Though the transcript weight is most germane to the analysis used in this report, the full weights did 

produce two additional differences between freshened and unfreshened senior samples: in NELS:88, there was a 

similar one-point higher percentage of Whites in the unfreshened sample as in the freshened sample; and in 

ELS:2002, there was a one point lower percentage of Hispanic seniors in the unfreshened sample compared to the 

freshened sample. 

10 The HS&B analysis samples used here are based on base year and first follow-up files, not on the four-round 

longitudinal files currently available as an Electronic Codebook (ECB) from NCES. 

A-18 
 

 

 

Appendix A. Technical Notes and Methodology 

Table A-3. Percentage distribution of selected student characteristics and mean math score for 

1980 senior cohort and 1980 sophomore cohort two years later (in 1982) of HS&B: 1980 

and 1982 

Sophomore cohort of 1980, 

Characteristic Senior cohort of 1980 as seniors in 1982 

Sex 

Male 48.1 49.4 

Female 51.9 50.6 

Race/ethnicity 

Asian 1.3 1.4 

Hispanic 6.3 11.7* 

Black 11.5 11.2 

White 79.0 74.5* 

American Indian 0.7 1.0 

Other 1.2 0.3 

SES 

1st (low) quartile 27.4 23.8* 

Middle 2 quartiles 48.1 50.2* 

4th (high) quartile 24.5 26.0 

Region 

New England 6.9 7.0 

Mid Atlantic 16.0 16.5 

South Atlantic 15.4 16.3 

East south central 5.3 5.4 

West south central 9.7 9.9 

East north central 19.9 20.3 

West north central 8.7 8.2 

Mountain 5.1 4.8 

Pacific 13.0 11.5 

Math test (mean number right) 10.8 10.4* 

* Statistically significantly different (p < .05) from senior cohort of 1980. 

NOTE: SES = socioeconomic status. Black includes African American, Hispanic includes Latino, Asian includes 

Native Hawaiian or Other Pacific Islander, and American Indian includes Alaska Native. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond 

Longitudinal Study of 1980 Sophomores (HS&B-So:80/82); and High School and Beyond Longitudinal Study of 1980 

Seniors (HS&B-Sr:80). 

Coursetaking results for freshened versus unfreshened senior samples in NELS:88 

and ELS:2002. The final analysis examines the impact of freshening on the coursetaking 

estimates presented in this report; it compares the full (freshened) senior samples to the 

longitudinal (unfreshened) samples of NELS:88 and ELS:2002 (in the case of NELS:88, the 

relevant longitudinal sample is the representative cohort of 10th graders in 1990 two years later, 

not the 8th-grade cohort in 1988 four years later). For each survey, estimates were computed for 

mathematics and science coursetaking, both in average number of credits earned and the level 

(pipeline) of courses taken. These estimates included estimates for both the full sample and for 

student subgroups defined by sex, race/ethnicity, socioeconomic status, school sector, and 

educational expectations. The statistical difference between each pair of estimates was tested; a 

summary of the results is presented in table A-4. 

A-19 
Appendix A. Technical Notes and Methodology 

For both NELS:88 and ELS:2002 surveys, no statistical differences in estimates were 

observed in comparisons between the freshened senior cohort and the unfreshened senior cohort. 

Though there is an apparent tendency for the unfreshened estimates to be slightly larger than the 

freshened estimates (particularly in the NELS:88 estimates of course credits earned), none of 

these differences were statistically significant. Questions about the direction or magnitude of bias 

are thus not applicable to the unfreshened versus freshened coursetaking estimates, as no 

statistical bias was observed. 

Conclusion. Very few differences were observed in student characteristics, and no 

differences in actual coursetaking estimates were observed, when available full senior cohorts 

(freshened samples) were compared to longitudinal senior cohorts (unfreshened samples based 

on seniors who were sophomores two years earlier). These findings suggest that bias resulting 

from the lack of cohort freshening in HS&B is not of major concern for this report. 

A-20 
 

Appendix A. Technical Notes and Methodology 

Table A-4. Summary of comparisons of coursetaking estimates computed from freshened and 

unfreshened senior samples of NELS:88 and ELS:2002: 1992 and 2004 

Summary Mathematics Science Overall 

NELS:88 

All comparisons 

Total number of comparisons 132 132 264 

Number of statistically significant differences 0 0 0 

Percentage of comparisons significantly different (p < .05) 0 0 0 

Percentage of statistically significant differences in which 

unfreshened estimate > freshened estimate † † † 

Comparisons of means (course credit estimates) 

Number of means comparisons 24 24 48 

Percentage of comparisons in which unfreshened estimate > 

freshened estimate (all differences statistically 

nonsignificant) 79.2 79.2 79.2 

Comparisons of percentages (course level estimates) 

Number of percentage comparisons 108 108 216 

Percentage of comparisons in which unfreshened estimate > 

freshened estimate (all differences statistically 

nonsignificant) 61.1 54.6 57.9 

ELS:2002 

All comparisons 

Total number of comparisons 138 138 276 

Number of statistically significant differences 0 0 0 

Percentage of comparisons significantly different (p < .05) 0 0 0 

Percentage of statistically significant differences in which 

unfreshened estimate > freshened estimate † † † 

Comparisons of means (course credit estimates) 

Number of means comparisons 24 24 48 

Percentage of comparisons in which unfreshened estimate > 

freshened estimate (all differences statistically 

nonsignificant) 50.0 79.2 64.6 

Comparisons of percentages (course level estimates) 

Number of percentage comparisons 114 114 228 

Percentage of comparisons in which unfreshened estimate > 

freshened estimate (all differences statistically 

nonsignificant) 55.3 48.2 51.8 

† Not applicable 

NOTE: NELS:88 unfreshened senior sample based on 10th-grade (first follow-up) freshened cohort. Transcript weights used in both 

NELS:88 and ELS:2002. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88/92), "Second Follow-up, Transcript Survey, 1992"; and Education Longitudinal Study of 2002 (ELS:2002), "First Followup, High School Transcript Study, 2004." 

A.6 Procedures for Selecting the Final Analysis Transcript Samples 

The following filters were used to identify high school senior cohort graduates, who 

graduated on time and with a set of full transcripts. 

A-21 
Appendix A. Technical Notes and Methodology 

A.6.1 High School and Beyond (HS&B) 

The weight used with the 1982 HS&B sample was the transcript weight TRWT. Filters 

were added to ensure that only students in school and in 12th grade were used. HS&B did not 

freshen its 1982 12th grade sample. 

• Sample members were kept in the analysis if the reason that they left school was 

graduation (IF RESNLEFT = 1). The variable is a transcript variable from the last 

school the student attended. 

• Sample members were kept if they graduated during the 1981–82 school year or prior 

to the 1982–83 school year (using a combination of YEARLEFT and MONLEFT). 

YEARLEFT and MONLEFT are transcript variables obtained from the graduating 

school. SAS code is reproduced below. 

IF 80 < YEARLEFT < 83 THEN DO; 

IF YEARLEFT = 81 AND MONLEFT < 08 THEN DELETE; 

ELSE IF YEARLEFT = 82 AND MONLEFT > 10 THEN DELETE; 

END; 

ELSE 

DELETE; 

• The following code was added to ensure selection of students who graduated, 

graduated with a standard or honors diploma, and not a diploma/special education. 

Legal values are 1 through 6. Values 1 (special education) and 4 (special and 

bilingual) are removed. 

IF ENROLLED IN(2,3,5,6); 

• Filters using composite variables were also used. RTOT and RI3 are composite 

variables created using the Secondary School Taxonomy (SST) definitions of the 

transcript variable CSSC (Classification of Secondary School Courses). RTOT is the 

total of earned standard Carnegie credits. A value of 16 was used to identify a full 

set. This limit does not include any lump sum transfer credits. RI3 is the total of 

earned credits in English. It was thought that a student must have some English 

credits to graduate. 

IF RTOT >= 16; 

IF RI3 > 0; 

A.6.2 National Education Longitudinal Study of 1988 (NELS:88) 

The weight used with the 1992 NELS:88 sample was the second follow-up transcript 

weight, F2TRSCWT. Additional filters were added to ensure that only students in school and in 

grade were used. NELS:88 freshened its 1992 senior sample; these cases are included in the 

analysis sample. 

• A flag was used to identify those students in the survey who also participated in the 

transcript study (IF F2TRSCFL = 1). 

A-22 
Appendix A. Technical Notes and Methodology 

• A transcript variable was used to identify those students who were part of the 12thgrade cohort. Only spring and other 1992 cohort members were kept (IF 1 <= 

G12RCHRT <= 2). 

• A filter was used to identify students who had an exit status from school being a 

standard or honors diploma (IF 1 <= F2RTROUT <= 2). 

• Filters using composite variables were also used. RTOT and RI3 are composite 

variables created using SST definitions of transcript variable CSSC. RTOT is the 

total of earned standard Carnegie credits. A value of 16 was used to identify a full 

set. This limit does not include any lump sum transfer credits. RI3 is the total of 

earned credits in English. It was thought that a student must have some English 

credits to graduate. 

IF RTOT >= 16; 

IF RI3 > 0; 

A.6.3 Education Longitudinal Study of 2002 (ELS:2002) 

The weight used for the 2004 ELS:2002 sample was the transcript weight F1TRSCWT. 

Additional filters were added to ensure that only students in school and in grade were used. 

ELS:2002 freshened its 2004 senior sample; these cases are included in the analysis sample. 

• A flag was used to identify those students in the survey who also participated in the 

transcript study (IF F1RTRFLG >= 1). 

• A transcript variable was used to identify those students who were part of the 12thgrade cohort (IF G12COHRT = 1). 

• A filter was used to identify those students having an exit status from school being a 

standard or honors diploma (IF 1 <= F1RTROUT <= 4). 

• A filter was used to identify students having an exit status during 2004 (IF 20040000 

<= F1RDTLFT <= 20041231). 

• Filters using credit variables were also used. F1RHTUN is the total of earned 

standard Carnegie credits. A value of 16 was used to identify a full set. F1RENG_C 

is a composite variable created using SST definitions of transcript variable CSSC that 

indicates the total of earned credits in English. It was thought that a student must 

have some English credits to graduate. 

IF F1RHTUN >= 16; 

IF F1RENG_C > 0; 

A.7 Glossary of Classification and Transcript Variables 

This glossary gives further information about the following classification variables for 

this report: educational expectations, race/ethnicity, school sector, sex, and socioeconomic status 

(SES). It also provides information about transcript variables employed. 

A-23 
 

Appendix A. Technical Notes and Methodology 

A.7.1 Classification Variables. 

Educational expectations (as of spring term senior year). All three studies asked (in 

slightly variant ways) about students’ expectations for future educational attainment. For this 

report, the more extensive original categories were collapsed into four: high school or less, two 

or fewer years of college, attainment of a bachelor’s degree, and attainment of a graduate or 

professional degree. In ELS:2002 (but not HS&B or NELS:88) missing educational expectations 

data were statistically imputed. 

Race/ethnicity. The race categories used in this report are: American Indian or Alaska 

Native; Asian or Pacific Islander; Black or African American; Hispanic or Latino; More than one 

race; White. Hispanic ethnicity was asked separately from race, and Hispanic respondents may 

have been of any race. The category “more than one race” applies only to ELS:2002. It is 

unknown how an individual in this category in ELS:2002 would have been placed in a race or 

ethnicity category of the two prior studies. In all three studies, race was self-reported, and based 

on a response in the student questionnaire. 

School sector (as of 12th grade). Public, Catholic, and Other Private are the school 

sector categories used in this report. All three studies oversampled non-public schools to some 

degree, the better to represent this comparatively rare population. 

Sex. Consistently across the three studies, respondents were asked whether their sex was 

female or male. In NELS:88 and ELS:2002, name was used to impute sex in the rare cases this 

information was not supplied by the respondent. 

Socioeconomic status (SES). The socioeconomic status (SES) variable offers a good 

example of the subtle differences that may exist between the same variable in different studies, 

despite efforts to maximize cross-cohort consistency of measures. Continuities and differences in 

SES constituents and construction in the three studies are summarized in tables A-5 and A-6. 

Note that socioeconomic status is a continuous variable. However, a categorical version is also 

available for all three studies and was employed in this report. The categorical version provides 

the quartiles into which the continuous version falls, based on the weighted marginal 

distribution. 

A-24 
Table A-6. Elements of the socioeconomic status (SES) composite, ELS:2002: 2004 

Preferred source Student report substitution if missing 

(parent reported) from parent Imputed if still missing 

Father’s occupation Father’s occupation Father’s occupation 

Mother’s occupation Mother’s occupation Mother’s occupation 

Father’s education Father’s education Father’s education 

Mother’s education Mother’s education Mother’s education 

Family income — Family income 

— Not available. 

SOURCE: Education Longitudinal Study of 2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

 

Appendix A. Technical Notes and Methodology 

Table A-5. Elements of the socioeconomic status (SES) composite, HS&B and NELS:88: 1980 and 

1992 

HS&B NELS:88 NELS:88 student substitutions 

(primarily student reported) (primarily parent reported) if missing from parent 

Father’s occupation Father’s occupation Father’s occupation 

— Mother’s occupation Mother’s occupation 

Father’s education Father’s education Father’s education 

Mother’s education Mother’s education Mother’s education 

Family income Family income Household items 

Household items — — 

— Not available. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 

1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; and National Education Longitudinal Study of 1988 

(NELS:88/92), “Second Follow-up, Transcript Survey, 1992.” 

In all three studies, the composite is based on five equally weighted, standardized 

components; however, these components differ somewhat. In HS&B, the household items (e.g., 

appliances, books) were directly used; in NELS:88, they were used only as a proxy for missing 

income data. In HS&B, mother’s occupation was available from the data set but was not used in 

calculating SES. In NELS:88 and ELS:2002, both mother’s and father’s occupation are elements 

of SES. In HS&B, student data were used to construct this composite. In NELS:88 and 

ELS:2002, parent data were used to construct the SES composite. In both NELS:88 and 

ELS:2002, student data were substituted where parent data were missing. However, for parent 

education and occupation, where both parent and student reports were missing, ELS:2002 

education and occupation values were imputed. Family income was not asked of students in 

NELS:88 or ELS:2002. While in NELS:88 a student-provided household item index (see below 

for more information about the household item scale), which served as an income proxy, was 

substituted when income data were missing, a different procedure was followed in ELS:2002: 

when parent data on income were missing, income was statistically imputed. 

The impact of imputation on the intercohort comparability of the SES composite was 

investigated by comparing two versions of 2002 SES, one based on the ELS:2002 specifications, 

the other on NELS:88 specifications. The basic finding was of no impact or extremely small 

impact on estimates. Details are given in Ingels et al. (2005), appendix C. The impact of 

imputation on other aspects of trend estimation was also considered in the same source. 

Some differences in the treatment of SES across the studies are based on differences in 

design. The studies had different starting points. HS&B base-year respondents were sophomores 

or seniors. NELS:88 base-year respondents were 8th-graders. ELS:2002 base-year respondents 

A-25 
 

 

Appendix A. Technical Notes and Methodology 

were sophomores. A parent interview was sought for all NELS:88 and ELS:2002 base-year 

student respondents. HS&B had a parent survey, but it only encompassed a modest subsample of 

student respondents. Because the quality of reporting on parental occupation and education 

increases with student age or grade, it may be of concern whether reports were gathered at grade 

8, 10, or 12. However, since parent reports are markedly superior to student reports in these 

matters, it may be of concern that only in NELS:88 and ELS:2002 are the data primarily parent 

reported. Likewise, students are poor reporters of family income, but the income question was 

asked of students in HS&B and of parents alone in NELS:88 and ELS:2002. 

A.7.2 Transcript Variables. 

Mean course credits: total Carnegie units in mathematics. A Carnegie unit represents 

the completion of a course (i.e., receipt of a passing grade) that meets one period per day (45-60 

minutes) for 1 academic year. “Mathematics” includes courses in (among other areas) general 

mathematics, consumer mathematics, pre-algebra, algebra 1, geometry, algebra 2 and 3, 

trigonometry, analytical geometry, mathematical analysis, precalculus, calculus, Advanced 

Placement (AP) calculus, International Baccalaureate (IB) mathematics, probability and 

statistics, unified mathematics (an integrated course sequence usually taught over 2 or 3 years) 

and occupationally related mathematics. 

Mean course credits: total Carnegie units in science. A Carnegie unit represents the 

completion of a course (i.e., receipt of a passing grade) that meets one period per day (45-60 

minutes) for 1 academic year. “Science” includes courses in (among other areas) survey science, 

biological science (including biology and related specialized courses such as botany, zoology, 

anatomy and physiology), chemistry, physics, astronomy, geology, earth science, physical 

science, and engineering. 

Math and science course-taking pipeline. An ordinal composite variable was 

constructed to indicate the highest level of math for which the student received non-zero credit 

while in high school. For this report, the eight levels were collapsed into six to report the highest 

level of math taken in high school: (1) No math or low academic math; (2) Algebra I/plane 

geometry; (3) Algebra II; (4) Algebra III/trigonometry/analytic geometry; (5) Pre-calculus; (6) 

Calculus. 

An ordinal composite variable indicates the highest level of science for which the student 

received non-zero credit while in high school. This variable captures the “breadth and depth” of a 

student’s science coursetaking histories using four criteria: (1) subject matter taken, (2) when 

taken (e.g., freshman, sophomore, junior, or senior year), (3) whether taken with another science 

course, and (4) academic difficulty. The continuum reflects the order of the most common 

science curriculum used in schools where students take general science courses first, followed by 

biology, then chemistry, and finally physics. Recent analyses of science coursetaking using 

NCES data have realigned the positioning of advanced biology. The current science coursetaking 

pipeline measure contains eight categories, collapsed to six for purposes of this report: (1) No 

science or low-level science; (2) Secondary physical science and basic biology; (3) General 

biology; (4) Chemistry I or physics I; (5) Chemistry I and physics I; (6) Chemistry II, physics II, 

or advanced biology. 

A-26 
Appendix B 

Standard Error Tables 

Appendix B. Standard Error Tables 

This appendix presents standard errors of all estimates in this report. By definition, a 

standard error represents the deviation of the sample estimate from the true population estimate 

or a measure of the accuracy of the estimate; thus, the smaller the standard error, the more 

accurate the estimate. 

Table B-1. Standard errors for figure 1: Percentage of high school graduates who completed 

different levels of mathematics courses: 1982, 1992, and 2004 

Levels of mathematics 1982 1992 2004 

No math or low academic math 0.75 0.61 0.33 

Algebra I/plane geometry 0.75 0.78 0.68 

Algebra II 0.61 0.95 0.75 

Algebra III/trigonometry/analytic geometry 0.64 0.77 0.78 

Precalculus 0.37 0.60 0.63 

Calculus 0.44 0.77 0.55 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 

1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First 

Follow-up, High School Transcript Study, 2004.” 

Table B-2. Standard errors for figure 2: Mean credits earned in mathematics by high school 

graduates, by sex: 1982, 1992, and 2004 

Male Female 

Year Sample (n) SE SD Sample (n) SE SD 

1982 5,300 0.03 1.16 5,800 0.02 1.03 

1992 6,700 0.04 0.93 6,800 0.02 0.83 

2004 5,300 0.02 0.94 5,500 0.02 0.90 

NOTE: SE = standard error; SD = standard deviation. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 

1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First 

Follow-up, High School Transcript Study, 2004.” 

Table B-3. Standard errors for figure 3: Percentage of high school graduates who completed 

different levels of mathematics courses, by sex: 1982, 1992, and 2004 

Male Female 

Levels of mathematics 1982 1992 2004 1982 1992 2004 

No math or low academic math 1.00 0.95 0.45 0.92 0.65 0.40 

Algebra I/plane geometry 1.00 1.14 0.81 0.99 0.92 0.79 

Algebra II 0.81 1.38 0.89 0.77 1.19 0.95 

Algebra III/ trigonometry/analytic geometry 0.81 1.14 0.83 0.79 0.88 0.96 

Precalculus 0.49 0.65 0.72 0.44 0.84 0.84 

Calculus 0.60 1.23 0.74 0.49 0.72 0.64 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 

1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First 

Follow-up, High School Transcript Study, 2004.” 

B-3 
 

 

 

Appendix B. Standard Error Tables 

Table B-4. Standard errors for figure 5: Mean credits earned in mathematics by high school 

graduates, by race/ethnicity: 1982, 1992, and 2004 

1982 1992 2004 

Race/ethnicity Sample (n) SE SD Sample (n) SE SD Sample (n) SE SD 

American Indian 150 0.13 0.12 130 0.09 0.88 80 0.13 0.89 

Asian 310 0.09 0.99 1,000 0.07 0.77 1,100 0.04 0.98 

Black 2,200 0.04 1.02 1,400 0.05 0.86 1,200 0.05 0.93 

Hispanic 7,000 0.02 1.01 9,800 0.05 0.83 1,400 0.04 0.96 

White 1,500 0.04 0.93 1,100 0.03 0.88 6,600 0.02 0.99 

NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, 

and American Indian includes Alaska Native. SE = standard error; SD = standard deviation. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 

1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First 

Follow-up, High School Transcript Study, 2004.” 

B-4 
Table B-5. Standard errors for figure 6: Percentage of high school graduates who completed different levels of m

by race/ethnicity: 1982, 1992, and 2004 

American Indian Asian Black Hispanic 

Levels of mathematics 1982 1992 2004 1982 1992 2004 1982 1992 2004 1982 1992 2004 No math or low academic 

math 8.45 5.60 5.21 2.32 1.95 0.50 2.35 1.74 1.09 1.72 1.69 1.04 

Algebra I/plane geometry 5.93 5.19 4.84 2.82 1.73 1.30 1.80 3.16 1.62 1.59 2.12 2.02 Algebra II 4.22 4.64 6.17 3.17 3.12 1.96 2.03 2.21 1.92 1.12 2.79 1.63 Algebra III/trigonometry/ 

analytic geometry 2.43 3.65 4.55 2.92 1.86 1.32 1.06 1.90 2.30 0.88 2.96 1.58 

Precalculus † 1.07 3.27 3.21 2.84 1.89 0.43 1.54 1.44 0.68 1.00 1.39 Calculus 1.16 0.67 2.72 2.47 2.38 2.50 0.60 1.73 0.69 0.48 0.86 0.87 

† Not applicable. NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and American IndiaSOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and E

2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

B-5 
 

Appendix B. Standard Error Tables 

Table B-6. Standard errors for figure 8: Mean credits earned in mathematics by high school 

graduates, by socioeconomic status: 1982, 1992, and 2004 

First quartile (lowest) Second quartile Third quartile Fourth quartile (highest) 

Sample Sample Sample Sample 

Year (n) SE SD (n) SE SD (n) SE SD (n) SE SD 

1982 2,800 0.04 1.10 2,500 0.03 1.02 2,500 0.03 1.09 3,000 0.03 1.04 

1992 2,300 0.03 0.87 3,000 0.03 0.84 3,300 0.03 0.84 4,400 0.05 0.84 

2004 2,100 0.03 0.95 2,500 0.03 0.95 2,700 0.03 0.90 3,500 0.03 0.85 

NOTE: SE = standard error; SD = standard deviation. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 

1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First 

Follow-up, High School Transcript Study, 2004.” 

B-6 
Table B-7. Standard errors for figure 9: Percentage of high school graduates who completed different levels of m

by socioeconomic status: 1982, 1992, and 2004 

First quartile (lowest) Second quartile Third quartile 

Levels of mathematics 1982 1992 2004 1982 1992 2004 1982 1992 2004 No math or low academic math 1.52 1.48 0.89 1.46 1.01 0.62 1.08 0.78 0.49 Algebra I/plane geometry 1.46 1.55 1.43 1.35 1.81 1.22 1.32 1.19 0.98 

Algebra II 1.04 1.83 1.36 1.20 1.95 1.21 1.03 1.49 1.21 Algebra III/trigonometry/analytic geometry 0.71 1.36 1.15 0.92 1.42 1.20 1.13 1.13 1.12 Precalculus 0.19 0.66 0.86 0.49 0.86 0.99 0.69 1.03 1.04 Calculus 0.29 0.40 0.70 0.54 0.53 0.64 0.61 1.14 0.76 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Ed

2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

Table B-8. Standard errors for figure 11: Mean credits earned in mathematics by high school graduates, by educa

1982, 1992, and 2004 

High school diploma/GED or less Some postsecondary education Baccalaureate degree 

Year Sample (n) SE SD Sample (n) SE SD Sample (n) SE SD Samp

1982 1,800 0.03 0.87 3,100 0.02 0.95 2,700 0.03 0.97 2

1992 520 0.06 0.86 2,800 0.03 0.78 4,300 0.04 0.83 42004 400 0.06 0.93 1,600 0.03 0.91 3,800 0.02 0.87 4

NOTE: GED = General Educational Development certificate; SE = standard error; SD = standard deviation. SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Ed

2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

B-7 
Table B-9. Standard errors for figure 12: Percentage of high school graduates who completed different levels of m

by educational expectations: 1982, 1992, and 2004 

High school diploma/ Some postsecondary 

GED or less education Baccalaur degeate 

ree 

Levels of mathematics 1982 1992 2004 1982 1992 2004 1982 1992 2004 

No math or low academic math 1.68 3.34 2.35 1.15 1.80 1.07 0.85 0.52 0.33 Algebra I/plane geometry 1.70 3.59 2.97 1.30 1.75 1.60 1.25 1.09 0.82 

Algebra II 1.08 4.46 2.51 0.86 1.62 1.58 1.27 1.91 1.04 Algebra III/trigonometry/analytic geometry 0.61 0.69 1.94 0.74 1.14 1.09 1.28 1.53 1.16 Precalculus 0.11 0.55 0.67 0.29 0.27 0.79 0.76 1.18 1.00 Calculus 0.25 0.81 0.31 0.38 0.12 0.28 0.78 1.03 0.65 

NOTE: GED = General Educational Development certificate. SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Ed

2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

Table B-10. Standard errors for figure 14: Mean credits earned in mathematics by high school graduates, by schoo

and 2004 

Public Catholic O

Year Sample (n) SE SD Sample (n) SE SD Sample 

1982 8,400 0.02 1.09 2,100 0.07 0.99 7

1992 11,500 0.02 0.86 800 0.06 0.68 1,2

2004 8,300 0.02 0.93 1,600 0.03 0.66 1,0

NOTE: SE = standard error; SD = standard deviation. SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Ed

2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

B-8 
Table B-11. Standard errors for figure 15: Percentage of high school graduates who completed different levels of m

by school sector: 1982, 1992, and 2004 

Public Catholic 

Levels of mathematics 1982 1992 2004 1982 1992 2004 198

No math or low academic math 0.81 0.65 0.36 1.31 0.47 0.16 2.7Algebra I/plane geometry 0.80 0.81 0.74 2.67 2.06 0.87 3.9

Algebra II 0.65 1.00 0.80 1.96 3.21 2.23 3.5

Algebra III/trigonometry/ analytic geometry 0.65 0.73 0.83 2.47 3.43 2.25 5.1

Precalculus 0.35 0.63 0.67 2.05 2.65 2.49 3.0Calculus 0.37 0.49 0.56 1.59 3.64 1.86 6.3

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey”; and Educ2002 (ELS:2002), “High School Transcript Study.” 

B-9 
 

Appendix B. Standard Error Tables 

Table B-12. Standard errors for figure 17: Percentage of high school graduates who completed 

different levels of science courses: 1982, 1992, and 2004 

Levels of science 1982 1992 2004 

No science or low level science 0.68 0.29 0.29 

Secondary physical science and basic biology 0.82 0.60 0.34 

General biology 1.01 1.02 0.88 

Chemistry I or physics I 0.55 0.98 0.91 

Chemistry I and physics I 0.41 0.60 0.82 

Chemistry II, physics II, or advanced biology 0.72 0.80 0.78 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 

1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First 

Follow-up, High School Transcript Study, 2004.” 

Table B-13. Standard errors for figure 18: Mean credits earned in science by high school 

graduates, by sex: 1982, 1992, and 2004 

Male Female 

Year Sample (n) SE SD Sample (n) SE SD 

1982 5,300 0.03 1.20 5,800 0.03 1.11 

1992 6,700 0.03 1.07 6,800 0.03 1.00 

2004 5,300 0.03 1.12 5,500 0.02 1.01 

NOTE: SE = standard error; SD = standard deviation. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 

1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First 

Follow-up, High School Transcript Study, 2004.” 

Table B-14. Standard errors for figure 19: Percentage of high school graduates who completed 

different levels of science courses, by sex: 1982, 1992, and 2004 

Male Female 

Levels of science 1982 1992 2004 1982 1992 2004 

No science or low level science 0.81 0.43 0.44 0.86 0.30 0.24 

Secondary physical science and basic biology 1.04 1.03 0.41 0.92 0.41 0.38 

General biology 1.19 1.49 1.00 1.22 1.15 1.04 

Chemistry I or physics I 0.71 1.38 0.98 0.71 1.25 1.13 

Chemistry I and physics I 0.63 0.66 0.90 0.42 0.89 0.97 

Chemistry II, physics II, or advanced biology 0.87 1.23 0.91 0.87 0.77 0.92 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 

1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First 

Follow-up, High School Transcript Study, 2004.” 

B-10 
Table B-15. Standard errors for figure 20: Mean credits earned in science by high school graduates, by race/ethnic

2004 

American Indian Asian Black Hispanic 

Sample Sample Sample Sample 

Year (n) SE SD (n) SE SD (n) SE SD (n) SE SD 

1982 150 0.09 1.03 310 0.11 1.37 1,500 0.05 0.99 2,200 0.03 0.95 

1992 130 0.09 0.88 1,000 0.09 1.19 1,100 0.07 1.01 1,400 0.04 0.84 

2004 80 0.19 1.05 1,146 0.06 1.28 1,200 0.04 1.01 1,400 0.04 0.98 

NOTE: SE = standard error; SD = standard deviation. Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiiaand American Indian includes Alaska Native. SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Ed

2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

Table B-16. Standard errors for figure 21: Percentage of high school graduates who completed different levels of s

race/ethnicity: 1982, 1992, and 2004 

American Indian Asian Black Hispanic 

Levels of science 1982 1992 2004 1982 1992 2004 1982 1992 2004 1982 1992 2004 

No science or low level 

science 3.87 2.89 1.93 1.74 0.55 0.53 1.85 0.75 0.64 1.75 0.71 0.74 

Secondary physical science 

and basic biology 10.53 4.49 3.14 2.21 1.69 0.41 2.10 2.28 0.59 1.66 2.37 1.00 

General biology 7.08 4.81 8.90 4.07 3.89 1.49 2.37 3.16 1.86 1.91 2.66 1.87 

Chemistry I or physics I 3.83 2.89 6.72 3.01 2.07 1.86 1.42 2.12 2.25 0.96 2.70 1.82 

Chemistry I and physics I 1.68 3.86 5.64 2.95 2.62 1.76 0.65 2.18 1.72 0.49 1.20 1.74 

Chemistry II, physics II, or 

advanced biology 3.27 2.69 3.16 3.28 2.29 2.52 1.59 1.64 1.41 0.88 1.13 1.02 

NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and American IndiaSOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Ed

2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

B-11 
 

Appendix B. Standard Error Tables 

Table B-17. Standard errors for figure 22: Mean credits earned in science by high school 

graduates, by socioeconomic status: 1982, 1992, and 2004 

First quartile (lowest) Second quartile Third quartile Fourth quartile (highest) 

Sample Sample Sample Sample 

Year (n) SE SD (n) SE SD (n) SE SD (n) SE SD 

1982 2,800 0.04 1.04 2,500 0.03 1.08 2,500 0.04 1.15 3,000 0.04 1.20 

1992 2,300 0.04 0.95 3,000 0.04 0.95 3,300 0.04 1.03 4,400 0.04 1.02 

2004 2,100 0.03 1.04 2,500 0.03 1.03 2,700 0.03 1.04 3,500 0.03 1.05 

NOTE: SE = standard error; SD = standard deviation. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 

1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First 

Follow-up, High School Transcript Study, 2004.” 

B-12 
Table B-18. Standard errors for figure 23: Percentage of high school graduates who completed different levels of s

socioeconomic status: 1982, 1992, and 2004 

First quartile (lowest) Second quartile Third quartile 

Levels of science 1982 1992 2004 1982 1992 2004 1982 1992 2004 No science or low level science 1.44 0.80 0.60 1.21 0.65 0.42 0.91 0.28 0.38 Secondary physical science and basic biology 1.35 1.05 0.80 1.48 1.30 0.60 1.18 0.72 0.47 

General biology 1.61 1.98 1.60 1.60 1.92 1.46 1.55 1.57 1.36 

Chemistry I or physics I 0.77 1.82 1.49 0.90 2.00 1.39 0.99 1.53 1.37 Chemistry I and physics I 0.35 0.72 0.91 0.64 0.68 1.08 0.64 1.24 1.15 

Chemistry II, physics II, or advanced biology 0.88 0.71 1.01 1.02 0.96 1.03 1.11 0.95 1.10 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Ed

2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

Table B-19. Standard errors for figure 24: Mean credits earned in science by high school graduates, by educationa

1992, and 2004 

High school diploma/ 

GED or less Some postsecondary education Baccalaureate degree 

Year Sample (n) SE SD Sample (n) SE SD Sample (n) SE SD Sam

1982 1,800 0.03 0.83 3,100 0.03 0.94 2,700 0.03 1.12 

1992 520 0.07 0.91 2,800 0.03 0.85 4,300 0.03 0.94 

2004 400 0.06 1.02 1,600 0.03 0.88 3,800 0.03 0.98 

NOTE: GED = General Educational Development certificate. SE = standard error; SD = standard deviation. SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Ed

2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

B-13 
Table B-20. Standard errors for figure 25: Percentage of high school graduates who completed different levels of s

educational expectations: 1982, 1992, and 2004 

High school diploma/ Some postsecondary 

GED or less education Baccalaureate degree 

Levels of science 1982 1992 2004 1982 1992 2004 1982 1992 2004 No science or low level science 1.68 1.30 2.03 1.06 0.71 0.79 0.68 0.24 0.30 

Secondary physical science and basic biology 1.52 2.09 2.22 1.26 1.66 0.93 1.09 0.45 0.35 

General biology 1.88 4.04 3.00 1.51 1.89 1.72 1.42 1.41 1.16 

Chemistry I or physics I 0.60 4.72 2.26 0.76 1.45 1.59 1.20 2.03 1.24 

Chemistry I and physics I 0.22 0.52 0.74 0.43 0.37 0.61 0.88 1.26 1.22 

Chemistry II, physics II, or advanced biology 0.71 0.63 1.74 0.76 0.73 0.92 1.30 0.95 0.97 

NOTE: GED = General Educational Development certificate. SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Ed

2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

Table B-21. Standard errors for figure 26: Mean credits earned in science by high school graduates, by school sec

2004 

Public Catholic Oth

Year Sample (n) SE SD Sample (n) SE SD Sample (n) 1982 8,400 0.02 1.16 2,100 0.07 1.10 730 

1992 11,500 0.03 1.05 780 0.08 0.89 1,200 

2004 8,300 0.02 1.08 1,600 0.06 0.83 1,000 NOTE: SE = standard error; SD = standard deviation. SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophom“High School Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Ed

2002 (ELS:2002), “First Follow-up, High School Transcript Study, 2004.” 

B-14 
Appendix B. Standard Error Tables 

Table B-22. Standard errors for figure 27: Percentage of high school graduates who completed 

different levels of science courses, by school sector: 1982, 1992, and 2004 

Public Catholic Other private 

Levels of science 1982 1992 2004 1982 1992 2004 1982 1992 2004 

No science or low level 

science 0.76 0.32 0.32 1.14 0.54 0.54 0.77 0.23 † 

Secondary physical science 

and basic biology 0.89 0.64 0.37 2.58 0.72 0.75 2.72 2.61 0.26 

General biology 1.04 1.04 0.94 3.82 3.46 2.36 7.11 5.51 2.15 

Chemistry I or physics I 0.59 1.00 0.97 1.89 2.99 2.70 2.58 8.34 3.71 

Chemistry I and physics I 0.39 0.59 0.86 1.38 4.01 3.02 4.27 3.04 4.69 

Chemistry II, physics II, or 

advanced biology 0.72 0.63 0.83 3.31 2.95 2.11 5.73 10.85 3.92 

† Not applicable. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), “High School Transcript Study”; National Education Longitudinal Study of 

1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudinal Study of 2002 (ELS:2002), “First 

Follow-up, High School Transcript Study, 2004.” 

B-15 
 

 

 

 

 

Appendix B. Standard Error Tables 

Table B-23. Standard errors for appendix table A-2: Percentage distribution of selected student 

characteristics and mean math IRT score for freshened versus unfreshened samples 

(transcript weight) of NELS:88 and ELS:2002 seniors: 1992 and 2004 

Characteristic 

Sex 

NELS:88: 1992 

Seniors who were Full senior cohort 

sophomores two (freshened 

years earlier sample) 

ELS:2002: 2004 

Seniors who were Full senior cohort 

sophomores two (freshened 

years earlier sample) 

Male 0.92 0.87 0.60 0.57 

Female 0.92 0.87 0.60 0.57 

Race/ethnicity 

Asian/Pacific Islander 

Hispanic 

Black 

0.34 

0.84 

0.88 

0.33 

0.81 

0.86 

0.28 

0.82 

0.68 

0.30 

0.85 

0.68 

White 1.26 1.21 1.04 1.04 

American Indian/Alaska 

Native 

0.25 0.25 0.22 0.21 

More than one race — — 0.26 0.26 

SES 

1st (low) quartile 

Middle 2 quartiles 

4th (high) quartile 

0.78 

1.04 

1.21 

0.78 

1.02 

1.17 

0.68 

0.68 

0.79 

0.67 

0.67 

0.80 

School control 

Public 1.02 0.92 0.36 0.35 

Catholic 0.54 0.49 0.22 0.21 

NAIS private 

Other private 

0.55 

0.50 

0.48 

0.46 

— 

0.29 

— 

0.28 

Region 

Northwest 1.20 1.15 0.83 0.82 

Midwest 1.01 0.95 0.81 0.79 

South 

West

1.09 

 0.87 

1.04 

0.85 

0.79 

0.86 

0.77 

0.83 

Math test (mean IRT score) 0.33 0.33 0.29 0.29 

— Not available. 

NOTE: IRT = item response theory. SES = socioeconomic status. NAIS = National Association of Independent 

Schools. Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific 

Islander, and American Indian includes Alaska Native. 

SOURCE:U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal 

Study of 1988 (NELS:88/92), "Second Follow-up, 1992"; and Education Longitudinal Study of 2002 (ELS:2002), "First 

Follow-up, 2004." 

B-16 
 

 

 

Appendix B. Standard Error Tables 

Table B-24. Standard errors for appendix table A-3: Percentage of selected student characteristics 

and mean math score for 1980 senior cohort and 1980 sophomore cohort two years 

later (in 1982) of HS&B: 1980 and 1982 

Characteristic 

Sex 

Male 

Female 

Senior cohort of 1980 

0.51 

0.51 

Sophomore cohort of 1980, 

as seniors in 1982 

0.52 

0.52 

Race/ethnicity 

Asian/Pacific Islander 

Hispanic 

Black 

White 

American Indian/Alaska Native 

Other 

0.16 

0.27 

0.69 

0.80 

0.11 

0.13 

0.16 

0.34 

0.66 

0.83 

0.16 

0.04 

SES 

1st (low) quartile 

Middle 2 quartiles 

4th (high) quartile 

0.62 

0.53 

0.69 

0.60 

0.57 

0.74 

Region 

New England 

Mid Atlantic 

South Atlantic 

East south central 

West south central 

East north central 

West north central 

Mountain 

Pacific 

0.99 

1.32 

1.30 

0.76 

1.06 

1.41 

1.01 

0.81 

1.17 

1.04 

1.35 

1.38 

0.78 

1.10 

1.43 

0.98 

0.80 

1.09 

Math test (mean number right) 0.06 0.07 

NOTE: SES = socioeconomic status. Black includes African American, Hispanic includes Latino, Asian includes 

Native Hawaiian or Other Pacific Islander, and American Indian includes Alaska Native. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond 

Longitudinal Study of 1980 Sophomores (HS&B-So:80/82); and High School and Beyond Longitudinal Study of 1980 

Seniors (HS&B-Sr:80). 

B-17 

Appendix C 

Sample Size Tables for Select Subgroups 

Appendix C. Sample Size Tables for Select Subgroups 

This appendix presents approximate sample sizes for select subgroups. The sample sizes 

are approximate because restricted-use data are used, and in accordance with National Center for 

Education Statistics (NCES) Statistical Standards (Seastrom 2003), exact sample sizes from 

restricted-use data files cannot be published unless the data are perturbed in some way. The 

perturbation approach taken here was to round the exact sample sizes of cells to 10s (for two or 

three-digit numbers) or 100s (for larger numbers). 

C-3 
Table C-1. Sample sizes for each level of the mathematics pipeline, by student characteristics: 1982, 1992, and 2

No mathematics or Algebra III/ 

low academic Algebra I/plane trigonometry/analytic 

mathematics geometry Al Igebra I geometry Precalculus 

Characteristic 1982 1992 2004 1982 1992 2004 1982 1992 2004 1982 1992 2004 1982 1992 20

Gender 

Male 1,200 850 240 1, 1,400 400 910 1,960 1,500 300 1,990 100 950 340 1,860 0

Female 1,300 700 180 1, 1,900 400 830 1, 1,100 1,800 400 1,900 200 1,100 300 1,890 2

Race/ethnicity 

Americ Indian an 50 30 10 50 40 20 20 40 30 20 10 10 # 10 

Asian 30 50 20 50 120 120 60 170 200 80 160 140 40 180 2Black 480 220 70 420 290 210 280 300 370 190 140 310 50 80 1Hispanic 710 200 80 730 470 320 390 380 410 280 150 190 60 130 2

White 1,200 1,000 230 2,000 1,900 980 1,300 2,400 1,500 1,300 1,700 1,300 490 1,300 1,4

Sc sect hool or 

Public 2,300 1,500 410 2,600 2,700 1,600 1,500 2,900 2,100 1,200 1,800 1,400 330 1,300 1,5Catholic 140 10 10 590 80 70 480 200 340 490 170 380 190 190 4

Ot privher ate 40 10 10 110 50 90 100 150 190 160 250 190 120 280 2

Socioeconomi statuc s 

First quartil (l e owest) 1,100 540 190 940 730 560 430 590 620 290 190 320 50 130 2

Second quartile 650 480 120 810 840 590 470 790 700 360 440 450 90 280 3

Third quartile 440 320 90 780 750 370 550 930 720 450 590 550 150 410 6

Fourth quartile 

(highest) 240 110 30 660 420 230 590 900 610 760 940 680 330 890 9

Educational 

expectations 

High school diploma/ 

GED or less 880 220 90 620 170 170 190 90 90 100 20 40 10 10 

Some postsecondary 

education 860 700 160 1, 1,200 100 580 550 680 540 370 230 210 70 70 1

Baccalaureate 

degree 250 220 70 690 770 480 1,680 1,300 100 640 900 830 230 650 8

Graduate degree 150 150 40 420 410 300 510 910 730 640 880 810 280 1,890 2

# Rounds to zero. NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and American India

race categories exclude Hispanic or Latino origin. GED = General Educational Development certificate. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophomores (HSTranscript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudina

“First Follow-up, High School Transcript Study, 2004.” 

C-4 
Table C-2. Sample sizes for each level of the science pipeline, by student characteristics: 1982, 1992, and 2004 

Secondary physical 

No science or low- science and basic Chemistry I or Chemistry I and 

level science biology General biology physics I physics I 

Characteristic 1982 1992 2004 1982 1992 2004 1982 1992 2004 1982 1992 2004 1982 1992 20

Gender 

Male 670 240 130 760 1, 460 2, 160 1, 800 200 1, 300 1, 880 700 600 1, 450 990 

1

Female 730 160 80 880 2, 370 2, 140 1, 100 1, 400 2, 200 2, 000 000 000 280 800 

9

Race/ethnicity 

American Indian 20 10 # 20 20 # 60 60 30 20 20 20 10 10 

Asian 20 30 20 30 40 10 70 190 150 80 240 310 40 200 2

Black 200 30 20 210 110 30 570 440 360 250 290 470 80 110 1

Hispanic 340 60 50 420 170 60 850 610 390 310 330 500 100 130 2

White 800 280 110 940 2, 480 3, 170 1, 300 1, 200 2, 400 2, 200 800 1, 100 1, 500 

300 

3

School sector 

Public 1,300 1, 400 210 300 3, 800 4, 260 2, 000 1, 200 3, 100 2, 300 100 1, 800 1, 440 

400 

3

Catholic 110 # 10 310 30 30 710 180 240 440 240 490 190 150 4

Other private 10 10 # 40 # 10 240 170 120 180 380 310 90 240 2

C-5 Socioeconomic status First quartile (lowest) 530 140 90 470 290 100 1,200 1,100 720 340 470 730 90 150 2

Second quartile 370 130 60 410 250 100 940 1,300 730 350 770 840 110 280 3

Third quartile 270 90 50 380 170 60 850 1,200 610 470 1,000 940 170 430 5

Fourth quartile 

(highest) 170 30 30 330 80 40 830 880 410 1,690 1,300 100 340 890 9

Educational 

expectations 

High school diploma/ 

GED or less 460 50 50 350 90 40 800 300 190 100 60 80 10 10 

Some postsecondary 

education 500 190 60 590 330 110 1,300 1,500 710 360 530 540 80 80 

Baccalaureate 

degree 170 70 50 330 150 80 1,820 300 810 1,690 1,500 400 230 660 7

Graduate degree 90 40 30 180 100 40 540 830 490 610 1,300 1,300 340 930 1,1

# Rounds to zero. NOTE: Black includes African American, Hispanic includes Latino, Asian includes Native Hawaiian or Other Pacific Islander, and American India

race categories exclude Hispanic or Latino origin. GED = General Educational Development certificate. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School and Beyond Longitudinal Study of 1980 Sophomores (HS

Transcript Study”; National Education Longitudinal Study of 1988 (NELS:88/92), “Second Follow-up, Transcript Survey, 1992”; and Education Longitudina

“First Follow-up, High School Transcript Study, 2004.” 

Appendix D 

Course-Specific Completion Percentages 

Appendix D. Course-Specific Completion Percentages 

Appendix D presents the percentage distribution of courses in which graduating seniors 

earned credits, for each of the three studies included in this report. Tables D-1 and D-2 present 

data from the High School & Beyond (HS&B) graduating cohort of 1982. Tables D-3 and D-4 

present data from the National Education Longitudinal Study of 1988 (NELS:88) graduating 

cohort of 1992. Tables D-5 and D-6 present data from the Education Longitudinal Study of 2002 

(ELS:2002) graduating cohort of 2004. Only credits earned for courses taken during students’ 9th 

through 12th grade are included (even if the course has a 7th or 8th grade label). 

It is important to note that course codes as identified within each of the studies may differ 

over time. Courses were identified on the basis of the Classification Scheme of Secondary 

School Courses (CSSC) used to code the transcripts collected under NELS:88 (Ingels et al. 

1995); this framework was used to classify HS&B and ELS:2002 transcripts as well. However, 

there may be differences in course classifications across studies because the original coding of 

the transcripts used certain codes, descriptions, or titles, and not others. In addition, while some 

CSSC codes did not exist in the previous years, it does not mean that the courses were not 

available; they would have been included in another existing CSSC value. Directly comparing 

individual courses across years should be done with caution. 

D-3 
Pipeline level and CSSC1

 course title CSSC1 code Percentage Standard error 

(1) No or low academic math † 

Mathematics, Other General 270100 1.8 0.31 

Mathematics 72

 270101 0.1 0.05 

Mathematics 7, Accelerated2

 270102 # † 

Mathematics 82

 270103 0.1 0.04 

Mathematics 8, Accelerated2

 270104 0.1 0.04 

Mathematics 1, General 270106 25.4 0.90 

Mathematics 2, General 270107 10.6 0.66 

Science Mathematics 270108 0.2 0.07 

Mathematics in the Arts 270109 0.3 0.12 

Mathematics, Vocational 270110 1.7 0.25 

Technical Mathematics 270111 0.8 0.18 

Mathematics Review 270112 1.1 0.22 

Mathematics Tutoring 270113 0.2 0.11 

Consumer Mathematics 270114 8.3 0.55 

Actuarial Sciences, Other 270200 # 0.01 

Applied Mathematics, Other 270300 0.1 0.05 

Basic Math 13

 270601 # † 

Basic Math 23

 270602 # † 

Basic Math 33

 270603 # † 

Basic Math 43

 270604 # † 

Basic Math - old code3

 270105 7.2 0.52 

Vocational Math - old code3

 320108 0.5 0.14 

Pre-Algebra 270401 13.5 0.78 

Algebra 1, Part 1 270402 6.2 0.55 

Algebra 1, Part 2 270403 4.6 0.48 

Geometry, Informal 270409 3.3 0.41 

 

(2) Algebra I/plane geometry † 

Pure Mathematics, Other 270400 0.5 0.10 

Algebra 1 270404 58.6 0.96 

Geometry, Plane 270406 6.0 0.63 

Geometry, Solid 270407 0.8 0.17 

Geometry 270408 41.2 0.99 

Mathematics 1, Unified 270421 1.3 0.28 

Mathematics 2, Unified 270422 0.8 0.23 

Geometry, Part 14

 270425 † † 

Geometry, Part 24

 270426 † † 

Unified Math 1, Part 14

 270427 † † 

Unified Math 1, Part 24

 270428 † † 

Pre-IB Geometry4

 270429 † † 

IB Math Methods 14

 270431 † † 

IB Math Studies 14

 270432 † † 

Discrete Math 4 270436 † † 

Finite Math 4 270437 † † 

Algebra and Geometry4

 270441 † † 

Mathematics, Other 279900 0.5 0.11 

See notes at end of table. 

Appendix D. Course-Specific Completion Percentages 

Table D-1. Percentage and standard errors of graduating seniors who received credit in 

mathematics courses, by pipeline level: 1982 

D-4 
Appendix D. Course-Specific Completion Percentages 

Table D-1. Percentage and standard errors of graduating seniors who received credit in 

mathematics courses, by pipeline level: 1982—Continued 

Pipeline level and CSSC1 course title CSSC1 code Percentage Standard error 

(3) Algebra II † 

Algebra 2 270405 32.6 0.87 

Mathematics 3, Unified 270423 1.0 0.26 

Pre-IB Algebra 2/Trigonometry4

 270430 † † 

 

(4) Algebra III/trigonometry/analytic geometry † 

Algebra 3 270410 7.6 0.57 

Trigonometry 270411 7.8 0.52 

Analytic Geometry 270412 2.8 0.35 

Trigonometry and Solid Geometry 270413 0.5 0.13 

Algebra and Trigonometry 270414 4.7 0.45 

Algebra and Analytic Geometry 270415 0.5 0.14 

Linear Algebra 270417 0.9 0.19 

Mathematics, Independent Study 270424 0.9 0.19 

Statistics, Other 270500 # † 

Statistics 270511 0.3 0.09 

Probability 270521 # † 

Probability and Statistics 270531 0.8 0.13 

AP Statistics4

 270532 † † 

 

(5) Precalculus † 

Analysis, Introductory 270416 6.4 0.46 

IB Math Studies 24

 270433 † † 

 

(6) Calculus † 

Calculus and Analytic Geometry 270418 0.4 0.12 

Calculus 270419 4.0 0.37 

AP Calculus 270420 1.9 0.27 

IB Math Studies/Calculus4

 270434 † † 

AP Calculus CD4

 270435 † † 

# Rounds to zero. 

† Not applicable. 

1

 CSSC = Classification Scheme of Secondary School Courses. Each CSSC course code comprises six digits with an 

associated course title, alternate titles, and a course description. The first two digits identify the main program area (e.g., 

mathematics), the second set of two digits represents a subcategory of courses within the main program area (e.g., pure 

math), and the last two digits are associated with the specific courses in each of the main and subcategories (e.g., 

trigonometry). 

2

 Indicates lower grade (7-8) course levels that existed on transcripts. Only a few students have transcript records for grade 

levels lower than the 9th grade. For this reason, in these figures only those students who took the lower level courses in 

grade levels 9 through 12 were included in the percentages. 

3

 Indicates CSSC definitions that exist in later data collections. These definitions were usually redefined because they were 

split into many codes. 4

 Indicates CSSC definitions that may have not been used in the transcript collection or codes that did not exist at that time. 

It should be noted that in these cases it does not mean that no courses were taken in this course area, but that the courses 

may have been given different CSSC values. 

NOTE: Comparing individual courses from different studies across time may result in misleading conclusions. Some course 

codes have been consolidated, split, dropped, or added over time. Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School & Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), "High School Transcript Study." 

D-5 
Appendix D. Course-Specific Completion Percentages 

Table D-2. Percentage and standard errors of graduating seniors who received credit in science 

courses, by pipeline level: 1982 

Standard 

Pipeline level and CSSC1 course title CSSC1 code Percentage error 

(1) No science or low-level science † 

Science, Unified 300111 26.7 1.26 

Physical Science 400121 29.4 1.31 

Physical Science, Applied 400141 1.0 0.27 

Geological Sciences, Other 400600 0.1 0.07 

Earth Science 400611 12.1 1.00 

Earth Science, College Prep 400621 0.4 0.10 

Misc. Physical Sciences, Other 400700 # † 

 

(2) Secondary physical science and basic biology † 

Biology, Basic 1 260121 24.1 1.24 

Biology, Basic 2 260122 # † 

Biological and Physical Sciences, Other 300100 0.7 0.24 

Science Study, Independent 300121 0.8 0.20 

Outdoor Education 300131 0.2 0.06 

Futuristics 300611 0.3 0.09 

Environmental Science 300621 2.2 0.36 

Astronomy, Other 400200 0.1 0.05 

Astronomy 400211 1.4 0.26 

Astrophysics, Other 400300 # † 

Atmospheric Sciences and Meteorology 400400 # † 

Meteorology 400411 0.6 0.18 

Chemistry, Other 400500 0.4 0.14 

Chemistry, Introductory 400511 6.7 0.55 

Chemistry in the Community2

 400512 † † 

Organic Biochemistry 400531 0.2 0.08 

Physical Chemistry 400541 0.1 0.06 

Consumer Chemistry 400551 0.3 0.08 

Chemistry, Independent Study 400561 0.1 0.04 

AP Environmental Science3

 400622 † † 

Geology 400631 1.7 0.28 

Geology - Field Studies 400632 # † 

Mineralogy 400641 0.1 0.06 

Oceanography 400711 1.0 0.25 

Physics, Other 400800 0.2 0.07 

Physics 400811 3.4 0.35 

Electricity and Electronics Science 400841 0.3 0.11 

Acoustics 400851 # † 

Planetary Science, Other 400900 # † 

Rocketry and Space Science 400911 0.4 0.18 

Aerospace Science 401011 # † 

AP Environmental Science 300622 # † 

See notes at end of table. 

D-6 
Appendix D. Course-Specific Completion Percentages 

Table D-2. Percentage and standard errors of graduating seniors who received credit in science 

courses, by pipeline level: 1982—Continued 

Standard 

Pipeline level and CSSC1 course title CSSC1 code Percentage error 

(3) General biology † 

Biology, Other General 260100 1.0 0.30 

Biology, General 1 260131 50.0 1.32 

Biology, General 2 260132 # † 

Biology, Honors 1 260141 3.5 0.42 

Pre-IB Biology2

 260143 † † 

Ecology 260611 2.1 0.28 

Marine Biology 260621 1.3 0.26 

Marine Biology, Advanced 260622 0.1 0.05 

Zoology, Other 260700 # † 

Zoology 260711 1.0 0.18 

Zoology, Vertebrate 260721 0.1 0.09 

Zoology, Invertebrate 260731 # † 

Animal Behavior 260741 0.2 0.06 

Physiology, Human 260751 5.2 0.44 

Physiology, Advanced 260752 0.1 0.07 

Pathology 260761 0.1 0.04 

Comparative Embryology 260771 # † 

Life Sciences, Other 269900 # † 

 

(4/5) Chemistry I and/or physics I † 

Chemistry 1 400521 25.6 0.81 

Pre-IB Chemistry2

 400523 † † 

Physics 1 400821 11.9 0.56 

 

(6) Chemistry II, physics II, or advanced biology † 

Chemistry 2 400522 3.7 0.39 

IB Chemistry 22

 400524 † † 

IB Chemistry 32

 400525 † † 

AP Chemistry2

 400526 † † 

Physics 2 400822 1.5 0.19 

IB Physics2

 400823 † † 

AP Physics B2

 400824 † † 

AP Physics C: Mechanics2

 400825 † † 

AP Physics C: Electricity/Magnetism2

 400826 † † 

Physics 2 without Calculus 400831 # † 

Biology, Advanced 260142 7.9 0.57 

Field Biology 260151 0.6 0.20 

Genetics 260161 0.7 0.16 

Biopsychology 260171 0.1 0.04 

Biology, Seminar 260181 0.1 0.05 

Biochemistry and Biophysics, Other 260200 # † 

Biochemistry 260211 0.2 0.09 

Botany, Other 260300 0.1 0.08 

Botany 260311 0.7 0.16 

See notes at end of table. 

D-7 
Appendix D. Course-Specific Completion Percentages 

Table D-2. Percentage and standard errors of graduating seniors who received credit in science 

courses, by pipeline level: 1982—Continued 

Standard 

Pipeline level and CSSC1 course title CSSC1 code Percentage error 

(6) Chemistry II, physics II, or advanced biology—Continued † 

Cell and Molecular Biology, Other 260400 # † 

Cell Biology 260411 0.2 0.08 

Microbiology, Other 260500 # † 

Microbiology 260511 0.7 0.17 

Misc. Specialized Areas; Life Sciences, Other 260600 # † 

Anatomy 260631 0.6 0.14 

IB Biology 22

 260144 † † 

IB Biology 32 260145 † † 

AP Biology2

 260146 † † 

# Rounds to zero. 

† Not applicable. 

1

 CSSC = Classification Scheme of Secondary School Courses. Each CSSC course code comprises six digits with an 

associated course title, alternate titles, and a course description. The first two digits identify the main program area (e.g., life 

science), the second set of two digits represents a subcategory of courses within the main program area (e.g., biology), and 

the last two digits are associated with the specific courses in each of the main and subcategories (e.g., advanced). 2

 Indicates CSSC definitions that may have not been used in the transcript collection or codes that did not exist at that time. 

It should be noted that in these cases it does not mean that no courses were taken in this course area, but that the courses 

may have been given different CSSC values. 

3

 Indicates a CSSC definition that prior to the year 2000 did not exist, but existed as another code (300622). This code also 

existed in 2000. 

NOTE: Comparing individual courses from different studies across time may result in misleading conclusions. Some course 

codes have been consolidated, split, dropped, or added over time. Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, High School & Beyond Longitudinal 

Study of 1980 Sophomores (HS&B-So:80/82), "High School Transcript Study." 

D-8 
Appendix D. Course-Specific Completion Percentages 

Table D-3. Percentage and standard errors of graduating seniors who received credit in 

mathematics courses, by pipeline level: 1992 

Pipeline level and CSSC1 course title CSSC1 code Percentage Standard error 

(1) No or low academic math † 

Mathematics, Other General 270100 0.3 0.07 

Mathematics 72

 270101 # † 

Mathematics 7, Accelerated2

 270102 # † 

Mathematics 82

 270103 0.1 0.03 

Mathematics 8, Accelerated2 270104 # † 

Mathematics 1, General 270106 13.0 0.76 

Mathematics 2, General 270107 5.5 0.43 

Science Mathematics 270108 0.1 0.04 

Mathematics in the Arts 270109 0.5 0.28 

Mathematics, Vocational 270110 2.0 0.26 

Technical Mathematics 270111 0.6 0.14 

Mathematics Review 270112 1.3 0.26 

Mathematics Tutoring 270113 # † 

Consumer Mathematics 270114 9.7 0.59 

Actuarial Sciences, Other 270200 # † 

Applied Mathematics, Other 270300 0.3 0.11 

Basic Math 1 270601 6.2 0.41 

Basic Math 2 270602 2.4 0.31 

Basic Math 3 270603 0.6 0.12 

Basic Math 4 270604 0.4 0.10 

Basic Math - old code3

 270105 # † 

Vocational Math - old code3

 320108 # † 

Pre-Algebra 270401 20.2 1.02 

Algebra 1, Part 1 270402 4.6 0.47 

Algebra 1, Part 2 270403 3.9 0.40 

Geometry, Informal 270409 4.8 0.53 

 

(2) Algebra I/plane geometry † 

Pure Mathematics, Other 270400 0.7 0.47 

Algebra 1 270404 67.3 0.96 

Geometry, Plane 270406 3.7 0.45 

Geometry, Solid4

 270407 # † 

Geometry 270408 59.4 1.13 

Mathematics 1, Unified 270421 5.8 0.61 

Mathematics 2, Unified 270422 4.3 0.55 

Geometry, Part 14

 270425 † † 

Geometry, Part 24

 270426 † † 

Unified Math 1, Part 14

 270427 † † 

Unified Math 1, Part 24

 270428 † † 

Pre-IB Geometry4

 270429 † † 

IB Math Methods 14

 270431 † † 

IB Math Studies 14

 270432 † † 

Discrete Math4

 270436 † † 

Finite Math4

 270437 † † 

Algebra and Geometry4

 270441 † † 

Mathematics, Other 279900 0.8 0.22 

See notes at end of table. 

D-9 
Appendix D. Course-Specific Completion Percentages 

Table D-3. Percentage and standard errors of graduating seniors who received credit in 

mathematics courses, by pipeline level: 1992—Continued 

Pipeline level and CSSC1 course title CSSC1 code Percentage Standard error 

(3) Algebra II † 

Algebra 2 270405 53.0 1.14 

Mathematics 3, Unified 270423 3.6 0.44 

Pre-IB Algebra 2/Trigonometry4

 270430 † † 

 

(4) Algebra III/trigonometry/analytic geometry † 

Algebra 3 270410 5.6 0.50 

Trigonometry 270411 10.9 0.65 

Analytic Geometry 270412 2.9 0.27 

Trigonometry and Solid Geometry 270413 0.4 0.17 

Algebra and Trigonometry 270414 9.8 0.78 

Algebra and Analytic Geometry 270415 1.0 0.21 

Linear Algebra 270417 0.5 0.15 

Mathematics, Independent Study 270424 1.4 0.30 

Statistics, Other 270500 # † 

Statistics 270511 0.8 0.18 

Probability 270521 0.1 0.06 

Probability and Statistics 270531 1.3 0.19 

AP Statistics4

 270532 † † 

 

(5) Precalculus † 

Analysis, Introductory 270416 16.5 0.96 

IB Math Studies 24

 270433 † † 

 

(6) Calculus † 

Calculus and Analytic Geometry 270418 0.4 0.13 

Calculus 270419 4.7 0.63 

AP Calculus 270420 5.9 0.40 

IB Math Studies/Calculus4

 270434 † † 

AP Calculus CD4

 270435 † † 

# Rounds to zero. 

† Not applicable. 

1

 CSSC = Classification Scheme of Secondary School Courses. Each CSSC course code comprises six digits with an 

associated course title, alternate titles, and a course description. The first two digits identify the main program area (e.g., 

mathematics), the second set of two digits represents a subcategory of courses within the main program area (e.g., pure 

math), and the last two digits are associated with the specific courses in each of the main and subcategories (e.g., 

trigonometry). 2

 Indicates lower grade (7-8) course levels that existed on transcripts. Only a few students have transcript records for grade 

levels lower than the 9th grade. For this reason, in these figures only those students who took the lower level courses in 

grade levels 9 through 12 were included in the percentages. 

3

 Indicates CSSC definitions that exist in later data collections. These definitions were usually redefined because they were 

split into many codes. 4

 Indicates CSSC definitions that may have not been used in the transcript collection or codes that did not exist at that time. 

It should be noted that in these cases it does not mean that no courses were taken in this course area, but that the courses 

may have been given different CSSC values. 

NOTE: Comparing individual courses from different studies across time may result in misleading conclusions. Some course 

codes have been consolidated, split, dropped, or added over time. Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 

1988 (NELS:88/92), "Second Follow-up, Transcript Survey, 1992." 

D-10 
Appendix D. Course-Specific Completion Percentages 

Table D-4. Percentage and standard errors of graduating seniors who received credit in science 

courses, by pipeline level: 1992 

Pipeline level and CSSC1 course title CSSC1 code Percentage Standard error 

(1) No science or low-level science † 

Science, Unified 300111 15.4 0.94 

Physical Science 400121 41.9 1.46 

Physical Science, Applied 400141 2.5 0.30 

Geological Sciences, Other 400600 # † 

Earth Science 400611 19.2 1.10 

Earth Science, College Prep 400621 1.5 0.26 

Misc. Physical Sciences, Other 400700 # † 

 

(2) Secondary physical science and basic biology † 

Biology, Basic 1 260121 9.8 0.74 

Biology, Basic 2 260122 0.2 0.07 

Biological and Physical Sciences, Other 300100 0.2 0.08 

Science Study, Independent 300121 0.5 0.11 

Outdoor Education 300131 0.1 0.06 

Futuristics 300611 0.9 0.20 

Environmental Science 300621 4.4 0.48 

Astronomy, Other 400200 # † 

Astronomy 400211 2.1 0.42 

Astrophysics, Other 400300 # † 

Atmospheric Sciences and Meteorology 400400 # † 

Meteorology 400411 0.3 0.10 

Chemistry, Other 400500 0.1 0.03 

Chemistry, Introductory 400511 9.4 0.90 

Chemistry in the Community2

 400512 † † 

Organic Biochemistry 400531 0.2 0.07 

Physical Chemistry 400541 0.2 0.12 

Consumer Chemistry 400551 0.7 0.13 

Chemistry, Independent Study 400561 # † 

AP Environmental Science3

 400622 † † 

Geology 400631 1.4 0.22 

Geology - Field Studies 400632 # † 

Mineralogy 400641 # † 

Oceanography 400711 0.9 0.18 

Physics, Other 400800 # † 

Physics 400811 4.5 0.46 

Electricity and Electronics Science 400841 0.1 0.03 

Acoustics 400851 # † 

Planetary Science, Other 400900 # † 

Rocketry and Space Science 400911 0.1 0.05 

Aerospace Science 401011 0.2 0.06 

AP Environmental Science 300622 # † 

See notes at end of table. 

D-11 
Appendix D. Course-Specific Completion Percentages 

Table D-4. Percentage and standard errors of graduating seniors who received credit in science 

courses, by pipeline level: 1992—Continued 

Pipeline level and CSSC1 course title CSSC1 code Percentage Standard error 

(3) General biology † 

Biology, Other General 260100 1.0 0.57 

Biology, General 1 260131 75.4 1.06 

Biology, General 2 260132 6.7 0.71 

Biology, Honors 1 260141 8.4 0.57 

Pre-IB Biology2

 260143 † † 

Ecology 260611 1.5 0.21 

Marine Biology 260621 2.5 0.35 

Marine Biology, Advanced 260622 0.1 0.03 

Zoology, Other 260700 # † 

Zoology 260711 1.4 0.49 

Zoology, Vertebrate 260721 0.1 0.04 

Zoology, Invertebrate 260731 # † 

Animal Behavior 260741 0.2 0.07 

Physiology Human 260751 7.7 0.61 

Physiology, Advanced 260752 0.2 0.06 

Pathology 260761 # † 

Comparative Embryology 260771 # † 

Life Sciences, Other 269900 0.4 0.14 

 

(4/5) Chemistry I and/or physics I † 

Chemistry 1 400521 46.6 1.17 

Pre-IB Chemistry2

 400523 † † 

Physics 1 400821 20.0 0.96 

 

(6) Chemistry II, physics II, or advanced biology 

Chemistry 2 400522 4.7 0.34 

IB Chemistry 22

 400524 † † 

IB Chemistry 32

 400525 † † 

AP Chemistry2

 400526 † † 

Physics 2 400822 3.2 0.28 

IB Physics2

 400823 † † 

AP Physics B2

 400824 † † 

AP Physics C: Mechanics2

 400825 † † 

AP Physics C: Electricity/Magnetism2

 400826 † † 

Physics 2 without Calculus 400831 0.1 0.05 

Biology, Advanced 260142 6.4 0.66 

Field Biology 260151 0.4 0.11 

Genetics 260161 0.2 0.06 

Biopsychology 260171 # † 

Biology, Seminar 260181 0.3 0.10 

Biochemistry and Biophysics, Other 260200 # † 

Biochemistry 260211 # † 

Botany, Other 260300 # † 

Botany 260311 0.5 0.12 

Cell and Molecular Biology, Other 260400 # † 

Cell Biology 260411 0.3 0.15 

See notes at end of table. 

D-12 
 

 

 

Appendix D. Course-Specific Completion Percentages 

Table D-4. Percentage and standard errors of graduating seniors who received credit in science 

courses, by pipeline level: 1992—Continued 

Pipeline level and CSSC1 course title CSSC1 code Percentage Standard error 

(6) Chemistry II, physics II, or advanced biology—Continued † 

Microbiology, Other 260500 # † 

Microbiology 260511 0.3 0.09 

Misc. Specialized Areas; Life Sciences, Other 260600 # † 

Anatomy 260631 0.6 0.17 

IB Biology 22

 260144 † † 

IB Biology 32

 260145 † † 

AP Biology2

 260146 † † 

# Rounds to zero. 

† Not applicable. 

1

 CSSC = Classification Scheme of Secondary School Courses. Each CSSC course code comprises six digits with an 

associated course title, alternate titles, and a course description. The first two digits identify the main program area (e.g., life 

science), the second set of two digits represents a subcategory of courses within the main program area (e.g., biology), and 

the last two digits are associated with the specific courses in each of the main and subcategories (e.g., advanced). 

2

 Indicates CSSC definitions that may have not been used in the transcript collection or codes that did not exist at that time. 

It should be noted that in these cases it does not mean that no courses were taken in this course area, but that the courses 

may have been given different CSSC values. 

3

 Indicates a CSSC definition that prior to the year 2000 did not exist, but existed as another code (300622). This code also 

existed in 2000. 

NOTE: Comparing individual courses from different studies across time may result in misleading conclusions. Some course 

codes have been consolidated, split, dropped, or added over time. Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 

1988 (NELS:88/92), "Second Follow-up, Transcript Survey, 1992." 

D-13 
Appendix D. Course-Specific Completion Percentages 

Table D-5. Percentage and standard errors of graduating seniors who received credit in 

mathematics courses, by pipeline level: 2004 

Pipeline level and CSSC1 course title CSSC1 code Percentage Standard error 

(1) No or low academic math † 

Mathematics, Other General 270100 3.8 0.45 

Mathematics 72

 270101 # † 

Mathematics 7, Accelerated2

 270102 # † 

Mathematics 82

 270103 # † 

Mathematics 8, Accelerated2 270104 0.1 0.05 

Mathematics 1, General 270106 5.6 0.41 

Mathematics 2, General 270107 1.7 0.29 

Science Mathematics 270108 # † 

Mathematics in the Arts 270109 0.3 0.09 

Mathematics, Vocational 270110 0.6 0.18 

Technical Mathematics 270111 2.2 0.28 

Mathematics Review 270112 1.7 0.32 

Mathematics Tutoring 270113 0.3 0.14 

Consumer Mathematics 270114 3.0 0.44 

Actuarial Sciences, Other 270200 # † 

Applied Mathematics, Other 270300 1.0 0.18 

Basic Math 1 270601 4.3 0.44 

Basic Math 2 270602 1.4 0.32 

Basic Math 3 270603 0.7 0.19 

Basic Math 4 270604 0.7 0.21 

Basic Math - old code3

 270105 # † 

Vocational Math - old code3

 320108 # † 

Pre-Algebra 270401 8.7 0.61 

Algebra 1, Part 1 270402 10.4 0.88 

Algebra 1, Part 2 270403 9.9 0.83 

Geometry, Informal 270409 5.4 0.64 

 

(2) Algebra I/plane geometry † 

Pure Mathematics, Other 270400 1.4 0.26 

Algebra 1 270404 61.0 1.21 

Geometry, Plane 270406 2.1 0.63 

Geometry, Solid 270407 # † 

Geometry 270408 68.4 1.24 

Mathematics 1, Unified 270421 8.2 0.75 

Mathematics 2, Unified 270422 7.0 0.73 

Geometry, Part 1 270425 0.6 0.18 

Geometry, Part 2 270426 0.5 0.15 

Unified Math 1, Part 1 270427 0.6 0.18 

Unified Math 1, Part 2 270428 0.4 0.14 

Pre-IB Geometry 270429 0.1 0.07 

IB Math Methods 1 270431 0.2 0.07 

IB Math Studies 1 270432 0.3 0.15 

Discrete Math 270436 1.8 0.32 

Finite Math 270437 0.2 0.07 

Algebra and Geometry 270441 1.1 0.38 

Mathematics, Other 279900 # † 

See notes at end of table. 

D-14 
Appendix D. Course-Specific Completion Percentages 

Table D-5. Percentage and standard errors of graduating seniors who received credit in 

mathematics courses, by pipeline level: 2004—Continued 

Pipeline level and CSSC1 course title CSSC1 code Percentage Standard error 

(3) Algebra II † 

Algebra 2 270405 60.0 1.17 

Mathematics 3, Unified 270423 5.2 0.66 

Pre-IB Algebra 2/Trigonometry 270430 0.1 0.07 

 

(4) Algebra III/trigonometry/analytic geometry † 

Algebra 3 270410 7.2 0.65 

Trigonometry 270411 9.8 0.82 

Analytic Geometry 270412 3.8 0.49 

Trigonometry and Solid Geometry 270413 0.1 0.04 

Algebra and Trigonometry 270414 10.0 0.96 

Algebra and Analytic Geometry 270415 0.7 0.18 

Linear Algebra 270417 0.1 0.03 

Mathematics, Independent Study 270424 0.9 0.17 

Statistics, Other 4

 270500 † † 

Statistics 270511 2.1 0.33 

Probability 270521 0.1 0.06 

Probability and Statistics 270531 2.8 0.33 

AP Statistics 270532 3.1 0.36 

 

(5) Precalculus † 

Analysis, Introductory 270416 28.6 0.85 

IB Math Studies 2 270433 0.4 0.18 

 

(6) Calculus † 

Calculus and Analytic Geometry 270418 0.2 0.05 

Calculus 270419 4.5 0.35 

AP Calculus 270420 8.8 0.43 

IB Math Studies/Calculus 270434 0.1 0.07 

AP Calculus CD 270435 1.7 0.24 

# Rounds to zero. 

† Not applicable. 

1

 CSSC = Classification Scheme of Secondary School Courses. Each CSSC course code comprises six digits with an 

associated course title, alternate titles, and a course description. The first two digits identify the main program area (e.g., 

mathematics), the second set of two digits represents a subcategory of courses within the main program area (e.g., pure 

math), and the last two digits are associated with the specific courses in each of the main and subcategories (e.g., 

trigonometry). 2

 Indicates lower grade (7-8) course levels that existed on transcripts. Only a few students have transcript records for grade 

levels lower than the 9th grade. For this reason, in these figures only those students who took the lower level courses in 

grade levels 9 through 12 were included in the percentages. 

3

 Indicates CSSC definitions that existed in earlier data collections. These definitions were usually redefined because they 

were split into many codes. 4

 Indicates CSSC definitions that may have not been used in the transcript collection or codes that did not exist at that time. 

It should be noted that in these cases it does not mean that no courses were taken in this course area, but that the courses 

may have been given different CSSC values. 

NOTE: Comparing individual courses from different studies across time may result in misleading conclusions. Some course 

codes have been consolidated, split, dropped, or added over time. Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Education Longitudinal Study of 2002 

(ELS:2002), "First Follow-up, High School Transcript Study, 2004." 

D-15 
Appendix D. Course-Specific Completion Percentages 

Table D-6. Percentage and standard errors of graduating seniors who received credit in science 

courses, by pipeline level: 2004 

Standard 

Pipeline level and CSSC1 course title CSSC1 code Percentage error 

(1) No science or low-level science † 

Science, Unified 300111 11.5 1.11 

Physical Science 400121 41.5 1.62 

Physical Science, Applied 400141 1.1 0.27 

Geological Sciences, Other 400600 # 0.01 

Earth Science 400611 13.3 1.03 

Earth Science, College Prep 400621 9.2 0.94 

Misc. Physical Sciences, Other2

 400700 † † 

 

(2) Secondary physical science and basic biology † 

Biology, Basic 1 260121 4.5 0.55 

Biology, Basic 2 260122 0.2 0.06 

Biological and Physical Sciences, Other 300100 1.0 0.26 

Science Study, Independent 300121 0.6 0.12 

Outdoor Education 300131 0.3 0.14 

Futuristics 300611 0.3 0.13 

Environmental Science 300621 9.8 0.77 

Astronomy, Other2

 400200 † † 

Astronomy 400211 3.3 0.43 

Astrophysics, Other 400300 # † 

Atmospheric Sciences and Meteorology 400400 # † 

Meteorology 400411 0.4 0.17 

Chemistry, Other 400500 # 0.04 

Chemistry, Introductory 400511 5.7 0.71 

Chemistry in the Community 400512 0.2 0.07 

Organic Biochemistry 400531 1.2 0.26 

Physical Chemistry 400541 # 0.04 

Consumer Chemistry 400551 0.6 0.17 

Chemistry, Independent Study 400561 0.1 0.03 

AP Environmental Science3

 400622 1.7 0.25 

Geology 400631 0.3 0.16 

Geology - Field Studies 400632 0.1 0.04 

Mineralogy 400641 # † 

Oceanography 400711 1.4 0.34 

Physics, Other 400800 # 0.02 

Physics 400811 4.9 0.62 

Electricity and Electronics Science 400841 0.1 0.10 

Acoustics 400851 0.1 0.08 

Planetary Science, Other 400900 # † 

Rocketry and Space Science 400911 0.1 0.07 

Aerospace Science 401011 0.1 0.07 

AP Environmental Science 300622 # † 

See notes at end of table. 

D-16 
Appendix D. Course-Specific Completion Percentages 

Table D-6. Percentage and standard errors of graduating seniors who received credit in science 

courses, by pipeline level: 2004—Continued 

Standard 

Pipeline level and CSSC1 course title CSSC1 code Percentage error 

(3) General biology † 

Biology, Other General 260100 # 0.01 

Biology, General 1 260131 73.6 1.19 

Biology, General 2 260132 6.5 0.85 

Biology, Honors 1 260141 13.1 0.79 

Pre-IB Biology 260143 0.4 0.15 

Ecology 260611 3.4 0.51 

Marine Biology 260621 3.4 0.38 

Marine Biology, Advanced 260622 0.2 0.06 

Zoology, Other 260700 0.1 0.01 

Zoology 260711 2.4 0.40 

Zoology, Vertebrate 260721 0.1 0.05 

Zoology, Invertebrate 260731 # 0.01 

Animal Behavior 260741 0.3 0.12 

Physiology Human 260751 14.2 0.68 

Physiology, Advanced 260752 0.4 0.13 

Pathology 260761 0.2 0.16 

Comparative Embryology 260771 # † 

Life Sciences, Other 269900 # 0.03 

 

(4/5) Chemistry I and/or physics I † 

Chemistry 1 400521 61.8 1.03 

Pre-IB Chemistry 400523 0.3 0.13 

Physics 1 400821 26.7 1.04 

 

(6) Chemistry II, physics II, or advanced biology † 

Chemistry 2 400522 3.5 0.46 

IB Chemistry 2 400524 0.2 0.10 

IB Chemistry 3 400525 0.1 0.05 

AP Chemistry 400526 3.0 0.26 

Physics 2 400822 1.9 0.29 

IB Physics 400823 0.2 0.08 

AP Physics B 400824 2.1 0.23 

AP Physics C: Mechanics 400825 0.5 0.13 

AP Physics C: Electricity/Magnetism 400826 0.1 0.04 

Physics 2 without Calculus 400831 # 0.03 

Biology, Advanced 260142 2.4 0.40 

Field Biology 260151 0.5 0.12 

Genetics 260161 0.8 0.19 

Biopsychology2

 260171 † † 

Biology, Seminar 260181 0.2 0.08 

Biochemistry and Biophysics, Other 260200 # † 

Biochemistry 260211 0.7 0.20 

Botany, Other 260300 # † 

Botany 260311 1.1 0.26 

See notes at end of table. 

D-17 
Appendix D. Course-Specific Completion Percentages 

Table D-6. Percentage and standard errors of graduating seniors who received credit in science 

courses, by pipeline level: 2004—Continued 

Standard 

Pipeline level and CSSC1 course title CSSC1 code Percentage error 

(6) Chemistry II, physics II, or advanced biology—Continued † 

Cell and Molecular Biology, Other 260400 # 0.02 

Cell Biology 260411 0.2 0.11 

Microbiology, Other 260500 # † 

Microbiology 260511 0.4 0.11 

Misc. Specialized Areas; Life Sciences, Other2

 260600 † † 

Anatomy 260631 0.5 0.13 

IB Biology 2 260144 0.3 0.08 

IB Biology 3 260145 0.1 0.05 

AP Biology 260146 4.6 0.32 

# Rounds to zero. 

† Not applicable. 

1

 CSSC = Classification Scheme of Secondary School Courses. Each CSSC course code comprises six digits with an 

associated course title, alternate titles, and a course description. The first two digits identify the main program area (e.g., life 

science), the second set of two digits represents a subcategory of courses within the main program area (e.g., biology), and 

the last two digits are associated with the specific courses in each of the main and subcategories (e.g., advanced). 2

 Indicates CSSC definitions that may have not been used in the transcript collection or codes that did not exist at that time. 

It should be noted that in these cases it does not mean that no courses were taken in this course area, but that the courses 

may have been given different CSSC values. 

3

 Indicates a CSSC definition that prior to the year 2000 did not exist, but existed as another code (300622). This code also 

existed in 2000. 

NOTE: Comparing individual courses from different studies across time may result in misleading conclusions. Some course 

codes have been consolidated, split, dropped, or added over time. Detail may not sum to totals because of rounding. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Education Longitudinal Study of 2002 

(ELS:2002), "First Follow-up, High School Transcript Study, 2004." 

D-18