Interim Report on the Evaluation of the 

Growth Model Pilot Project

Prepared by:

Thomas B. Hoffer

E. C. Hedberg

Kevin L. Brown

Marie L. Halverson

Sarah-Kathryn McDonald

National Opinion Research Center (NORC)

at the University of Chicago

Prepared for:

U.S. Department of Education

Office of Planning, Evaluation and Policy Development

Policy and Program Studies Service

2010
This report was prepared for the U.S. Department of Education under Contract Number ED-06-

CO-0053 with National Opinion Research Center at the University of Chicago. Andrew Abrams 

served as the contracting officer’s representative. The views expressed herein do not necessarily 

represent the positions or policies of the Department of Education. No official endorsement by the 

U.S. Department of Education is intended or should be inferred.

U.S. Department of Education

Arne Duncan

Office of Planning, Evaluation and Policy Development

Secretary

Carmel Martin

Policy and Program Studies Service

Assistant Secretary

Alan Ginsburg

April 2010

Director

This report is in the public domain. Authorization to reproduce it in whole or in part is granted. While 

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Education, Office of Planning, Evaluation and Policy Development, Policy and Program Studies Service, 

Interim Report on the Evaluation of the Growth Model Pilot Project, Washington, D.C., 2010.

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Evaluation of the Growth Model Pilot Project iii

Contents

List of Exhibits...............................................................................................................................v

Acknowledgments........................................................................................................................ ix

Executive Summary..................................................................................................................... xi

I. Introduction ...........................................................................................................................1

The status model of accountability under ESEA .....................................................................2

Limitations of the status model ...............................................................................................4

The Growth Model Pilot Project (GMPP)...............................................................................5

Types of growth models implemented in the pilot..................................................................9

How growth models are used for AYP determinations.........................................................17

Data sources and availability.................................................................................................19

Calculation of hypothetical growth-only percentages on-track to proficiency .....................19

Data limitations .....................................................................................................................20

II. Effects of Growth Models Implemented Under the GMPP on School AYP 

Determinations.....................................................................................................................23

State growth models and their effects on schoolwide AYP results.......................................23

Alaska’s growth model................................................................................................ 23

Arizona’s growth model.............................................................................................. 25

Arkansas’ growth model ............................................................................................. 27

Delaware’s growth model........................................................................................... 28

Florida’s growth model .............................................................................................. 30

Iowa’s growth model................................................................................................... 31

North Carolina’s growth model.................................................................................. 32

Tennessee’s growth model .......................................................................................... 33

Impact of GMPP on AYP......................................................................................................34

Discussion..............................................................................................................................35

III. School Characteristics Associated with AYP Outcomes..................................................37

Discussion..............................................................................................................................41

IV. Using Student Growth Indicators to Assess School Outcomes .......................................43

Comparisons of status and growth-only proficiency determinations for schools .................45

Growth-only proficiency results of schools making AYP by safe-harbor ............................47

Demographic characteristics of schools that made their AMO by status and 

growth criteria .......................................................................................................................49

Extent of longitudinal matching ............................................................................................50

Conclusions ...........................................................................................................................52

Conclusions...................................................................................................................................55

How have states in the pilot project implemented growth models?......................................55

How did each pilot state’s growth model affect the number and kinds of schools 

that make AYP?.....................................................................................................................56

Implications for future policy................................................................................................57

References.....................................................................................................................................59
Evaluation of the Growth Model Pilot Project iv

Appendix A. Comparison of GMPP Growth Models with State Accountability

Systems................................................................................................................61

Appendix B: State GMPP Model Summaries........................................................................67
Evaluation of the Growth Model Pilot Project v

Exhibits

Exhibit S.1 Percentage of Schools That Made AYP Before and After the Application 

of the Growth Model, in Eight States, in 2006–07 ..............................................xiii

Exhibit S.2 Percent of Schools Making AYP Because of Use of the Growth Model, 

Percentage Increase in Number of Schools That Made AYP Due to 

Growth, and Percentage Decrease in Number of Schools That Did Not 

Make AYP Due to Growth, by State, 2006–07 ................................................... xiv

Exhibit 1 Determining AYP Under Status Model.................................................................. 4

Exhibit 2 Conceptual Map of How Growth Patterns Compare With Status Model 

AYP Designations................................................................................................... 5

Exhibit 3 Seven Core Principles of the Growth Model Pilot Project ..................................... 7

Exhibit 4 Determining AYP Under Status, Safe-Harbor, and Growth................................... 9

Exhibit 5 Illustration of How the Iowa Transition Matrix Model Classifies 

Students................................................................................................................. 10

Exhibit 6 Illustration of How the Delaware Transition Matrix Model Assigns 

Points to Students’ Gains...................................................................................... 11

Exhibit 7 Illustration of How Trajectory Models Set Targets for Students Scoring 

Below Proficiency Thresholds.............................................................................. 12

Exhibit 8 Illustration of How Projection Models Evaluate Students Scoring Below 

Proficiency Thresholds......................................................................................... 14

Exhibit 9 Overview of Growth Models Approved for the GMPP in the 2006–07 

School Year........................................................................................................... 15

Exhibit 10 Overview of How Schools Are Classified as Making AYP Under the 

Status Augmented With Growth System.............................................................. 18

Exhibit 11 Alaska School AYP Determinations With Status and Safe-Harbor 

Results Augmented With Growth Model Results, 2006–07................................. 25

Exhibit 12 Arizona School AYP Determinations With Status and Safe-Harbor 

Results Augmented With Growth Model Results, 2006–07................................. 27

Exhibit 13 Arkansas School AYP Determinations With Status and Safe-Harbor 

Results Augmented With Growth Model Results, 2006–07................................. 28

Exhibit 14 Delaware School AYP Determinations With Growth Model Results 

Augmented With Status and Safe-Harbor Results, 2006–07................................ 29

Exhibit 15 Delaware School AYP Determinations With Status and Safe-Harbor 

Results Augmented With Growth Model Results, 2006–07................................. 30

Exhibit 16 Florida School AYP Determinations With Status and Safe-Harbor 

Results Augmented With Growth Model Results, 2006–07................................. 31

Exhibit 17 Iowa School AYP Determinations With Status and Safe-Harbor Results 

Augmented With Growth Model Results, 2006–07 ............................................. 32

Exhibit 18 North Carolina School AYP Determinations With Status and Safe-Harbor 

Results Augmented With Growth Model Results, 2006–07................................. 33
Evaluation of the Growth Model Pilot Project vi

Exhibit 19 Tennessee School AYP Determinations With Status and Safe-Harbor 

Results Augmented With Growth Model Results, 2006–07................................. 34

Exhibit 20 Percentage Increase in Number of Schools That Made AYP Due to 

Growth, and Percentage Decrease in Number of Schools That Did Not 

Make AYP Due to Growth, by State, 2006–07 .................................................... 35

Exhibit 21 Numbers of Schools Making AYP Under Status-Plus-Safe-Harbor and 

Growth, and Percentage Increase Due to Growth, by ESEA School 

Improvement Status, 2006–07 .............................................................................. 38

Exhibit 22 Numbers of Schools Making AYP Under Status-Plus-Safe-Harbor and 

Under Growth, and Percentage Increase in AYP Due to Growth, by 

School Poverty Concentration, 2006–07 .............................................................. 39

Exhibit 23 Numbers of Schools Making AYP Under Status-Plus-Safe-Harbor and 

Under Growth, and Percentage Increase in AYP Due to Growth, by 

School Minority Concentration, 2006–07............................................................. 40

Exhibit 24 Numbers of Schools Making AYP Under Status-Plus-Safe-Harbor and 

Under Growth, and Percentage Increase in AYP Due to Growth, by 

School Urbanicity, 2006–07 ................................................................................. 41

Exhibit 25 Conceptual Map of How Growth-Only Proficiency Designations 

Compare With Status Model Proficiency Designations for Students................... 44

Exhibit 26 Distribution of Students According to How Their Status and Growth 

Proficiency Classifications Compare, 2006–07.................................................... 45

Exhibit 27 How the Growth Model On-Track-to-Proficiency Designations Can 

Compare with AYP Designations for Schools...................................................... 46

Exhibit 28 Number and Distribution of Schools That Made AYP Based on Status 

Criteria, by Whether They Met AMOs Based on Growth Criteria, 

2006–07................................................................................................................. 47

Exhibit 29 Number and Distribution of Schools That Made AYP by Safe-Harbor 

Criteria, by Whether They Met AMOs Based on Growth Criteria, 

2006–07................................................................................................................. 48

Exhibit 30 Percentage of Schools That Met the AMO Under Status That Also Met 

the AMO Under Growth-Only, by School Poverty Level, 2006–07 .................... 50

Exhibit 31 Differences Between Matched and Unmatched Grade-Standardized 

Student Scores for Reading and Math for Alaska, Arkansas, Florida, 

Iowa, and Tennessee, 2006–07 ............................................................................. 51

Exhibit A.1 Overview of Growth Components of State Accountability Systems.................... 62

Exhibit B.1 Illustration of Alaska’s Method for Determining Whether a Student Is 

On-Track Toward Proficiency .............................................................................. 68

Exhibit B.2 Arizona Proficiency Standards Test Cutoffs for Grades 3 Through 8.................. 69

Exhibit B.3 Illustration of Arizona’s Method for Determining Whether a Student Is 

On-Track Toward Proficiency .............................................................................. 71

Exhibit B.4 Arkansas Benchmark Exam Proficiency Standards for Grades 3 

Through 8.............................................................................................................. 72

Exhibit B.5 Arkansas Growth Target Multipliers for Grades 3 Through 7 ............................. 72
Evaluation of the Growth Model Pilot Project vii

Exhibit B.6 Illustration of Arkansas’ Method for Determining Whether a Student Is 

On-Track Toward Proficiency .............................................................................. 74

Exhibit B.7 Example Comparison of Two Hypothetical Schools in Delaware to 

Illustrate Growth Model........................................................................................ 77

Exhibit B.8 Florida’s Cutoff Developmental Scale Scores to Be Considered 

Proficient on the FCAT for Grades 3 Through 7.................................................. 78

Exhibit B.9 Illustration of Florida’s Method for Determining Whether a Student Is 

On-Track Toward Proficiency in Reading............................................................ 79

Exhibit B.10 Grades and Tests Used for Trajectory Growth in North Carolina and 

the Percent of Difference Expected to Be Closed Per Year.................................. 80

Exhibit B.11 Illustration of Tennessee’s Method for Determining Whether a Student 

Is On-Track Toward Proficiency in Reading........................................................ 84
Evaluation of the Growth Model Pilot Project viii
Evaluation of the Growth Model Pilot Project ix

Acknowledgments

This report benefited from the efforts and thoughtful input of many individuals. Andrew Abrams 

at the U.S. Department of Education’s Policy and Program Studies Service (PPSS) directed the 

project and provided helpful guidance and encouragement at each stage. David Goodwin,

Daphne Kaplan, and Stephanie Stullich, also at PPSS, offered much constructive advice and 

feedback throughout the project.

The data analyzed in this report were drawn from the U.S. Department of Education’s EDFacts

archive and from each of the separate state departments of education participating in the Growth 

Model Pilot Project. We are grateful to Ross Santy and Susan Thompson-Hoffman for their 

generous help and patience with the EDFacts data. The Alaska, Arizona, Arkansas, Delaware, 

Florida, Iowa, North Carolina, and Tennessee state departments of education were very 

responsive to our various requests for data and information about their pilot programs, and we 

would particularly like to acknowledge the help of Les Morse, Robert Franciosi, Denise Airola,

Robin Taylor, Ed Croft, Thomas Deeter, Kenneth Barbour, and Dan Long.

We were very fortunate to receive thoughtful and timely reviews from several individuals both 

within and outside the U.S. Department of Education. In particular, we received extremely 

helpful guidance in the early stages of the project and detailed feedback on early drafts of the 

report from Patrick Rooney at the Office of Elementary and Secondary Education within ED. 

We also thank Abigail Potts and Victoria Hammer of OESE for sharing their expertise in the 

design and review stages.

The project had a Technical Working Group consisting of David Figilo, Thomas Fisher, Pete 

Goldschmidt, Rachel Quenemoen, and Keith Zvoch. The TWG provided guidance with the 

study design and analysis plans, and contributed many useful comments and corrections on an 

early draft of this report. 

At NORC, the project has benefited greatly at several key junctures from the insightful 

perspectives of Stephen Raudenbush and Larry Hedges. In the later stages of drafting the 

Interim Report, Marie Halverson and Cindy Simko joined the project as project director and 

associate project director, respectively, and contributed greatly to organizing and implementing 

the many reviewer comments. The task of formatting this report in each of its iterations was

handled with great skill and efficiency by Imelda Demus and Yajaira Gijon. 
Evaluation of the Growth Model Pilot Project x
Evaluation of the Growth Model Pilot Project xi

Executive Summary

The U.S. Department of Education (ED) initiated the Growth Model Pilot Project (GMPP) in 

November 2005 with the goal of approving up to ten states to incorporate growth models in 

school adequate yearly progress (AYP) determinations under the Elementary and Secondary 

Education Act (ESEA). After extensive reviews, eight states were fully approved for the pilot 

project in the 2006–07 school year: Alaska, Arizona, Arkansas, Delaware, Florida, Iowa, North 

Carolina, and Tennessee. Based on analyses of data provided by the U.S. Department of 

Education and by the pilot grantee states, this report describes the progress these states made in 

implementing the GMPP in the 2006–07 school year.

GMPP Objectives

Use of growth models for determining AYP is attractive to states and local districts because it 

offers a means to identify schools making progress even though they may not yet be reaching 

proficiency standards. Without recognition of their progress, these schools would be subject to 

school improvement actions that may not be appropriate in light of their demonstrable 

improvements.

The standard method of determining AYP has been the “status model,” in which school 

performance is mainly evaluated in terms of the proportion of students meeting or exceeding 

proficiency standards for reading and mathematics. Growth models measure how much students 

have gained from one year to the next using longitudinal records of individual student 

achievement in reading and mathematics. The models determine whether each student was “ontrack” to reach or exceed the state’s proficiency cut points (or thresholds) on the annual tests of 

reading and mathematics within three or four years or by a specified grade level (usually grade 

eight or nine) as defined by the state’s particular growth model. For purposes of determining 

AYP, students who were not proficient but on-track could be counted the same as proficient 

students. 

States Included in the Pilot Project

The GMPP began in 2005 with two states—North Carolina and Tennessee—approved to use 

growth models for ESEA accountability in the 2005–06 school year. The project expanded to 

include eight states approved to implement growth models in 2006–07, 11 states in 2007–08, and 

15 states in 2008–09. This interim report focuses only on the eight states approved for 2006–

07.1

 1 An evaluation by the Office of Elementary and Secondary Education of growth model results in North Carolina 

and Tennessee for the 2005–06 school year is available at 

http://www.ed.gov/admins/lead/account/growthmodel/gmeval0109.doc.

A final report will examine results for the 2007–08 school year for the eight states plus 

Ohio, which first implemented in 2007–08. In 2007 and 2008, six additional states were 

approved: Michigan and Missouri (beginning in the 2007–08 school year); and Colorado, 

Minnesota, Pennsylvania, and Texas (beginning in the 2008–09 school year). While the GMPP 

began in 2005 with a goal of approving up to 10 states, under current Title I regulations, there is 

no limit now on the number of states that can be approved.
Evaluation of the Growth Model Pilot Project xii

Findings

Features of growth models implemented by pilot states

The growth models implemented under the GMPP were all designed to augment rather than 

replace the standard status model and safe-harbor provisions for determining school AYP. The 

growth models resulted in more schools making AYP than would have been the case using only 

status and safe-harbor.

Seven of the eight states used growth criteria only after schools failed to make AYP under the 

status and safe-harbor provisions. Delaware was the exception, applying growth results before 

status and safe-harbor. The designs of the pilots in the other seven states applied growth criteria 

only to ESEA reporting groups that did not reach their annual measurable objectives (AMOs) or 

obtain AYP via safe-harbor provisions. Furthermore, in all but two of those seven states, the 

growth criteria were applied within the ESEA reporting groups only to the students who did not 

reach the proficiency threshold. The number of non-proficient but on-track students was added 

to the number of proficient students and the reporting group was counted as meeting the AMO if 

the total was high enough. 

Comparing AYP by growth with status and safe-harbor

The growth models in the eight states that provided data for the 2006–07 school year resulted in 

some schools making AYP that would not have made AYP under status or safe-harbor alone (see 

Exhibit S.1). Among all schools, 3 percent made AYP uniquely because of the growth model 

(that is, they did not make AYP by status or safe-harbor). The percentages of all schools that 

made AYP uniquely by growth varied widely among the states, ranging from zero or one percent 

of all schools in Alaska, Arizona, North Carolina, and Tennessee to 11 percent of all schools in 

Iowa. 
Evaluation of the Growth Model Pilot Project xiii

Exhibit S.1

Percentage of Schools That Made AYP Before and After the

Application of the Growth Model, in Eight States, in 2006–07

As the bar chart illustrates, the pilot states varied greatly in the proportion of their schools that 

made AYP under status or safe-harbor. The schools making AYP uniquely by growth 

represented a percentage increase in the schools making AYP (the dark gray column in Exhibit 

S.2) of 6 percent across all states, and ranged as high as 12 percent in Iowa, 14 percent in 

Arkansas, and 16 percent in Florida. 

Another measure of GMPP impact is the extent to which it reduced the number of schools that 

would not have made AYP had the growth model not been available. From this perspective, the 

number of schools that did not make AYP by either status or safe-harbor was reduced by 8 

percent overall because of the GMPP (the medium gray column in Exhibit S.2). The percentage 

reduction was highest in Iowa (69 percent), Arkansas (17 percent), and Tennessee (13 percent). 

77%

56%

66%

29%

85%

44%

89%

56%

66%

3%

3% 8%

1%

5%

11%

0%

20%

40%

60%

80%

100%

All Schools Alaska Arizona Arkansas Delaware Florida Iowa North

Carolina

Tennessee

Met AYP Without Growth Met AYP Due to Growth Model

66% 69%

59% 64%

77%

33%

95%

44%

91%

<1%

<1%

<1%
Evaluation of the Growth Model Pilot Project xiv

Exhibit S.2

Percent of Schools Making AYP Because of Use of the Growth Model, Percentage 

Increase in Number of Schools That Made AYP Due to Growth, and Percentage Decrease 

in Number of Schools That Did Not Make AYP Due to Growth, by State, 2006–07

Pilot States

Number 

of 

Schools

Number of 

Schools 

Making 

AYP by 

Status or 

SafeHarbor

Number of 

Schools 

Not Making 

AYP by 

Status or 

SafeHarbor

Number of 

Schools 

Not Making 

AYP by 

Status or 

SafeHarbor

That Met 

by Growth

Percent of 

All Schools 

That Met 

by Growth

Percentage 

Increase in 

Schools 

Making 

AYP Due to 

Growth

Percentage 

Decrease 

in Schools 

Not Making 

AYP Due to 

Growth

All Eight 

States 10,883 6,088 4,795 371 3% 6% 8%

Alaska 492 323 169 0 0% 0% 0%

Arizona 1,430 1,096 334 1 <1% <1% <1%

Arkansas 894 499 395 69 8% 14% 17%

Delaware 185 123 62 5 3% 4% 8%

Florida 3,209 925 2,284 149 5% 16% 7%

Iowa 1,104 936 168 116 11% 12% 69%

North 

Carolina 2,207 969 1,238 12 <1% 1% <1%

Tennessee 1,362 1,217 145 19 1% 2% 13%

Exhibit reads: A total of 10,883 schools in the pilot states included grade levels to which the growth models were 

applied, and 371 of those schools (3 percent) made AYP because of the growth model. Of the 6,088 schools that made 

AYP under either status or safe-harbor, use of the growth model increased the number of schools making AYP by 6 

percent. Of the 4,795 schools that did not make AYP under either status or safe-harbor, use of the growth model 

reduced that number by 8 percent. 

Source: U.S. Department of Education, EDFacts and the Alaska, Arizona, Delaware, North Carolina, Ohio, and 

Tennessee state departments of education.

Impact of Growth Models on AYP Rates Among High-Poverty Schools

Schools serving disadvantaged populations have been found to make AYP at much lower rates 

than those serving more affluent populations (U.S. Department of Education, 2007). The growth 

model pilots may reduce these associations to some extent by identifying high-growth schools 

serving low-income and minority communities.

The results of this analysis showed that schools serving economically disadvantaged student 

populations in all pilot states except for Delaware were more likely than more-advantaged 

schools to make AYP by growth. Across all eight states, the percentage increase in the number 

of high-poverty schools making AYP as a result of the growth model being available was 8 

percent, compared to 3 percent among low-poverty schools. The percentage increases among 

high-poverty schools in Arkansas, Florida, and Iowa were five to six times greater than those 

among low-poverty schools. 
Evaluation of the Growth Model Pilot Project xv

Hypothetical Results of Using Growth Models Instead of Status and Safe-Harbor

Some have suggested that growth should be the primary accountability indicator for all schools, 

including those that made AYP by status. The student data were used to assess the extent to 

which the schools that made AYP by status (excluding safe-harbor) would also have met or 

exceeded their AMO for reading and mathematics proficiency if the growth criteria of on-trackto-proficiency were used instead of the status criteria. 

Overall, 85 percent of the schools that made AYP by status criteria in the eight states also would 

have met their AMO strictly by using the growth criteria. Results varied widely among the 

states: only 45 percent of the Arizona schools that made AYP by status also met their AMO 

using growth criteria alone, but almost all of the North Carolina (99 percent) and Florida (97 

percent) schools that made AYP by status also met their AMO with the growth criteria.

The percentages of schools that made AYP by safe-harbor and that also met or exceeded their 

AMO under the growth-only criteria were also high (87 percent overall) and consistent across the 

six states with safe-harbor schools (Alaska and Arizona had none), ranging from 75 percent in 

Tennessee to 99 percent in North Carolina. 

Qualifications and Implications 

The results of this analysis show that use of growth models will generally add to the number of 

schools making AYP, especially among schools serving low-income populations, which can help 

administrators identify schools “on-track” and those that may need help to get “on-track.”

The growth targets identified by the growth models are tied to the ESEA goal of universal 

proficiency by 2014. This means that substantial student performance improvements that do not 

reach the 2014-driven targets are not recognized by the GMPP growth models. However, growth 

models could be adapted to other targets with the result that more schools would be identified as 

making AYP than is currently the case.

The generally low rates of making AYP by growth also reflect the impact of the various other 

(non-growth) methods for determining AYP available in those states for schools to make AYP 

by status and safe-harbor (e.g., confidence intervals and multiyear averaging), such that the 

status and safe-harbor methods picked up schools which would have made AYP by growth had 

those various provisions not been available.

Reasons for the variation among states in the percentages of schools making AYP by growth are 

not examined systematically in this report but are likely to be some combination of differences in 

the assessments and proficiency cutpoints used, the features of the growth models implemented, 

the states’ AMOs, and the actual levels of growth realized by the students. The final report will 

explore these factors in more detail.

An implication for future policy is that states could clarify each school’s progress by applying 

growth criteria to all their schools and groups before status and safe-harbor. The main advantage 

of applying the growth model before the status and safe-harbor models is that it would identify 

schools that are realizing adequate progress toward universal proficiency. This would clearly 

distinguish those schools from schools making AYP under status criteria but not realizing growth 
Evaluation of the Growth Model Pilot Project xvi

sufficient to continue meeting their AMOs. The latter are probably not a large number but 

identifying such schools would serve as an early warning mechanism of possible problems. The 

exploratory analyses in this report also indicate that applying growth criteria before safe-harbor

could usefully reclassify most of the current safe-harbor schools as making AYP by growth, and 

would clearly identify those that are not on-track to proficiency and thus headed for 

improvement status in the near future. 

Another reporting option is to classify each school in terms of both growth and status. Schools 

making AYP would be distinguished as making AYP by both growth and status, by growth only, 

by status only, by a mix of status and growth, or by safe-harbor only. This would have the 

advantage of uniquely identifying different sets of schools (those making AYP in terms of both 

growth and status). 
Evaluation of the Growth Model Pilot Project 1

I. Introduction

A key goal of the Elementary and Secondary Education Act (ESEA), as amended in 2001, is that 

all students attain proficiency in reading and mathematics by the year 2014. ESEA requires 

states to: (a) develop grade-level specific proficiency standards in both subjects for grades 3–8 

and one or more high school grades, and (b) to assess the performance of all students in those 

grades each year. The states’ proficiency standards progressively increase with all students 

expected to be proficient by 2014. Based on their students’ scores, every public school is 

evaluated to determine whether or not it is making adequate yearly progress (AYP), and 

consequences are applied to schools not making AYP for more than two consecutive years. 

The U.S. Department of Education initiated the Growth Model Pilot Project (GMPP) in 

November 2005 with the goal of approving up to ten states to incorporate growth models in 

school AYP determinations under ESEA. Growth models are defined as complements or 

alternatives to the standard status model for determining school AYP. The status model bases 

AYP on the proportion of a school’s students attaining proficiency in reading and mathematics in 

a given year. Growth models, in contrast, base AYP in part on some measure of how much 

additional proficiency students gain in these subjects from one year to the next relative to the 

target of 100 percent proficiency by the year 2014. Growth models promise to provide a fuller 

understanding of school effectiveness and the progress each school’s students are making toward 

their proficiency goals. The main objectives of the GMPP are to help states develop and 

implement models for determining school-level AYP that incorporate measures of student 

growth. 

This interim evaluation of the GMPP is restricted to the eight states approved for participation in 

the pilot project as of September 2006.

2

1) How have states in the pilot project implemented growth models?

It is designed to answer three questions:

2) How does each pilot state’s growth model affect the number and kinds of schools that 

make AYP?

3) What are the implications of the pilot project experience for extending and strengthening 

growth models within the context of ESEA? 

 2 The states approved for participation in the pilot project as of September 2006 were: North Carolina and 

Tennessee (approved for implementation beginning in the 2005–06 school year); and Alaska, Arizona, Arkansas, 

Delaware, Florida, and Iowa (approved for implementation beginning in the 2006–07 school year). Ohio was 

approved to begin implementation in the 2007–08 school year and will be discussed in the final report. In June 2008 

and January 2009 Secretary Spellings announced the approval of six additional pilot growth models, in Michigan 

and Missouri (approved for use in the 2008–09 school year), and Colorado, Minnesota, Pennsylvania, and Texas 

(beginning in the 2008–09 school year). While the GMPP began in 2005 with a goal of approving up to 10 states, 

under current Title I regulations, there is no limit now on the number of states that can be approved. See “U.S. 

Secretary of Education Margaret Spellings Approves Additional Growth Model Pilots” retrieved June 2008 and 

January 2009 from http://www.ed.gov/news/pressreleases/2008/06/06102008.html and 

http://www.ed.gov/news/pressreleases/2009/01/01082009a.html.
Evaluation of the Growth Model Pilot Project 2

The remainder of this chapter considers how the GMPP models compare with status models in 

approaches to evaluating student achievement. Chapters II and III consider, for each of eight

pilot grantee states in the 2006–07 school year, the impact of the state’s GMPP model on its 

AYP determinations. Chapter IV addresses a number of hypothetical questions about how 

results might change if the data collected as part of the pilot project were used differently. A 

final project report is planned to address the same research questions with data collected for the 

2007–08 school year for all eight states plus Ohio, as well as additional questions about the 

impact of technical features of the models which are not addressed in the current report. 

The status model of accountability under ESEA

Under ESEA, each state develops a standards-based system of student achievement measures and 

targets, and conducts annual assessments to determine whether its schools and local education 

agencies (LEAs) are making AYP.3

Each step in the path to achieving universal proficiency in reading and mathematics is known as 

the “annual measurable objective” or “AMO”.

 Each school has a certain percentage of students who score 

proficient or higher each year on the mathematics and reading or language arts achievement tests

and this constitutes an annual measure of a school’s performance. That percentage is expected to 

reach 100 percent by the end of the 2013–14 school year in incremental steps. In addition, ESEA

requires each school to meet or exceed statewide standards on one or more “other academic 

indicators,” typically defined in terms of average daily attendance for elementary schools and 

graduation rate for high schools.

4

In order for the school to make AYP under the ESEA status model, several conditions must be 

met. These conditions are required by the law and are intended to improve the reliability and 

validity of the accountability results. First, the school must test at least 95 percent of its students

in each of the ESEA reporting groups in both reading or language arts and mathematics. The

ESEA reporting groups consist of all students plus the major racial and ethnic subgroups, 

students with disabilities, limited English proficient students, and students from low-income 

households. Within each school, a reporting group may be excluded from federal accountability 

requirements if the number of “full academic year” students from that group is below a minimum 

“n” size. Most states define a full academic year as starting in the fall when enrollments are 

finalized (typically around Oct. 1) and extending through the end of the testing window in the 

 The AMO is the standard that schools and 

districts use to determine whether or not they are making adequate yearly progress. AMO’s do 

not increase uniformly across states, including the states in this study. Some increase in a 

consistent linear fashion toward 2014, while others increase more in the years closer to 2014 than 

in those closer to the 2002 start of the AYP requirements.

 3 See “What is adequate yearly progress (AYP)?” (retrieved May 2008 from http://answers.ed.gov/cgibin/education.cfg/php/enduser/std_adp.php?p_faqid=6&p_created=1095256734&p_sid=biCz1Gli&p_lva=&p_sp=c

F9zcmNoPSZwX3NvcnRfYnk9JnBfZ3JpZHNvcnQ9JnBfcm93X2NudD0xMTUmcF9wcm9kcz0mcF9jYXRzPSZw

X3B2PSZwX2N2PSZwX3BhZ2U9MQ**&p_li=&p_topview=1); U.S. Department of Education, Office of the 

Secretary, Office of Public Affairs. (2003). No Child Left Behind: A Parents Guide, Washington, D.C. (retrieved 

May 2008 from http://www.ed.gov/parents/academic/involve/nclbguide/parentsguide.pdf). 

4 AMOs are defined by the states and have different targets for each school year, and can be different within each 

year across grades and subjects. In any case, states were required to follow strict federal guidelines in setting the 

AMOs. 
Evaluation of the Growth Model Pilot Project 3

spring, while the state-defined minimum n sizes for reporting groups range from a low of no 

minimum to 50 students. Second, the percentage of tested students scoring proficient or higher 

must meet or exceed the AMO in both subjects for eligible reporting groups. These percentages 

are calculated only for students enrolled for the full academic year. If a single subgroup fails to 

achieve the AMO, the school does not make AYP. 

In order to reduce the chances of incorrectly classifying schools as not making AYP, the states 

are allowed to apply additional steps within the status model. If any one or more of the ESEA

reporting groups did not make AYP, the school may:

• Apply confidence intervals to the group’s percent proficient and compare the upper 

bound to the AMO. Analogous to the sampling errors typically reported on results from 

political and other opinion polls based on random samples, a confidence interval 

represents the range of values within which the true value is expected to fall at a given 

level of statistical certainty. The higher the standard of certainty asked for, the wider the 

confidence interval. For a given standard of certainty, the smaller the number of 

students, the wider the confidence interval. If the higher limit of that confidence interval 

is greater than the AMO, then the subgroup is considered to make AYP.

• Average the test results for the group over two or three years and compare the average to 

the AMO (this is often referred to as “multiyear averaging”).

• Apply safe-harbor, whereby the group makes AYP if the percentage of non-proficient 

students in the group decreased by 10 percent or more from the prior year. 

• Apply safe-harbor but assess whether the reduction in the percentage non-proficient was 

10 percent or more from the average percent non-proficient over the prior two or three 

years.

This basic method of determining school AYP is used in all states and is referred to as the status 

model. A simplified version of the decision tree (excluding the full academic year, minimum n, 

confidence intervals, and multiyear averaging conditions) is illustrated in Exhibit 1.
Evaluation of the Growth Model Pilot Project 4

Exhibit 1

Determining AYP Under Status Model

Limitations of the status model

One characteristic of the status model is that it does not recognize real improvements in student 

achievement unless they result in higher percentages of students meeting or exceeding 

proficiency standards in a given year. Schools whose students are demonstrating learning gains, 

but whose gains overall fall short of the AMO standard will not be judged to be making adequate 

yearly progress. Conversely, schools whose students meet the AMO standard will be judged to 

be making AYP even if little is done to advance student achievement beyond that minimum 

proficiency target. 

The fact that schools either make AYP or not, with no credit given for improvement other than 

safe-harbor, has raised concerns that, in the short term, instructional resources may be focused on 

students who are closest to the proficiency threshold. Students less likely to attain proficiency 

from a given amount of instructional effort—e.g., those farthest below the proficiency 

threshold—may receive less attention. There is not a substantial amount of empirical research 

supporting this hypothesis and, in any case, this type of strategy becomes less relevant as AMOs 

converge on the target of universal proficiency by 2014. On the other side of the ledger, students 

unlikely to fall below proficiency may also receive less attention because there are no statutory

consequences for failing to improve achievement among proficient students. This possible 
Evaluation of the Growth Model Pilot Project 5

tendency is tied to the use of a minimum threshold and would thus not be affected by the 2014 

target.5

Another characteristic of the status model is that it does not take account of changes in a school’s 

student composition from one year to the next. Thus a school classified as not making AYP in 

one year could be judged to make AYP in the next if more proficient students enrolled or if lessproficient students left. Conversely, a school making AYP one year may not reach the AMO 

standard the following year if student composition shifted the other way. 

The Growth Model Pilot Project (GMPP)

The U.S. Department of Education (ED) initiated the Growth Model Pilot Project (GMPP) in 

November 2005 with the goal of approving up to 10 states to incorporate growth models in 

school AYP determinations under ESEA. Growth models are defined as complements or 

alternatives to the standard status model for determining school AYP; they base AYP on some 

measure of how much students have gained from one year to the next. 

Growth models are intended to recognize schools’ progress moving students toward proficiency. 

As suggested above, school-level student growth patterns may overlap or may diverge from the 

school-level assessments of students’ proficiency generated by the application of the status 

model; these are illustrated in Exhibit 2. Ideally, all schools would be in cell A, meeting the 

status requirements and realizing high rates of annual progress. The basic goal of the GMPP is 

to identify schools in cell B, that is, schools with high numbers of students making progress but 

not yet attaining the grade-level proficiency thresholds necessary to meet AYP standards. 

Schools in cell C—those with low rates of progress but still making AYP—are also of interest to 

the GMPP but, as will be discussed further at various points in this report, were not targeted in 

the project. For the ESEA as a whole, the overarching goal is to ensure that no schools are in cell 

D, not meeting the status model requirements and not making sufficient gains to be on-track to 

meet the requirements in the near future. 

Exhibit 2

Conceptual Map of How Growth Patterns Compare With

Status Model AYP Designations

Achievement Growth Pattern in the School

School AYP Designation Under the Status Model

Made AYP Did Not Make AYP

High rates of progress A B

Low rates of progress C D

 5 Research on the extent to which schools have adopted these sorts of strategies has been conducted by Naomi 

Chudowsky, Victor Chudowsky, and Nancy Kober (2009) “Is the Emphasis on "Proficiency" Shortchanging Higherand Lower-Achieving Students? Retrieved on July 30, 2009 from http://www.cepdc.org/index.cfm?fuseaction=document_ext.showDocumentByID&nodeID=1&DocumentID=280 ; Derek Neal and 

Diane Whitmore Schantzenbach (2008), “Left Behind By Design: Proficiency Counts and Test-Based 

Accountability” retrieved on September 26, 2008 from 

http://derek.a.neal.googlepages.com/restat_rev_final_200809.pdf ; and Jennifer Booher-Jennings (2005), “Below the 

Bubble: ‘Educational Triage’ and the Texas Accountability System,” American Educational Research Journal, 42:

231–268. 
Evaluation of the Growth Model Pilot Project 6

The U.S. Department of Education used a rigorous peer review process to evaluate the adequacy 

of the technical aspects of the proposed models and to ensure that the models aligned with seven 

core principles.6

The second principle stipulates that growth expectations cannot be based on student background 

or school characteristics. This is consistent with the ESEA rule that proficiency targets must be 

the same for all students in a given grade and cannot be modified for different kinds of students 

or schools. In the growth model context, this excludes use of models that would give AYP credit 

to schools or subgroups within schools strictly on the basis of realizing average or even higherthan-average annual growth rates. The key criterion is “meeting grade-level proficiency.” 

Students scoring below proficiency must not only gain more per year than one grade-level 

equivalency, but those gains must also point to attaining proficiency standards within a specified 

time frame.

 In general, these core principles required all pilot states to set annual “growth 

targets” for ensuring proficiency by 2014 and to track individual students across schools and 

measure their progress across grades in both reading and mathematics. The first principle 

requires that the growth model, like the status model, be applied to each targeted subgroup as 

well as all students in the school. This means that growth outcomes are to be monitored 

separately, or “disaggregated,” for the main racial and ethnic groups, limited English proficient 

(LEP) students, special education students, and low-income students. 

7

 6 See U.S. Department of Education (Nov. 18, 2005) “Press Release: Secretary Spellings Announces Growth Model 

Pilot, Addresses Chief State School Officers’ Annual Policy Forum in Richmond” (retrieved May 2008 from 

http://www.ed.gov/news/pressreleases/2005/11/11182005.html), and U.S. Department of Education (July 2007) “No 

Child Left Behind: Growth Models—Ensuring Grade-Level Proficiency for All Students by 2014” (retrieved May 

2008 from http://www.ed.gov/admins/lead/account/growthmodel/proficiency.pdf ).

 A full list of the seven core principles of the Growth Model Pilot Project is 

provided in Exhibit 3.

7 This guiding principle precludes the use of growth models referred to as “value added” models (VAM), at least 

when they include statistical adjustments for student social background variables or school characteristics. In general 

terms, value-added formulations seek to separate the impacts of various factors on student growth in order to make 

attributions about the marginal effectiveness of the factors on achievement gains. Inputs are variously defined, 

depending on the purpose of the analysis, but often include student social background variables, teachers, and 

instructional programs. If used for evaluation of schools, value-added models estimate growth for a common 

“average type” of student in each school and the schools are then compared in terms of that backgroundstandardized estimate. In that sense, VAM are typically measures of relative school effectiveness, not absolute 

student proficiency. The latter is the purpose of GMPP, and VAM are generally inappropriate for that purpose.
Evaluation of the Growth Model Pilot Project 7

Exhibit 3

Seven Core Principles of the Growth Model Pilot Project

States approved for participation in the GMPP were required to meet seven core principles in the ESEA

accountability plans they submitted for incorporating growth models in their AYP measurements:

1. Ensure that all students are proficient by 2014, and set annual goals to ensure that the achievement gap is 

closing for all groups of students;

2. Set expectations for annual achievement based on meeting grade-level proficiency, not on student 

background or school characteristics; 

3. Hold schools accountable for student achievement in reading or language arts and mathematics;

4. Ensure that all students in tested grades are included in the assessment and accountability system, hold 

schools and districts accountable for the performance of each student subgroup, and include all schools and 

districts; 

5. Include assessments in each of grades 3–8 and in high school for both reading or language arts and 

mathematics, and ensure that they have been operational for more than one year and receive approval 

through the NCLB peer review process. The assessment system must also produce comparable results from 

grade to grade and year to year; 

6. Track student progress as part of the state data system; and 

7. Include student participation rates and student achievement on a separate academic indicator in the state 

accountability system.

Source: See “Peer Review Guidance for the NCLB Growth Model Pilot Applications” (retrieved May 2008 from 

http://www.ed.gov/policy/elsec/guid/growthmodelguidance.pdf).

Other significant features of pilot growth models were allowed to vary, as long as the technical 

specifications passed review by a panel of nationally recognized experts.8

Of the 20 states that submitted proposals by February 2006, 13 asked for approval to use growth 

models for immediate use in the 2005–06 school year while the others proposed to start in 

2006–07. Eight of these proposals passed the initial evaluation, and revised proposals were 

forwarded to the peer reviewers.

 Reviewers had a 

series of meetings to discuss the Peer Review Guidance document and the Department’s 

expectations for the process. Proposals that passed an initial review by Department staff and a 

round of clarification by states were forwarded to the peer reviewers. The Department then set 

up conference calls between the states and the peer review team, after which the reviewers met 

again to discuss the proposals and make recommendations for use by the secretary in deciding 

which proposals to approve for the pilot project. 

9

 8 See “Peer Review Guidance for the NCLB Growth Model Pilot Applications” (retrieved May 2008 from 

http://www.ed.gov/policy/elsec/guid/growthmodelguidance.pdf).

 Two states, North Carolina and Tennessee, received approval 

to use growth models for 2005–06, while Delaware, Arkansas, and Florida revised their 

9 These reviewers included Eric Hanushek, Stanford University, Chris Schatschneider, Florida State University, 

David Francis, University of Houston, Margaret Goertz, University of Pennsylvania, Kati Haycock, The Education 

Trust, William Taylor, Citizens Commission on Civil Rights, Sharon Lewis, Council of Great City Schools (retired), 

Robert Mendro, Dallas Independent School District, Jeff Nellhaus, Massachusetts Department of Education, and 

Mitchell Chester, then at the Ohio Department of Education.
Evaluation of the Growth Model Pilot Project 8

proposals and were approved in a subsequent peer review to implement their proposed models 

for the following school year (2006–07). A second round of proposals was solicited in October 

2006. Six previous applicants submitted revised proposals along with submissions from three 

new states.10 Of these, Alaska, Arizona, and Iowa received immediate or conditional approval to 

use their growth models beginning with the 2006–07 school year, while Ohio was approved to 

begin in the 2007–08 school year.

11

The approved pilot states were all required to calculate whether each student in the target grade 

levels was on-track to be proficient within a specified number of years or by a particular grade 

level. Students who were on-track to be proficient could be counted as proficient for purposes of 

AYP determinations. However, the states were given a variety of options on how to incorporate

the student growth indicator in their AYP determinations.12

• only the growth measure to calculate the percentage on-track to proficiency for AMO 

assessment;

These included using:

• both the status and the growth measures to calculate the percentage proficient or on-track

for AMO assessment;

• the status measure to calculate the percentage proficient, applying safe-harbor provisions

if needed, and using the growth measure either in conjunction with the status measure or 

alone if AYP not met with safe-harbor; and

• safe-harbor provisions and the growth measure for AMO assessment.

While the approved models differ from one another in a number of important ways, all use statespecific assessment data to measure student progress and proficiency, and the method of 

incorporating growth outcomes in AYP determinations was generally the same. Seven of the 

eight pilot states proposed to apply growth criteria only after schools failed to make AYP under 

the status and safe-harbor provisions rather than determining AYP solely on the basis of student 

improvement. More specifically, the designs of the pilots in these seven states applied growth 

criteria only to those students who were members of ESEA reporting groups that did not reach 

their AMOs or attain AYP via safe-harbor provisions. This basic method of augmenting status 

 10 See “Secretary Spellings Approves Additional Growth Model Pilots for 2006–2007” retrieved June 2008 from 

http://www.ed.gov/news/pressreleases/2006/11/11092006a.html). This panel of reviewers included Anthony Bryk, 

Stanford University, Harold Doran, American Institutes for Research, Chrys Dougherty, National Center for 

Educational Accountability, Lou Fabrizio, North Carolina Department of Public Instruction, Tom Fisher, 

Independent Consultant, Pete Goldschmidt, University of California at Los Angeles, Sharon Lewis, Council of Great 

City Schools (retired), Margaret McLaughlin, University of Maryland, Robert Mendro, Dallas Independent School 

District, Jeff Nellhaus, Massachusetts Department of Education, Ann O’Connell, University of Connecticut, Dianne 

Piché, Citizens Commission on Civil Rights, Sandy Sanford, Riverside County Office of Education, Chris 

Schatschneider, Florida State University, William Taylor, Citizens Commission on Civil Rights, and Martha 

Thurlow, University of Minnesota.

11 In December 2007, the Department moved to expand participation in the growth model project and extended an 

invitation to all states to apply for inclusion. At the time of writing, 15 states have been approved to implement 

growth models in AYP determinations.

12 See “Peer Review Guidance for the NCLB Growth Model Pilot Applications” (retrieved May 2008 from 

http://www.ed.gov/policy/elsec/guid/growthmodelguidance.pdf)
Evaluation of the Growth Model Pilot Project 9

with growth results is shown in Exhibit 4 (again, this is a simplification in that provisions for 

using confidence intervals and multiyear averaging prior to applying growth results are not 

represented).

Exhibit 4

Determining AYP Under Status, Safe-Harbor, and Growth

Delaware adopted a different order, applying growth first and then applying status and safeharbor only to schools and subgroups that did not meet AYP under the growth criteria. This 

procedure thus classified schools as making AYP by growth even if they also would have made 

AYP by status or safe-harbor criteria. In contrast, schools in the other states were identified as 

making AYP by growth only in cases in which AYP was not met by status or safe-harbor.

Types of growth models implemented in the pilot

The states approved for the pilot study proposed to employ either a status-augmented-withgrowth or (in Delaware) a growth-augmented-with-status method of determining AYP, but the 

models used by the pilot states varied in how they established growth targets that define whether 

individual students were “on-track” to reach proficiency in the allotted time frame. We have 

identified three basic types of growth models being used in the GMPP: the transition matrix

model, the trajectory model, and the projection model.

13

 13 See the CCSSO’s Implementer’s Guide to Growth Models for an alternative, more extensive, typology of growth 

models (retrieved May 2008 from http://www.ccsso.org/content/pdfs/IGG%20Final%20AP.pdf).
Evaluation of the Growth Model Pilot Project 10

Transition Matrix. 

An illustration of the transition matrix model used in Iowa is shown in Exhibit 5. Students who 

scored below the proficiency threshold in year 1 (the first three rows) were classified as “ontrack” to proficiency if their test performances improved enough in year 2 to move up at least 

one level. All students who were proficient or advanced in year 1 and who were proficient or 

advanced in year 2 were classified as on-track. For the purpose of determining AYP, the Iowa

model counted students who were on-track toward proficiency as being fully proficient. All 

students in the gray-shaded cells are not on-track and do not count as proficient for AYP 

purposes.

This type of model evaluates student progress from year to year in terms of a 

relatively small set of discrete performance levels. The levels are defined in general terms that 

are applied to all grades (e.g., below proficient, proficient, advanced). Student growth is indexed 

by movement (“transitions”) from lower to higher categories. Delaware and Iowa used models 

of this type.

Exhibit 5

Illustration of How the Iowa Transition Matrix Model Classifies Students

Year 1 

Performance 

Level

Year 2 Performance Level

Weak Low Marginal High Marginal Proficient Advanced

Weak Off-track On-track On-track On-track On-track

Low marginal Off-track Off-track On-track On-track On-track

High marginal Off-track Off-track Off-track On-track On-track

Proficient Off-track Off-track Off-track On-track On-track

Advanced Off-track Off-track Off-track On-track On-track

Delaware used a somewhat different type of transition matrix model; it is illustrated in Exhibit 6. 

It used a point system that gave a maximum of 300 points to all students who attained 

proficiency in year 2 but gave only partial credit to students who scored below proficiency in 

year 1 and who made gains but did not reach the proficiency standard in year 2. Students who 

scored below the proficiency threshold in year 1 and did not move up to a sufficiently higher 

level in year 2 (the gray-shaded cells) were assigned no points for determining AYP. Points 

were summed within subgroups and divided by the number of students in each subgroup to 

calculate an “average growth value” which was compared to annual growth targets. 
Evaluation of the Growth Model Pilot Project 11

Exhibit 6

Illustration of How the Delaware Transition Matrix Model

Assigns Points to Students’ Gains

Year 1 Performance Level

Year 2 Performance Level

PL 1A PL 1B PL 2A PL 2B PL 3, 4, and 5

PL 1A: lowest level below 

proficiency 0 150 225 250 300

PL 1B 0 0 175 225 300

PL 2A 0 0 0 200 300

PL 2B: highest level below 

proficiency 0 0 0 0 300

PL 3, 4, and 5:

Proficient or higher 0 0 0 0 300

Trajectory. 

An example of a trajectory model is shown in Exhibit 7. The Y axis represents student 

achievement on a vertically aligned scale, and the X axis represents successive grades. The large 

solid dots indicate the level of achievement necessary to be considered proficient at each time 

point (“p1” for proficiency at time 1, “p2” for proficiency at time 2, and “p3” for proficiency at 

time 3). The hollow dots represent a student’s actual achievement at time points 1 and 2, marked 

“s1” and “s2” respectively. 

This type of model uses the gap between a student’s baseline test score and a 

performance standard several years out to calculate the amount of growth he or she must attain to 

become proficient. This performance “trajectory” is divided up into annual growth targets that, 

taken together, put the student on-track to proficiency within the allotted years. Alaska, Arizona, 

Arkansas, Florida, and North Carolina used trajectory models.
Evaluation of the Growth Model Pilot Project 12

Exhibit 7

Illustration of How Trajectory Models Set Targets for

Students Scoring Below Proficiency Thresholds

At grade 3, the student is not considered proficient because his or her achievement (at level “d”

on the Y axis) is lower than what is necessary at that time (level “c”). Under a trajectory model, 

each student has a growth target that must be met to be considered “on-track” and count as 

proficient. In the illustration above, this is done by drawing a line from the student’s 

achievement at grade 3 (“s1”) to the proficiency point for grade 5 (“p3”). This line intersects 

point “s2” at grade 4, indicating that “s2” is what the student must achieve in grade 4 to be 

considered “on-track” to proficiency. The level of achievement targeted by the trajectory model 

is lower than what is expected under the status model. Under the status model, a student must 

have a level of achievement at or above point “p2”. 

This illustration shows that trajectory models allow students to score below the proficiency 

thresholds between the year they first miss proficiency (“s1”) and the year when they must be 

proficient under status criteria (“p3”). Because expected growth is based on a trajectory from the 

student’s initial achievement and the target year, trajectory models distribute the growth required 

to meet status expectations among the intervening years. Finally, while this illustration used a 

linear trajectory, some states, such as Arkansas, use a nonlinear method to calculate growth 

targets. 

Projection. This type of model uses current and past test scores to statistically predict 

performance several years ahead based on how all students in the state or school with similar 

patterns of scores generally perform. Such “projections” utilize multiple test scores to estimate a 

prediction equation using multiple regression techniques and use that equation to predict how 

each student will score at the end of the time frame. If that predicted score is equal to or greater 
Evaluation of the Growth Model Pilot Project 13

than the proficiency cut point, the student is classified as on-track to proficiency. Ohio (starting 

in 2007–08) and Tennessee are using projection models.

Exhibit 8 illustrates a simple projection model. The projection model determines a projected 

level of achievement for a future time point for each student. Depending on the specifics of a 

state’s model, students who do not make the proficiency threshold under a status model at grade 

5 may still be counted as proficient if the projection model predicts that they will make 

proficiency by grade 6. Like the trajectory model illustration, the Y axis represents student 

achievement on some vertical scale. The X axis represents grades. Again, the solid dots 

represent grade-level proficiency thresholds at grades 3 (p1) through 6 (p4), and the hollow dots 

represent a student’s achievement over consecutive grades. The solid line represents the 

projection equation based on the current and past data for that student (points “s1” through “s3”). 

Though illustrated here with data for just one student, both the Ohio and Tennessee models 

estimate this projection equation from a regression analysis of current and past data for all 

students in the school so that the projection represents statistically expected scores for students 

similar to the focal student. The dotted line is the extension of that projection equation to a 

future time point specified by the state’s growth model.

Under a status model, a student who reached the level of “s3” would not be considered proficient 

at grade 5, because her score is lower than that of point “p3”. However, under a growth model 

using projections based on student data, that student would be considered “on-track” because her

projected score qualifies as proficient at grade 6 (the dotted line is above “p4” in the figure). 
Evaluation of the Growth Model Pilot Project 14

Exhibit 8

Illustration of How Projection Models Evaluate

Students Scoring Below Proficiency Thresholds

Exhibit 9 presents each pilot state’s growth model organized by type of model used and provides 

brief model summaries along dimensions that may affect final AYP outcomes. These include

which grades receive growth calculations, how many years of growth are allowed, what tests are 

used to measure achievement, the standards applied for determining adequate yearly growth, and 

the growth required for students to be recognized as “on-track-to-proficiency” and therefore 

counted positively for school AYP determinations. More detailed information about the 

technical features of each model can be found in the growth model summaries appended to this 

report (Appendix A).
Evaluation of the Growth Model Pilot Program 15

Exhibit 9

Overview of Growth Models Approved for the GMPP in the 2006–07 School Year

State

Type of 

Model

First Year 

Used

Grades 

Included

Minimum 

Subgroup

Size

Years to 

Proficient

Achievement Measures 

Used Growth Standards Applied

Student On-Track-toProficiency Determined

Delaware Transition 

Matrix

2006–07 3–10 40 N/A Scale scores for reading 

and math via the 

Delaware Student 

Testing Program

Four levels of “below the 

standard” are used to 

categorize non-proficient 

students 

Points are awarded for 

proficiency and for 

movement to higher levels 

of below proficient and 

are then averaged to 

make AYP determinations 

Iowa Transition 

Matrix

2006–07 4–8 30 4 Scale scores based on 

biannual Iowa Test of 

Basic Skills (ITBS) math 

and reading results

Three categories of 

performance are used to 

classify non-proficient 

students

Students who move to a 

higher category of nonproficiency make 

Adequate Yearly Growth 

(AYG) and are counted as 

proficient for AYP 

determinations

Alaska Trajectory 2006–07 4–9 25 4 Adjusted scale scores 

for math and language 

arts (reading + writing) 

on the Standards Based 

Assessment (SBA) Test

Annual growth targets for 

each student are based 

on the test score gains 

needed to reach 

proficiency in four years 

or by tenth grade. Each 

student’s targets are 

reset every year to reflect 

his or her latest score.

Students who close the 

score gap by one-fourth, 

one-third, and one-half

annually (depending on

the distance from target 

year) are “on-track” to 

reach proficiency and are 

counted as proficient for 

AYP determinations

Arizona Trajectory 2006–07 4–7 40 3 Scale scores for math 

and reading on the 

Arizona Instrument to 

Measure Standards 

(AIMS) tests

Growth targets are set 

using the increment in 

base year score needed 

to reach proficiency in 

three years or by eighth 

grade

Students who test “below 

the standard” but are 

estimated to meet their 

growth targets are 

counted as proficient for 

AYP determinations

Exhibit 9, continues next page
Evaluation of the Growth Model Pilot Program 16

Exhibit 9

Overview of Growth Models Approved for the GMPP in the 2006–07 School Year

continued from previous page

State

Type of 

Model

First Year 

Used

Grades 

Included

Minimum 

Subgroup

Size

Years to 

Proficient

Achievement Measures 

Used Growth Standards Applied

Student On-Track-toProficiency Determined

Arkansas Trajectory 2006–07 4–7 40 4 Scale scores for literacy 

and math on the 

Arkansas Benchmark

Exams

Growth targets are set 

using the annual 

increment in current test 

score needed to reach 

proficiency by eighth 

grade

Non-proficient students 

meeting their growth 

targets are counted as 

proficient for AYP 

determinations

Florida Trajectory 2006–07 3–10 30 3 Developmental Scale 

Scores (DSS) for math 

and reading on the 

Florida Comprehensive 

Assessment Test 

(FCAT)

Growth targets are based 

on the gap between initial 

score and proficiency 

cutoffs three years later

Students who close the 

original gap by one-third 

(one-half for ninthgraders) annually are 

counted as proficient for 

AYP determinations

North 

Carolina

Trajectory 2005–06 3–7 40 4 Scale scores on third 

grade pretest and/or 

annual North Carolina 

End-of-Grade Math and 

Reading Tests

Growth targets are based 

on closing the gap 

between baseline test 

score and proficiency 

cutoff in four years or by 

eighth grade

Students who close the 

test score gap by onefourth each year meet 

growth targets and are 

counted as proficient for 

AYP determinations

Tennessee Projection 2005–06 4–8 45 4 Scale scores for math 

and reading/

language arts from the 

Tennessee 

Comprehensive 

Assessment Program 

(TCAP)

Proficiency standards for 

each grade are based on 

cutoffs for proficiency 

three years later using 

test results on the TCAP 

starting in 2002–03

Students with predicted 

scores above the cutoff, 

using regression methods 

to calculate predicted 

scores, are counted as 

proficient for AYP 

determinations
Evaluation of the Growth Model Pilot Project 17

How growth models are used for AYP determinations

The pilot states used the student-level indicators of on-track-to-proficiency generated by the 

GMPP growth models to augment the status indicators of proficiency in order to make AYP 

determinations for their schools. An overview of how the growth models’ on-track-toproficiency data fit into the overall scheme in most of the eight pilot states is shown in Exhibit 

10. This exhibit resembles a checklist, showing all the criteria that must be met in order to make 

AYP and (at the bottom of the table) how schools are classified in terms of making AYP. 

The key point is that when a school is designated as “making AYP under growth,” it means that 

use of the growth model changed the designation for one or more targeted subgroups. Further, 

within the affected subgroups for a given school, the growth criterion is usually applied only to 

the students who did not achieve at or above the proficiency level. Simply stated, “making AYP 

under growth” does not mean that all students are on-track to proficiency, and it can mean as few

as one non-proficient student is on-track if a sufficient number of others in the subgroup are 

proficient.

Seven of the eight states with data available for 2006–07 used the status-and-safe-harboraugmented-with-growth methodology shown in Exhibit 10. In contrast, Delaware used a 

growth-augmented-with-status-and-safe-harbor method for determining AYP, and many of the 

schools listed as making AYP under growth would also have made AYP under status. As 

discussed more fully in Chapter II, the particular type of growth model used in Delaware actually 

functioned similarly to the other states’ models in terms of classifying students as proficient, ontrack to proficiency, and not on-track. 
Evaluation of the Growth Model Pilot Project 18

Exhibit 10

Overview of How Schools Are Classified as Making AYP

Under the Status Augmented With Growth System

ESEA Outcomes

Exempt by 

Minimum N 

Criterion?

Met AMO by 

Status? 

(Applies Only 

if “Exempt” is 

No)

Met AYP by 

Safe-Harbor? 

(Applies Only if 

“Met by Status”

is No)

Met AMO by 

Growth? (Applies

Only if “Met by 

Safe-Harbor” is No)

Reading or Language Arts

All students Not Applicable Y/N Y/N Y/N

Asian Y/N Y/N Y/N Y/N

American Indian Y/N Y/N Y/N Y/N

Black Y/N Y/N Y/N Y/N

Hispanic Y/N Y/N Y/N Y/N

White Y/N Y/N Y/N Y/N

LEP Y/N Y/N Y/N Y/N

Low income Y/N Y/N Y/N Y/N

Students w/ disabilities Y/N Y/N Y/N Y/N

Mathematics

All students Not Applicable Y/N Y/N Y/N

Asian Y/N Y/N Y/N Y/N

American Indian Y/N Y/N Y/N Y/N

Black Y/N Y/N Y/N Y/N

Hispanic Y/N Y/N Y/N Y/N

White Y/N Y/N Y/N Y/N

LEP Y/N Y/N Y/N Y/N

Low income Y/N Y/N Y/N Y/N

Students w/ disabilities Y/N Y/N Y/N Y/N

Other Academic Indicator

(e.g., Average Daily

Attendance)

Not Applicable Y/N Not Applicable Not Applicable

School AYP Classification School still 

receives AYP 

classification 

from status, 

safe-harbor, or 

growth based 

on the “all 

students”

group even if 

all subgroups 

are exempt. 

“By status” if 

all except 

exempt 

groups are 

Yes

“By safe-harbor”

if one or more 

are Yes and the 

rest are Yes by 

status or exempt

“By growth” if one or 

more are Yes and 

the rest are Yes 

either by safeharbor or status or 

exempt
Evaluation of the Growth Model Pilot Project 19

Data sources and availability

Data employed for the analyses in this report were provided by the U.S. Department of 

Education and the pilot grantee states. The data from the Department were extracted from the 

EDFacts database. EDFacts is the main repository for school, district, and state data on ESEA

requirements related to making AYP determinations, as well as enrollment and demographic 

data. All states are required to submit standard data elements on all their districts and K-12 

schools each year to EDFacts. For the 2006–07 school-year data that are the focus of this report, 

the standard reporting variable on whether the school made AYP was modified to collect 

information on whether each school made AYP because of the growth model. This variable was 

defined in EDFacts with a set of mutually exclusive categories: “made AYP by regular 

determination,” “made AYP by growth,” or “did not make AYP.”

The “made AYP by regular determination” category included all methods of making AYP except 

by growth criteria. The main methods included regular status criteria, status with confidence 

intervals, status with multiyear averaging, and safe-harbor. Use of confidence intervals and 

multiyear averaging were not reported in EDFacts, but safe-harbor was reported with respect to 

subgroup AMO results for reading and mathematics. The standard EDFacts reporting variable 

for AMO results included the mutually exclusive categories of “met by status,” “met by safeharbor,” “exempt by minimum n,” and “did not meet” for each subject area. For purposes of this 

report, schools were classified as “made AYP by safe-harbor” if one or more subgroups were 

classified in EDFacts as “met by safe-harbor” for either the reading or mathematics AMO.

The eight GMPP states approved for 2006–07 school year were additionally required as a 

condition for continued participation in the pilot to collect and make available for evaluation 

purposes data on results of using their approved growth models. The data obtained directly from 

the pilot states consisted of scale scores and proficiency designations in reading or language arts 

and mathematics for each student in the grades involved in the GMPP. Of particular importance 

to this study were the proficiency designations, for these included the indicator of whether the 

student was “on-track” to achieve proficiency within the time frame specified by the approved 

growth model. Additional data elements included various background characteristics including 

school identifier codes, grade level of current enrollment, and ESEA subgroup memberships.

Five of the eight states had provided both the EDFacts and student-level data required to address 

the two study questions which are the focus of this interim report. The other three states 

(Arizona, North Carolina, and Tennessee) had not reported GMPP results to the EDFacts archive 

but provided school-level indicators of which schools were classified as having made AYP by 

growth in 2006–07. 

Calculation of hypothetical growth-only percentages on-track to proficiency

As noted above, states had the options of making AYP determinations using (a) only growth 

results and (b) growth criteria before status and safe-harbor criteria. While these options were 

generally not exercised, it is possible to estimate what would happen if they had been. That 

information may prove useful to states in the process of developing growth models, as well as 

current pilot states contemplating changes to their models. Toward that end, a number of 

hypothetical “what if” questions are addressed in Chapter IV using the indicators of whether 
Evaluation of the Growth Model Pilot Project 20

students are on-track to proficiency. These data are used to calculate the percentages of on-track 

students in reading and mathematics for each ESEA subgroup in each school, and these 

percentages are compared to the state’s “annual measurable objectives,” or AMOs. These results 

are then used to assess the extent to which schools currently making AYP by status and safeharbor would be able to reach their AMOs using growth-only percentages of students on-track to 

proficiency.

Data limitations

The data described above have a number of limitations that are important to note at the outset 

and which will be reiterated at various points in this report. First, the EDFacts data for 2006–07 

only reported growth-model results in terms of how each school was classified for AYP 

reporting. EDFacts did not identify which ESEA reporting groups (all students and the eight 

subgroups) made their AMOs for reading or mathematics by growth. 

As noted above, both the school AYP and subgroup AMO results were defined in EDFacts with 

a set of mutually exclusive categories. It was not possible to determine from these data, for the 

schools classified as having made AYP by growth, whether particular subgroups made their 

AMOs as a result of the GMPP growth provisions. An additional category of “met by growth” 

was added to subgroup AMO reports beginning in 2007–08 and this should overcome the 

limitation.

A second limitation is that the mutually exclusive AYP categories reported by EDFacts made it 

impossible to determine the extent to which schools that made AYP under status and safe-harbor

would also have made AYP if only growth criteria were considered. The student-level on-trackto-proficiency indicators described in the preceding subsection can be used to calculate growthbased AMO determinations for each ESEA reporting group and for the school as a whole. 

However, it should be emphasized that these growth-based AMO determinations are based solely 

on information regarding students’ reading or language arts and mathematics performances and 

do not necessarily indicate whether a school would make AYP under a growth-only system. 

Under ESEA, schools must also meet additional conditions to make AYP. These conditions 

include the requirements that the school (a) meet or exceed a minimum level on an “other 

academic indicator,” typically average daily attendance for elementary and middle schools; and 

(b) realize at least a 95 percent participation rate on the annual assessments. We were unable to 

consider these criteria in our calculations because the requisite data were not available. (The 

“other academic indicator data” are school-level determinations that were not provided in the 

student files and were unevenly reported in EDFacts. The student files from some states also did 

not include the information needed to calculate participation rates.14

 14 Participation rates are calculated on the basis of students enrolled for the “full academic year” (FAY), but FAY 

and non-FAY students were not distinguished in some of the state data files. And some states were only able to 

provide student data on students with test results from both 2005–06 and 2006–07 (i.e., students for whom growth 

could be calculated). The FAY indicators as well as test score data and results for all current students (not just the 

ones with prior-year test scores) are being requested for the final report, which will analyze the 2007–08 school year 

results. 

) This means that some 
Evaluation of the Growth Model Pilot Project 21

schools meeting the AMO on the achievement outcomes using the growth criteria identified in 

this report may have officially missed AYP on the additional criteria.15

Given the potential discrepancies between the growth-based AMO designations and the official 

ESEA designations, the results presented in Chapter IV of this report should be regarded as 

suggestive rather than definitive. With that caveat, these comparisons allow an assessment of the 

extent to which schools making AYP by status or safe-harbor criteria might also have made AYP 

if only growth criteria were used.

 15 The number of such “false positives” is probably small. National data from 2003–04 show that about 3 percent of 

all schools did not make AYP solely because of not making acceptable levels on the other academic indicator or low 

(below 95 percent) participation rates for the achievement testing (U.S. Department of Education, 2007, p. 43.)
Evaluation of the Growth Model Pilot Project 22
Evaluation of the Growth Model Pilot Project 23

II. Effects of Growth Models

Implemented Under the GMPP on School AYP Determinations

The data available from the 2006–07 school year allow for a variety of analyses that address the 

guiding research questions. Before examining the data, it is useful to provide more detail on how 

the approved growth models in general, and each pilot state’s model in particular, fit into the 

accountability framework of ESEA. This chapter provides an overview of how test results (in 

reading or language arts, mathematics, and other subjects) and other criteria are used to make 

school AYP determinations, and how student-level data from the growth models fit into those 

decisions. While each state has a model that is unique in important ways, the approved models 

generally group into three types. Recognizing key distinguishing features of these three basic 

approaches is helpful both in clarifying the details of each state’s model and understanding the 

results it produces. 

This chapter presents overviews of models implemented in the eight pilot states, focusing on the 

methods they employ to (1) set expectations, (2) measure growth, and (3) incorporate these 

growth results into their AYP determinations. These summaries are based on a review of extant 

documentation, including the approved GMPP proposals, decision letters from the U.S. 

Department of Education, and correspondence with the Department concerning feedback and 

suggested revisions from the peer review panels; growth model descriptions found in state 

accountability workbooks, school report cards, and other online technical documentation; and 

edits by state officials to draft model summaries provided to each pilot state at a December 2008 

summit meeting in Washington, D.C. Any inconsistencies in model summaries were then 

resolved through e-mail correspondence and follow-up phone calls with state officials over the 

course of the evaluation. More detailed technical summaries of the states’ growth models are 

included in Appendix B.

Following the overview of each state’s model, we present data on the impact of the growth 

model on AYP outcomes. These analyses address the research question “How many schools 

made AYP under the growth model that would not have made it under the ESEA status model?” 

This question can be answered for all states except Delaware by analyzing data reported by states 

to the federal EDFacts system plus (in three of the states) additional information from the state 

departments of education on which schools made AYP by growth; as discussed below in the 

section focused on the Delaware model, the Delaware Department of Education provided the 

additional data required to address this question for that state.

State growth models and their effects on schoolwide AYP results

The eight states approved for the GMPP in the 2006–07 school year provided data on the results 

of their pilot growth models to the EDFacts system. It is these eight states, then, which are the 

subject of this interim report, and we summarize here the key features of these eight pilot grantee 

states’ growth models. 

Alaska’s growth model

Alaska was formally accepted into the Growth Model Pilot Project on July 3, 2007. Alaska’s 

growth model includes fourth- through ninth-graders only, with all other students expected to be 
Evaluation of the Growth Model Pilot Project 24

proficient under the status model criteria. The growth model defines targets for each student at 

each grade based on the student’s scores on the Standards Based Assessment (SBA) tests for 

mathematics and language arts. The SBA test was first given in the 2004–05 school year to 

students in grades 3–9. The SBA is scaled such that students in every grade must score 300 or 

above to be considered proficient in math and a combined reading and writing score of 600 or 

above to be considered proficient in language arts.16

Starting in the 2006–07 school year, fourth- through sixth-grade students scoring below the 

proficiency cutoff were counted as proficient for AYP purposes if they were on-track to reach 

proficiency by the seventh grade, and eighth- and ninth-graders were counted as proficient if 

they were on-track to reach proficiency by the tenth grade. Students are always classified only 

by the status model in grades 3 and 7. Annual growth targets for all fourth-, fifth-, sixth-, 

eighth-, and ninth-graders who scored below proficiency were set by dividing the difference 

between the student’s “baseline” test scores and the proficiency cutoffs (300 in math and 600 in 

language arts) by the number of years allowed. 

The baseline scores were defined as those from the first year the student scored below the 

proficiency cutoff. For students in grades 4 and 5 in the 2006–07 school year, this could go back 

to the third grade. The baseline score for sixth-graders in 2006–07 could go back to the fourth

grade (i.e., to 2004–05 when the SBA was first administered). Concretely, for fourth-grade 

students who scored below proficiency in both the third and fourth grades, the baseline is the 

third-grade score. For fifth-grade students who scored below proficiency in the third and fourth

grades, their third-grade scores would also be the baselines used to define their trajectories to 

proficiency by grade 7. The baseline for students in grades 8 and 9 who score below proficiency 

can go back to seventh grade.

Thus a third-grade student who scored below proficiency has four years of allowable growth and 

must make up one-quarter of the gap between adjusted score and proficiency cutoff in the first 

year, one-third of this proficiency gap the second year, one-half of the gap the third year, and 

must score at or above the cutoff the fourth year in order to be counted as proficient for AYP 

determinations. Similarly, a seventh-grader scoring below proficiency must close the gap by onethird in grade 8 and by half in grade 9.

17

The Alaska growth model only applies to students who score below proficient on the SBA in 

their first year of eligibility. This means that students achieving a proficient score in the third

through eighth grades but scoring below the cutoff in following years are not eligible for the 

growth model. Students who change schools or districts carry their baseline score with them.

The Alaska growth model uses a “status-plus-growth” method for determining whether reporting 

groups meet the AMOs for language arts and mathematics. That is, first, the reporting group is 

assessed in terms of the percentage of students who scored at or above proficiency. If that 

 16 Alaska estimates a “true score” for the SBA by adjusting for the annual reliability of the tests. This has the effect 

of raising scores that are below average. The estimated true score is calculated by subtracting an estimated “reliable 

deviation” of the student’s observed score from the statewide average for students in the same grade.

17 Note that a ninth-grader must close the proficiency gap by 100 percent by the tenth grade, meaning that the 

growth model is equivalent to the status model for all ninth-graders who score below proficiency.
Evaluation of the Growth Model Pilot Project 25

percentage met the AMO, the group was classified as “met by status.” If the percentage did not 

meet the AMO but the percentage not proficient was 10 percent or more less than the percentage 

not proficient in the prior year, the group was classified as “met by safe-harbor.” If the group did

not meet the AMO by status or pass by safe-harbor, then the number of below-proficient students 

who are on-track to proficiency was added to the number of proficient students and this sum was

divided by the total number of students in the reporting group who took the test. If this 

percentage met the AMO, the group was classified as “met by growth.” If one or more reporting 

groups met by growth and the other AYP criteria noted below were also met, the school as a 

whole was classified as “made AYP by growth.”

Alaska’s ESEA accountability rules require a reporting subgroup to have more than 25 students 

before it is included in school AYP determinations. Subgroups larger than 40 students will count 

only if 95 percent of them participate in testing, while smaller subgroups require that no more 

than two students fail to participate. Schools with students and subgroups who meet the AMO 

within a 99 percent confidence interval, which varies by school size, are determined to have 

made AYP.

The AYP results for Alaska in 2006–07 are shown in Exhibit 11. Of the 323 schools that met 

AYP requirements for that year, representing 66 percent of all eligible schools, no school made 

AYP via the state’s pilot growth model.

Exhibit 11

Alaska School AYP Determinations With Status and Safe-Harbor Results Augmented 

With Growth Model Results, 2006–07

School AYP Under Status-PlusGrowth Model Number Percent

Met with Status 323 66%

Met with Safe-Harbor 0 0%

Met with Growth 0 0%

Not Met 169 34%

All Eligible Schools 492 100%

Exhibit reads: For Alaska’s schools overall, 323 met AYP under status, which was 66 percent of all eligible 

schools.

Source: U.S. Department of Education, EDFacts.

Arizona’s growth model

Arizona’s participation in GMPP was approved on July 3, 2007, for use beginning in the 

2006–07 school year. The Arizona growth model includes students in grades 4 through 7 and 

uses scores on the Arizona Instrument to Measure Standards (AIMS) tests for reading and 

mathematics, which is vertically scaled for grades 3 through 8. Proficiency levels are set for 

each grade, and a student scoring “below the standard” for either reading or math has three years 

to reach the cutoff or by eighth grade, whichever comes first. Growth targets are set by dividing 

the difference between initial score and proficiency cutoff three grades later into equal parts. In 
Evaluation of the Growth Model Pilot Project 26

order to be counted as proficient for AYP purposes, a student in grades 3 through 5 must make 

up one third of the shortfall in each of the next three years. A sixth-grader must cover half of the 

shortfall in each of the two years of eligibility remaining.18

For the purposes of its growth model, Arizona adjusts AIMS scores using past scores to correct 

for improvement that might be due to chance. These “predicted” scores are then subject to a 95

percent confidence interval, so that a score just below the growth target can still be counted as 

proficient if it is within the range of statistical error due to the prediction itself. The state also 

uses a 99 percent confidence interval around annual AMOs for AYP determinations.

Students who leave the Arizona 

school system before reaching proficiency have new growth targets set upon their return.

19

Arizona applied the results of the growth model after applying status and safe-harbor criteria. 

Growth model results were only applied to ESEA reporting groups that did not make AYP by 

status or safe-harbor. For those groups the number of students identified as “on-track to 

proficiency” was added to the number of proficient students and that sum was divided by the 

number of test-takers in the reporting group. That percentage was then compared to the AMO. 

If the school met all AYP criteria and had one or more reporting group meeting the AMO 

because of the addition of on-track students, the school as a whole was classified in EDFacts as 

making AYP by growth.

ESEA

subgroups are counted in such determinations only if they have at least 40 students and if no 

fewer than 95 percent of these students participate in annual testing. Students who have 

estimated scores above the proficiency cutoff but who also fail to meet their growth targets 

continue to be counted as proficient for AYP purposes.

EDFacts data for the 2006–07 school year indicate that Arizona’s growth model resulted in only 

one school making AYP that would have missed if only status and safe-harbor were applied

(Exhibit 12). The other 1,096 schools that met AYP requirements did so using status criteria 

alone.

 18 Note that an eighth-grader must close the proficiency gap by 100 percent in the first year, meaning that the growth 

model is equivalent to the status model in this grade.

19 Confidence intervals around the AMO (as opposed to around the percent proficient) are calculated using the 

number of full academic year students in the reporting group as the basis for the estimate. If the percent proficient in 

the group meets or exceeds the lower bound of this confidence interval, the group is classified as meeting the AMO.
Evaluation of the Growth Model Pilot Project 27

Exhibit 12

Arizona School AYP Determinations With Status and Safe-Harbor Results Augmented 

With Growth Model Results, 2006–07

School AYP Under StatusPlus-Growth Model Number Percent

Met with Status 1,096 77%

Met with Safe-Harbor 0 0%

Met with Growth 1 <1%

Not Met 333 23%

All Eligible Schools 1,430 100%

Exhibit reads: For Arizona’s schools overall, 1,096 met AYP under status, which was 77 percent of all 

eligible schools.

Source: U.S. Department of Education, EDFacts.

Arkansas’ growth model

Arkansas received approval to implement its proposed growth model in the 2006–07 school year. 

Arkansas uses a trajectory model that calculates growth for students in grades 4 through 7 using 

results of the Arkansas Benchmark Exams for mathematics and literacy, which are administered 

in grades 3 through 8 (plus grade 11 for literacy). Proficiency levels for these vertically scaled 

exams are set for each grade, and growth targets are based on the annual exam score increment 

needed to reach the proficiency standard in eighth grade. The annual increment that a student 

must attain in order to be classified as on-track to proficiency is calculated using grade-specific 

growth target multipliers of 0.295 in fourth grade, 0.319 in fifth grade, 0.385 in sixth grade, and 

0.542 in seventh grade. These multipliers indicate the proportion of the total difference between 

the eighth-grade standard (a score of 700) and the student’s current score that the student must 

gain over the next year in order to be on-track for eighth-grade proficiency. They contrast with 

the multipliers in other trajectory states (which all represent fractions of whole years – e.g., onefourth, one-third, one-half) because Arkansas Benchmark Exams are not scaled to have a linear 

progression from one year’s cut point to the next (see Appendix B for more detail and 

illustrations). 

An important feature of this model is that it resets the growth target every year rather than setting 

a series of annual targets based on the first below-proficient exam score. For example, a thirdgrader who scores a 480 on the Arkansas Benchmark Exams is 20 points below the standard for 

that grade. Since the eighth-grade standard is 700, the student must gain 65 points (= (700–480) 

* 0.295) to be counted as on-track to proficiency. If the student scores a 539 in fourth grade 

(again 20 points below the standard), he or she fails to reach this threshold and now needs to gain 

51 points (=(700–539) * 0.319) in fifth grade to be counted as on-track to proficiency. Arkansas 

students who make sufficient growth are counted as proficient for AYP determinations.

Arkansas’ growth model requires students who score above the proficiency threshold to improve 

toward the eighth-grade standard of 700 at the same basic grade-level rate as non-proficient 

students in order to count as on-track to proficiency. This means that above-proficient students 
Evaluation of the Growth Model Pilot Project 28

who continue to score above the proficiency threshold can nonetheless fail to realize adequate 

growth to count toward school AYP determinations under the growth model.

Like Arizona, Arkansas applies confidence intervals to the grade-specific AMOs. In contrast, 

the other states in the GMPP apply confidence intervals to the percentages of proficient students. 

The confidence interval is 95 percent and is applied by using the number of students enrolled in 

the school’s tested grades for each reporting subgroup. 

The data reported to EDFacts by Arkansas for the 2006–07 school year show that 24 percent of 

the schools made AYP according to the status model, 32 percent made AYP under safe-harbor

provisions, and 8 percent made AYP under the growth model (Exhibit 13). These 8 percent 

represent schools that would not have made AYP had the GMPP not been available.

Exhibit 13

Arkansas School AYP Determinations With Status and Safe-Harbor Results Augmented 

With Growth Model Results, 2006–07

School AYP Under StatusPlus-Growth Model Number Percent

Met with Status 212 24%

Met with Safe-Harbor 287 32%

Met with Growth 69 8%

Not Met 326 36%

All Eligible Schools 894 100%

Exhibit reads: For Arkansas’ schools overall, 212 met AYP under status, which was 24 percent of all 

eligible schools.

Source: U.S. Department of Education, EDFacts.

The percentage of Arkansas schools making AYP with safe-harbor (32 percent) is much higher 

than in any of the other GMPP states, but it is not clear why this occurred. 

Delaware’s growth model

Delaware also received approval to use its proposed growth model starting with the 2006–07 

school year. Delaware’s model includes students in grades 3 through 10 and does not limit the 

number of years students have to make proficiency. The Delaware Student Testing Program 

(DSTP) yields vertically aligned scale scores for mathematics and language arts (a combination 

of reading and writing). Mathematics and reading tests are administered starting in grade 2 and 

growth can be assessed in grade 3 and above, but the writing component of the language arts 

scores do not start until grade 3. 

The Delaware model is an example of the transition matrix type. Delaware uses a “value table” 

method for AYP determinations that assigns points for students depending on the type and extent 

of changes between the performance levels (see Exhibit 6). Points in the value table increase 

with the level of proficiency, so that a student scoring at the bottom receives fewer points for 
Evaluation of the Growth Model Pilot Project 29

moving up one level (150) than a student moving from that level to the next (175). Conversely, 

students who move up two levels are awarded more points (225) than a student who moves to the 

same level in one step (175 or 200). All students who surpass their grade level cutoff receive 

300 points regardless of how high they score or whether their underlying scores actually declined 

from the prior year. AYP is determined by calculating the average points for the school and its 

subgroups in the two required subject areas and comparing these averages with the state’s AMO 

levels.

Delaware was unique in the pilot project in that it applied both the status model and the growth 

model to all schools, and classified all schools that made AYP under the growth model as “met 

AYP by growth” even if they also met AYP by status. The other states employed the status-plusgrowth model shown in Exhibit 4. Delaware’s arrangement makes it impossible to determine 

from EDFacts whether the schools making AYP under growth also made AYP under status, and 

thus to answer the question of how many Delaware schools failed to make AYP under status but 

did make it under growth. 

Drawing on the state reports in EDFacts, 83 of 180 schools in Delaware made AYP under the 

growth model in the 2006–07 school year (Exhibit 14). As a result of using the procedure of 

employing the growth model results before applying the status and safe-harbor provisions, the 

percentage of Delaware schools reported in EDFacts as making AYP under growth (46 percent) 

is much higher than any other state. Many of these 83 schools would have made AYP under 

status or safe-harbor, had those criteria been applied before (as was done in the other GMPP 

states) the growth criteria.

Exhibit 14

Delaware School AYP Determinations With Growth Model Results Augmented With

Status and Safe-Harbor Results, 2006–07

School AYP Under GrowthPlus-Status Model Number Percent

Met with Status but not Growth 21 12%

Met with Safe-Harbor but not Growth 19 11%

Met with Growth 83 46%

Not Met 57 31%

All Schools 180 100%

Exhibit reads: For Delaware’s schools overall, 21 met AYP under status but not growth, which was 12

percent of all eligible schools.

Source: U.S. Department of Education, EDFacts.

The EDFacts reporting on school AYP outcomes used mutually exclusive categories of “by 

status” and “by growth” and it was thus not possible to address the question of how many 

Delaware schools that made AYP under their growth model would have missed AYP under the 

status model or by safe-harbor. However, data provided by the state directly to the evaluation 

team indicate that only five schools, or 3 percent of the schools in the state, made AYP because 
Evaluation of the Growth Model Pilot Project 30

of the growth model provisions (Exhibit 15).20

Exhibit 15

Delaware School AYP Determinations With Status and Safe-Harbor Results Augmented 

With Growth Model Results, 2006–07

 These were the only schools that were 

reclassified from not making AYP to making AYP as a direct result of the Delaware GMPP 

growth criteria. 

School AYP Under StatusPlus-Growth Model Number Percent

Met with Status 101 55%

Met with Safe-Harbor 22 12%

Met with Growth 5 3%

Not Met 57 31%

All Eligible Schools 185 100%

Exhibit reads: For Delaware’s schools overall, 101 met AYP under status, which was 55 percent of all 

eligible schools.

Source: Delaware Department of Education.

Florida’s growth model

Florida’s growth model proposal was approved for use starting with the 2006–07 school year. 

The growth model applies to students in grades 3 through 10 using the Developmental Scale 

Scores (DSS) from the Florida Comprehensive Assessment Tests (FCAT) for mathematics and 

reading. The state uses a trajectory model that bases growth targets on the score required for 

proficiency three years after the first year tested (normally, grade 3). To be counted as 

proficient, a student who was not proficient at the baseline must close the gap between their 

baseline score and the proficiency cutoff three grades later by one-third each year.21

Florida retains third-graders who score below proficient, and the growth model incorporates such 

students by using their two third-grade scores on the FCAT DSS. Otherwise, only students in the 

fourth grade or later will have the two scores required to calculate growth. 

Students 

who continue to score below the cutoff after three years start the process over and have new 

growth targets set.

For determining school AYP, Florida applies growth-model results for students only in ESEA

reporting groups that do not meet their AMOs by status or safe-harbor. An important feature of 

Florida’s accountability model is that, for groups not meeting their AMO, the growth-model data 

 20 These were final (summer) data for 2006–07 school year provided to NORC by Robin Taylor, associate secretary 

of education for the Delaware Department of Education’s Assessment and Accountability Branch, on Aug. 14, 2008. 

The data differed from the EDFacts reports in that both status and growth results were included for all schools and 

ESEA reporting groups. The data also included five schools not reported in EDFacts. 

21 This means that a student can only make proficiency by growth for two years since the gap must be fully closed in 

the third year, i.e., a student must meet or exceed the minimum proficiency score in year 3. A student first enrolled 

in grade 9 must close the gap by half to be counted as “on-track.” 
Evaluation of the Growth Model Pilot Project 31

are used exclusively. That is, the number of non-proficient but on-track students is not added to 

the number of proficient students as is done in several other pilot states. Instead, the growth 

model results for both the proficient and non-proficient students are used. This means that 

students who are proficient but who are not on-track to maintain proficiency in three years are 

counted as “not proficient” for AYP purposes in these reporting groups. Groups not meeting 

AMO by status or safe-harbor must thus meet the AMO entirely on the basis of “on-track” 

students. 

The AYP results for Florida in 2006–07 are shown in Exhibit 16. A total of 34 percent of 

Florida schools made AYP, with 24 percent making it under status, 5 percent by safe-harbor, and 

5 percent by growth. The percentage of schools that made AYP in Florida is much lower than 

the other GMPP states, but this may reflect higher standards for proficiency rather than lower 

performance. 

Exhibit 16

Florida School AYP Determinations With Status and Safe-Harbor Results Augmented 

With Growth Model Results, 2006–07

School AYP Under StatusPlus-Growth Model Number Percent

Met with Status 770 24%

Met with Safe-Harbor 155 5%

Met with Growth 149 5%

Not Met 2,135 67%

All Eligible Schools 3,209 100%

Exhibit reads: For Florida’s schools overall, 770 met AYP under status, which was 24 percent of all 

eligible schools.

Source: U.S. Department of Education, EDFacts.

Iowa’s growth model

Iowa’s growth model was approved for use with students in grades 3 through 8 beginning in the 

2006–07 school year. Iowa uses third-grade math and reading scores on the Iowa Test of Basic 

Skills (ITBS) as a baseline, so growth calculations begin in fourth grade. Iowa’s growth model 

is a type of transition matrix model (see Exhibit 5). To calculate growth, Iowa uses two 

categories of proficient (Intermediate and High) and three categories of below proficient (Weak, 

Low Marginal, and High Marginal). Proficiency thresholds for each category are set using 

national percentile ranks for each grade, with ITBS scale scores in the 40th percentile considered 

below proficient and 10th percentile scores considered Weak. Non-proficient students can still 

make Adequate Yearly Growth (AYG) if they improve to a higher category of below proficient 

within four years of the first year tested.

An important feature of Iowa’s model is that students cannot fall back to a non-proficient 

category and still make AYG. This means that High Marginal students who decline to Low 

Marginal or Weak cannot make AYG simply by regaining High Marginal status, and that Low 
Evaluation of the Growth Model Pilot Project 32

Marginal students who decline to Weak must score in the High Marginal category to make 

adequate growth. Iowa counts all students making AYG as proficient for ESEA reporting groups

that fail to make AYP when the status and safe-harbor provisions have been applied.

The 2006–07 AYP results for Iowa show that 11 percent of the schools made AYP with the 

growth model in the status-plus-growth framework (Exhibit 17). This was on top of 75 percent 

of the schools making AYP with status and 10 percent via safe-harbor. The percentage making 

AYP by growth was the highest of the eight pilot states, and the overall rate of AYP among Iowa 

schools (above 95 percent) was higher than any of the other GMPP states. The concurrence of 

high rate of making AYP by status and by growth suggests there is not necessarily a “ceiling 

effect” on making AYP, at least with Iowa’s implementation.

Exhibit 17

Iowa School AYP Determinations With Status and Safe-Harbor Results Augmented 

With Growth Model Results, 2006–07

School AYP Under StatusPlus-Growth Model Number Percent

Met with Status 831 75%

Met with Safe-Harbor 105 10%

Met with Growth 116 11%

Not Met 52 5%

All Eligible Schools 1,104 100%

Exhibit reads: For Iowa’s schools overall, 831 met AYP under status, which was 75 percent of all eligible 

schools.

Source: U.S. Department of Education, EDFacts.

North Carolina’s growth model

North Carolina received approval on May 17, 2006, to use its growth model for the 2005–06 

school year. This model calculates growth in grades 3 through 7 using vertically equated North 

Carolina end-of-grade tests for mathematics and reading. Third-graders in North Carolina have 

four years to grow to proficiency because they take a test upon entering the third grade and a test 

at the end of the year. All other students take end-of-grade tests and thus have only three years 

to become proficient or until eighth grade, whichever comes first.

For students that take the third-grade pretest, growth targets are set by dividing the difference 

between the initial test score and the proficiency cut score for sixth grade into four equal parts. 

Thus third-grade students who make up one-fourth of the shortfall between the baseline score 

and sixth-grade standards by the end of third grade are considered to be “on-track” to 

proficiency. Students who enter the school system after third grade must close this gap more 

quickly since they will have fewer than four years until eighth grade, when all students are 

expected to make a proficient score. 
Evaluation of the Growth Model Pilot Project 33

For AYP purposes, North Carolina applies growth-model results after status and safe-harbor

criteria. For reporting groups not meeting their AMO by status or safe-harbor, the number of 

non-proficient students who are on-track to proficiency per the growth model is added to the 

number of proficient students in the group. A group that reaches the state’s AMO with the 

inclusion of “on-track” students is considered to have met the AMO by growth and the school as 

a whole is classified as having made AYP by growth. North Carolina applies a 95 percent

confidence interval before using the growth model for AYP determinations and only includes 

subgroups with at least 40 full academic year (starting on Oct. 1 of the current school year) 

students. The standard 95 percent participation rule also applies to subgroups and schools and is 

based on the full set of students enrolled in the current school year. 

Exhibit 18 shows that the pilot growth model resulted in 12 more North Carolina schools making 

AYP in 2006–07 than would have made AYP through status (661) and safe-harbor (308) alone.

More than half (56 percent) of schools in North Carolina did not meet their AYP requirements 

under the GMPP.

Exhibit 18

North Carolina School AYP Determinations With Status and Safe-Harbor Results 

Augmented With Growth Model Results, 2006–07

School AYP Under Status-PlusGrowth Model Number Percent

Met with Status 661 30%

Met with Safe-Harbor 308 14%

Met with Growth 12 1%

Not Met 1,226 56%

All Eligible Schools 2,207 100%

Exhibit reads: For North Carolina’s schools overall, 661 met AYP under status, which was 30 percent of 

all eligible schools.

Source: U.S. Department of Education, EDFacts.

Tennessee’s growth model

Tennessee received approval on May 17, 2006, to use its growth model beginning in the 

2005–06 school year.22

 22 This approval stipulated that Tennessee work with the U.S. Department of Education to ensure that results from 

alternate assessments using different achievement standards were included by the 2006–07 school year.

The state calculates growth for students in grades 4 through 8 using 

vertically aligned scores for mathematics and reading or language arts from the Tennessee 

Comprehensive Assessment Program (TCAP). Students are first tested in the third grade, and 

those who score below proficient are given until ninth grade to reach proficiency by growth. 

Tennessee’s model establishes growth targets for students by estimating a regression equation to 

predict each student’s ninth-grade achievement level on the basis of their current and prior test 

scores. The regressions are estimated using data from all students at each grade level in the state. 
Evaluation of the Growth Model Pilot Project 34

Students who score below proficiency but who are predicted to be above the TCAP cut scores by 

grade 9 are counted as proficient for AYP growth determinations.

For students past the fifth grade, proficiency cut scores are based on the TCAP high school 

graduation (or Gateway) assessments. Another important feature of Tennessee’s growth model 

is that projections are possible even if a student is missing prior achievement scores for some 

grades or subjects. Also, the model recalculates projections every year and calculates projections 

for students who score above proficiency. 

For AYP purposes, the growth-model results are applied only to ESEA reporting groups that did 

not meet their AMOs by status or safe-harbor. As in Florida, Tennessee uses growth-model 

results for all students in groups not meeting their AMO. That is, proficient students in those 

groups who are projected to score below the cutoff in three years count are not counted as 

proficient. Tennessee includes subgroups in AYP determinations if they have at least 45 full 

academic year students and applies a 95 percent confidence interval to the AMO (like Arizona 

and Arkansas) instead of to the percent proficient. A school in Tennessee making AYP is 

considered to have made it by growth if including students projected to be proficient allows all

non-proficient subgroups to meet the AMO.

Exhibit 19 shows that 1,217 (or 89 percent) of 1,362 Tennessee schools met AYP requirements 

in 2006–07 through status and safe-harbor criteria. An additional 19 schools (or one percent) 

that failed to meet these criteria made AYP by also applying the pilot growth model.

Exhibit 19

Tennessee School AYP Determinations With Status and Safe-Harbor Results 

Augmented With Growth Model Results, 2006–07

School AYP Under StatusPlus-Growth Model Number Percent

Met with Status 1,149 84%

Met with Safe-Harbor 68 5%

Met with Growth 19 1%

Not Met 126 9%

All Eligible Schools 1,362 100%

Exhibit reads: For Tennessee’s schools overall, 1,149 met AYP under status, which was 84 percent of all 

eligible schools.

Source: U.S. Department of Education, EDFacts.

Impact of GMPP on AYP

The pilot states varied in the proportion of their schools that made AYP under status or safeharbor, and the differences can obscure the impact of their growth models on AYP. One way to 

assess the impact is to calculate the percentage increase in the number of schools making AYP 

due to use of the growth model. The schools making AYP uniquely by growth represented a 

percentage increase in the schools making AYP of 6 percent across all states, and ranged as high 

as 12 percent in Iowa, 14 percent in Arkansas, and 16 percent in Florida (Exhibit 20).
Evaluation of the Growth Model Pilot Project 35

Another indicator of the impact of the GMPP is the extent to which the growth models affected 

the pool of schools identified as failing both the status and safe-harbor criteria for AYP. Across 

all eight states, 8 percent of the 4,795 schools that did not make AYP by status or safe-harbor

made AYP by growth (Exhibit 20). These rates ranged from a high of 69 percent of eligible 

schools in Iowa making AYP by growth to 1 percent or fewer of eligible schools in Alaska, 

Arizona, and North Carolina making AYP by growth.

Exhibit 20

Percentage Increase in Number of Schools That Made AYP Due to Growth, and 

Percentage Decrease in Number of Schools That Did Not Make AYP Due to Growth, by 

State, 2006–07

Pilot States

Number of 

Schools 

Making AYP 

by Status or 

Safe-Harbor

Number of 

Schools not 

Making AYP by 

Status or SafeHarbor

Number of 

Schools Not 

Making AYP by 

Status or SafeHarbor That

Met by Growth

Percentage 

Increase in 

Schools 

Making AYP 

Due to Growth

Percent of 

Schools Not 

Making AYP by 

Status or SafeHarbor That

Met by Growth

All Eight States 6,088 4,795 371 6% 8%

Alaska 323 169 0 0% 0%

Arizona 1,096 334 1 <1% < 1%

Arkansas 499 395 69 14% 17%

Delaware 123 62 5 4% 8%

Florida 925 2,284 149 16% 7%

Iowa 936 168 116 12% 69%

North Carolina 969 1,238 12 1% 1%

Tennessee 1,217 145 19 2% 13%

Exhibit reads: The 371 schools that made AYP by growth increased the number of schools making AYP from 6,088 

to 6,459 schools, which was a percentage increase of 6 percent. Of the 4,795 schools that did not make AYP under 

either status or safe-harbor, 371 or 8 percent made AYP using the growth model.

Source: U.S. Department of Education, EDFacts and the Alaska, Arizona, Delaware, North Carolina, and Tennessee 

state departments of education.

Discussion

The idea of using growth models to assess school academic performance is attractive and the 

data collection systems and database architecture needed to support such models are rapidly 

becoming available. The pilot models were strictly add-ons to the traditional status-plus-safeharbor models for determining AYP in all eight states. Even Delaware, the only state that 

applied the growth model and then augmented with the status model, used the growth model as 

an add-on instead of a replacement. While states had the option of applying growth criteria 

instead of status and safe-harbor, none exercised that option. Growth criteria were instead added 

to status and safe-harbor criteria in ways that could only increase the number of schools making 

AYP.
Evaluation of the Growth Model Pilot Project 36

States also had the option of applying growth criteria before status and safe-harbor were applied, 

but Delaware was the only state that did so. Delaware’s growth-plus-status procedure had the 

effect of officially recognizing about 40 percent of their schools as making AYP by growth, 

which was a much higher percentage than under the status-plus-growth procedure used in the 

other states. While this may have had a positive effect on the public visibility and understanding 

of the model in Delaware, the actual number of growth schools that would not have made AYP 

under status or safe-harbor was small. 

As shown in Exhibits 11 through 19, the percent of schools that made AYP using the growth 

provisions of the GMPP, and which would not have made AYP without those provisions, ranged

from a high of 11 percent of schools in Iowa to 0 percent in Alaska. Another perspective on 

these rates is gained when the number of schools making AYP under growth is compared not to 

the total number of schools in the state but instead to either the number of schools in the state 

that made AYP under either status or safe-harbor (the percentage increase due to growth) or the 

number that did not make AYP under either status or safe-harbor (percentage decrease in nonAYP due to growth). The percentage increases in schools making AYP ranged from a high of 16 

percent in Florida to less than 2 percent in Alaska, Arizona, North Carolina, and Tennessee. The

growth model decreased the number of schools identified as failing under the status-plus-safeharbor model by 69 percent in Iowa but by less than 1 percent in Alaska, Arizona, and North 

Carolina. The rate of making AYP by growth after missing by status and safe-harbor ranged 

from 7 percent to 17 percent in the remaining four pilot states.

Reasons for the variation among states in the percentages of schools making AYP by growth will 

be examined systematically in the final report but are likely to be some combination of 

differences in the assessments used and the proficiency cutpoints, the features of the growth 

models implemented, the states’ AMOs, and the actual levels of growth realized by the students. 

It is noteworthy that the percentages making AYP by growth are not correlated with the 

percentages making AYP by status or safe-harbor (both of which vary greatly among these 

states) or to whether the state adopted a transition matrix, trajectory, or projection type of growth 

model. The exceptionally high rate in Iowa may be at least partly due to a more inclusive 

definition of growth toward proficiency used there (that is, any improvement of one or more 

performance levels). In contrast, the very low rates in other states may reflect the impact of the 

various other (non-growth) methods for determining AYP available in those states for schools to 

make AYP by status and safe-harbor (e.g., confidence intervals and multiyear averaging), such 

that the status and safe-harbor methods picked up schools which would have made AYP by 

growth had those various provisions not been available.
Evaluation of the Growth Model Pilot Project 37

III. School Characteristics Associated with AYP Outcomes

This chapter addresses the question of whether certain school characteristics are associated with 

making AYP under growth but not status or safe-harbor. The school characteristics are 

organizational and demographic variables that include ESEA improvement status, poverty level, 

minority concentration, locality, and size. Of particular interest here is how pilot growth models

affect the AYP designation of schools serving disadvantaged populations. Because such schools 

have been found to make AYP at much lower rates than those serving more affluent populations 

(U.S. Department of Education, 2007), the GMPP may function to lessen the AYP gap on this 

dimension. 

The question addressed in this chapter is whether certain types of schools are more or less likely 

to make AYP by the growth criteria. To answer this question, the following analyses look at the 

percentage increase of schools of each type that made AYP because of the availability of the 

growth model under the GMPP. The percentage increase is calculated by dividing the number of 

schools making AYP by growth but not by status or safe-harbor by the number that made AYP 

by either status or safe-harbor. Any difference between comparison groups in the percentage 

increases of schools making AYP by growth will suggest that the GMPP had a disproportionate 

effect on certain types of schools. 

The U.S. Department of Education report State and Local Implementation of the No Child Left 

Behind Act, Volume II—Accountability Under NCLB: Interim Report (Le Floch, Martinez, 

O’Day, et al. 2007) found that certain school demographic characteristics were associated with 

the likelihood of making AYP. For example, the study found that high-poverty, high-minority, 

larger, and urban schools were less likely to make AYP by status criteria (Le Floch, Martinez, 

O’Day, et al. 2007: 39, 40). Another important characteristic considered here is the ESEA

improvement status classifications of schools. This chapter uses the data reported in EDFacts to 

characterize schools that made AYP under growth but not under status or safe-harbor. As 

discussed in Chapter II, Delaware reported results to EDFacts based on growth model results 

augmented with status and safe-harbor results. In order to identify the incremental impact of the 

growth model on schools’ likelihood of making AYP, we substitute data using status and safeharbor augmented with growth for the Delaware EDFacts report. 

ESEA School Improvement Status.

The overall results shown in Exhibit 21 indicate that the percentage increase in schools making 

AYP due to the growth model was greater among schools identified for improvement or 

corrective action (19 percent) than schools not identified for improvement or corrective action (5

 An important issue for ESEA accountability is the extent to 

which schools identified for improvement are, despite their relatively low levels of performance, 

actually making progress toward the goal of universal proficiency. The growth model pilot is in

part intended to identify such schools. States are required under ESEA to identify for 

improvement Title I schools that do not meet AYP for two consecutive years and to initiate a 

process of interventions designed to improve student outcomes; most states have applied a 

similar process for non–Title I schools. Schools not making AYP for two consecutive years are 

officially identified for improvement. If a school does not make AYP after two years in the 

improvement status, it is identified for corrective action. If the school misses AYP for an 

additional year, it moves into restructuring status (Le Floch, Martinez, O’Day, et al. 2007: 3-6).
Evaluation of the Growth Model Pilot Project 38

percent). The pilot states varied greatly in the impact of the GMPP on the different types of 

schools. No schools identified for improvement or corrective action in Alaska, Arizona, or 

Delaware made AYP by growth. In contrast, Arkansas and Florida had substantial numbers of 

schools identified for improvement or corrective action that made AYP by growth (21 and 37 

schools, respectively). These counts translated into percentage increases in AYP among schools 

identified for improvement or corrective action attributable to the GMPP of 27 percent in 

Arkansas and 34 percent in Florida.

Exhibit 21 

Numbers of Schools Making AYP Under Status-Plus-Safe-Harbor and Growth, and 

Percentage Increase Due to Growth, by ESEA School Improvement Status, 2006–07

Made AYP Based on Status or 

Safe-Harbor

Made AYP Due to 

Growth Model

Percentage Increase Due to 

Growth

Pilot States

Improvement 

or Corrective 

Action

RestructuringNot 

Identified 

Improvement 

or Corrective 

Action

RestructuringNot 

Identified 

Improvement 

or Corrective 

Action

RestructuringNot 

Identified 

All Eight 

States 351 23 5,618 66 3 302 19% 13% 5%

Alaska 68 9 246 0 0 0 0% 0% 0%

Arizona 36 5 1,055 0 0 1 0% 0% <1%

Arkansas 78 0 421 21 0 48 27% 0% 11%

Delaware 5 0 118 0 0 5 0% 0% 4%

Florida 110 1 814 37 2 110 34% 200% 14%

Iowa 1 0 935 5 0 111 500% 0% 12%

North 

Carolinaa 33 0 851 1 1 10 3% 0% 1%

Tennessee 20 8 1,178 20 8 1,178 10% 0% 1%

Exhibit reads: Of the schools across all eight pilot states that were either identified for improvement or 

under corrective action, 351 made AYP under status or safe-harbor in 2006–07 and another 66 schools 

made AYP under growth in 2006–07. The schools that made AYP under growth increased the number of 

schools that made AYP in 2006–07 by 19 percent.

a

Source: U.S. Department of Education, EDFacts.

Results for North Carolina are from 2005–06 since the state did not provide data on school improvement status in 

2006–07.

The 2007 Interim Report on the implementation of NCLB found that schools’ likelihood of 

making AYP under the status model was strongly correlated with student socioeconomic status 

and racial or ethnic minority representation (Le Floch, Martinez, O’Day, et al. 2007: 39).

23

 23 Poverty level is defined here in terms of the percentages of students eligible for the federal free and reduced-price 

lunch program (FRPL). Low-poverty schools enroll 25 percent or fewer FRPL-eligible students, medium-poverty 

schools enroll 26 percent to 75 percent FRPL-eligible students, and high-poverty schools enroll more than 75 

percent.

 

Exhibit 22 (below) shows that for all eight states combined, the percentage increase in schools 

making AYP due to the growth models was greater among high- and medium-poverty schools 8 

and 7 percent increases, respectively) than among low-poverty schools (3 percent increase). This 

pattern held in Arkansas, Florida, Iowa, North Carolina, and Tennessee but not in Alaska, 

Arizona, or Delaware, where no high-poverty schools made AYP by growth. The differential 
Evaluation of the Growth Model Pilot Project 39

impact of the pilot growth models on making AYP between low- and high-poverty schools was 

greatest in Arkansas, Florida, and Iowa.

Exhibit 22 

Numbers of Schools Making AYP Under Status-Plus-Safe-Harbor and Under Growth, and 

Percentage Increase in AYP Due to Growth, by School Poverty Concentration, 2006–07

Pilot States

Made AYP Based on 

Status or Safe-Harbor

Made AYP Due to 

Growth Model

Percentage Increase Due to 

Growth

High 

Poverty

Medium 

Poverty

Low 

Poverty

High 

Poverty

Medium 

Poverty

Low 

Poverty

High 

Poverty

Medium 

Poverty

Low 

Poverty

All Eight 

States 737 3,674 1,606 62 265 44 8% 7% 3%

Alaska 50 183 90 0 0 0 0% 0% 0%

Arizona 174 444 478 0 1 0 0% 0% 0%

Arkansas 43 403 53 16 50 3 37% 12% 6%

Delaware 3 87 33 0 3 2 0% 3% 6%

Florida 75 515 335 24 109 16 32% 21% 5%

Iowa 22 618 296 8 86 22 36% 14% 7%

North Carolina 99 665 172 3 8 1 3% 1% 1%

Tennessee 271 759 149 11 8 0 4% 1% 0%

Exhibit reads: Among high-poverty schools in the eight pilot states, 737 made AYP based on status or safeharbor in 2006–07 and an additional 62 schools made AYP due to the application of growth models, 

resulting in an 8 percent increase in the number of high-poverty schools that made AYP in those states.

Source: U.S. Department of Education, EDFacts.

Results for school minority composition are shown in Exhibit 23.24

 24 Minority level is defined here in terms of the percentages of nonwhite or Hispanic students. Low-minority schools 

enroll 25 percent or fewer nonwhite or Hispanic students, medium-minority schools enroll 26 percent to 75 percent 

nonwhite or Hispanic students, and high-minority schools enroll more than 75 percent.

The percentage increase in

high-minority schools making AYP by growth across all eight states (7 percent) was slightly 

higher than the percentage increase among low-minority schools (4 percent) and slightly lower 

than the percentage increase among medium-minority schools (9 percent). This pattern again 

held in all states except Alaska, Arizona, and Delaware, states where none of the high-minority 

schools made AYP by growth. The differential impact of the pilot growth models on AYP rates 

of low- and high-minority schools was greatest in Iowa, Arkansas, and Florida.
Evaluation of the Growth Model Pilot Project 40

Exhibit 23 

Numbers of Schools Making AYP Under Status-Plus-Safe-Harbor and Under Growth, and 

Percentage Increase in AYP Due to Growth, by School Minority Concentration, 2006–07

Pilot States

Made AYP Based on 

Status or Safe-Harbor

Made AYP Due to 

Growth Model

Percentage Increase Due to 

Growth

High

Minority

Medium 

Minority

Low 

Minority

High

Minority

Medium 

Minority

Low 

Minority

High

Minority

Medium 

Minority

Low 

Minority

All Eight 

States 865 2,032 3,189 59 173 139 7% 9% 4%

Alaska 102 116 105 0 0 0 0% 0% 0%

Arizona 274 544 277 1 0 0 0% 0% 0%

Arkansas 24 123 351 7 38 24 29% 31% 7%

Delaware 8 97 18 0 3 2 0% 3% 11%

Florida 174 391 360 38 88 23 22% 23% 6%

Iowa 3 87 846 2 32 82 67% 37% 10%

North Carolina 92 423 454 4 6 2 4% 1% 0%

Tennessee 188 251 778 7 6 6 4% 2% 1%

Exhibit reads: Among high-minority schools in the eight pilot states, 865 made AYP based on status or safeharbor in 2006–07 and an additional 59 schools made AYP due to the application of growth models, resulting 

in a 7 percent increase in the number of high-minority schools that made AYP in those states.

Source: U.S. Department of Education, EDFacts.

School location in an urban, suburban, or rural area is another variable that previous studies have 

found related to AYP results, with rural and suburban schools generally more likely to make 

AYP under status or safe-harbor than urban schools. Exhibit 24 shows that, in most states, the 

growth model moved relatively more urban schools than rural schools into AYP. Delaware was 

the only state among the eight to exhibit the opposite trend, and Alaska and Arizona had no 

schools making AYP by growth in any category. Except for Arkansas and Iowa, the percentage 

increases in urban and suburban schools making AYP were of similar magnitude. 
Evaluation of the Growth Model Pilot Project 41

Exhibit 24

Numbers of Schools Making AYP Under Status-Plus-Safe-Harbor and Under Growth, and 

Percentage Increase in AYP Due to Growth, by School Urbanicity, 2006–07

Pilot States

Made AYP Based on 

Status or Safe-Harbor

Made AYP Due to 

Growth Model % Increase Due to Growth

Urban Suburban Rural Urban Suburban Rural Urban Suburban Rural

All Eight 

States 1,446 2,035 2,440 104 174 84 7% 9% 3%

Alaska 57 65 200 0 0 0 0% 0% 0%

Arizona 479 371 178 0 0 0 0% 0% 0%

Arkansas 61 119 303 16 18 32 26% 15% 11%

Delaware 17 75 31 0 1 4 0% 1% 13%

Florida 202 553 146 36 91 18 18% 16% 12%

Iowa 126 232 545 37 54 24 29% 23% 4%

North Carolina 165 262 520 5 4 3 3% 2% 1%

Tennessee 339 358 517 10 6 3 3% 2% 1%

Exhibit reads: Among urban schools in the eight pilot states, 1,446 made AYP based on status or safe-harbor

in 2006–07 and an additional 104 schools made AYP due to the application of growth models, resulting in a 7 

percent increase in the number of urban schools that made AYP in those states.

Source: U.S. Department of Education, EDFacts.

Discussion

The answer to the question, “Is the likelihood of making AYP under growth models associated 

with school characteristics?” varied across the six pilot states where the growth models had an 

impact on AYP determinations. Looking first at schools identified for improvement under 

ESEA, the percentage increase of those schools making AYP due to the growth model was 

greater than among schools not identified for improvement. Turning to demographic 

characteristics of the schools, the growth component was more likely to identify schools as 

making AYP among those with higher concentrations of poverty-level and minority students 

compared to those with lower concentrations in Arkansas, Florida, Iowa, North Carolina, and 

Tennessee. In Delaware, more advantaged schools were more likely to have made AYP by 

growth than by status or safe-harbor. The effect of growth models on AYP was most 

pronounced among schools enrolling high proportions of students from poverty-level 

households. Across all pilot states combined, the percentage increase in AYP because of the 

growth model was greater among high-poverty schools than among low-poverty schools, and the 

differences in the increases were particularly large in Arkansas, Florida, and Iowa.
Evaluation of the Growth Model Pilot Project 42
Evaluation of the Growth Model Pilot Project 43

IV. Using Student Growth Indicators to Assess School Outcomes

This chapter addresses the hypothetical question of how AYP determinations would be affected 

if the data collected by the GMPP states were used in various different ways. Four specific 

questions are addressed: (1) How do the models compare in terms of the number of schools that 

made AYP by status criteria and also made their state-defined “annual measurable objective” 

(AMO) by growth criteria? (2) How do the models compare in terms of the number of schools 

that made AYP by safe-harbor and also reached their AMO by growth criteria? (3) How do the 

models compare in terms of the demographic characteristics of schools that made their AMO by 

status as well as by growth criteria? and (4) To what extent did the pilot states have test scores 

for two or more years for all students, and did the non-matched students differ from their 

matched counterparts? 

In theory, growth models could provide a more useful way of assessing school academic 

performance than the traditional status-plus-safe-harbor-model. The GMPP growth models are 

designed to assess whether or not each student is on-track to reach or exceed the proficiency 

standards within a specified time frame. Aggregated to the school level, the individual-student 

growth assessments could provide a better picture of whether the school is meeting the ESEA

goals of progress toward universal proficiency in two respects. First, the growth models can 

identify some schools as making AYP that would not have made AYP under status-plus-safeharbor alone. Second, some schools making AYP under status-plus-safe-harbor might not make 

AYP if growth criteria were applied instead. Schools making AYP under status may not make 

AYP under growth if sufficient numbers of proficient students were not improving their scores 

enough to stay on-track for their states’ proficiency standards in subsequent years. Similarly, 

schools making AYP under safe-harbor may not have sufficient numbers of students on-track to 

proficiency to make AYP in the years to come. Moving to the theoretically more attractive 

model would thus result in some changes both among the set of AYP schools and the set of nonAYP schools.

Underlying the school-level AYP determinations analyzed in Chapters II and III are AYP 

determinations for each of the subgroups targeted by ESEA, insofar as the various subgroups are 

represented in the school. And underlying the subgroup determinations are results for each 

student that is a member of a subgroup in question. The growth model results for subgroups 

were not collected for the EDFacts repository, nor were any individual student data. However, 

the GMPP states were required to compile growth model results for all students in the 

participating grade levels and those data make it possible to calculate subgroup and school-level

“growth only” results. Specifically, each of the pilot states included in this Interim Report 

provided student-level data with variables indicating (1) whether the student scored at the 

proficient level or higher on the state’s reading and mathematics tests, and (2) whether the 

student was on-track to attain (or maintain) proficiency in the two subjects according to the 

growth model. The analyses presented in this section draw on the indicators of whether each 

student was on-track to proficiency in reading and mathematics. These data are used to calculate 

the proficiency level of all students in the school as well as each subgroup, and these rates were 

used to determine whether the school met the AMO by the growth criteria for 2006–07. 
Evaluation of the Growth Model Pilot Project 44

As discussed in Chapter I with respect to schools, it is theoretically possible for a student to have 

different proficiency determinations for growth and status. These possibilities are illustrated in 

Exhibit 25, which outlines the four possible patterns. A student can be proficient under status

and growth (cell “A”), or can be proficient under growth but not status (cell “B”), or proficient 

under status but not growth (cell “C”), or not be proficient under status nor growth-only (cell 

“D”). The primary goal of the GMPP growth models is to identify students in cell B and to 

allow the schools to count those students the same as proficient students for accountability 

purposes.

Exhibit 25

Conceptual Map of How Growth-Only Proficiency Designations Compare With

Status Model Proficiency Designations for Students

Student Proficiency Under the Growth-Only

Model

Student Proficiency Under the Status Model

Proficient Not Proficient

On-Track to Reach or Maintain Proficiency A B

Not On-Track to Reach or Maintain Proficiency C D

The percentages of students in each cell are shown in Exhibit 26. The percentages in cell A 

range from lows of 36 percent in Florida and 39 percent in Arkansas to 85 percent in Tennessee 

and more than two-thirds in Alaska, Delaware, and Iowa. The extent of overlap in the 

proficiency and on-track designations is measured by the sum of cells A and D. These sums 

ranged from a high of 94 percent in Iowa to a low of 75 percent in Delaware, with an average of 

83 percent across the eight states. To the extent that a goal of the GMPP growth models is to 

provide information that goes beyond the proficiency designations under the status model, this 

high overlap, or redundancy in designations may represent a limitation of the growth models as 

currently allowed, particularly insofar as it entails relatively low rates of identifying nonproficient students who are on-track to proficiency. That is, the main expectation is that the 

growth model will identify some students in cell B (not proficient but on-track) and thus increase 

the percentage of students that contribute to positive AYP determinations (the sum of cells A and 

B). Comparing the percentages of students in cell B, the states ranged from highs of 25 percent 

of all students in Delaware and 20 percent in Alaska to lows of 3 percent in North Carolina and 5 

percent in both Arkansas and Iowa. The variations among states in the cell B percentages are 

likely to reflect a combination of factors, including the effectiveness of the states’ systems in 

moving below-proficient students to the on-track level as well as differences in the pool of 

eligible (non-proficient) students and the assessment instruments and standards.

It is clear that the percentages in cell B do not correlate with the percentages of schools that 

made AYP by growth documented in Chapter II. Alaska, for example, had no schools classified 

as making AYP by growth despite having a relatively high rate of non-proficient students 

identified as on-track to proficiency. The lack of correlation between the student and school 

results generally means the states differed in how the cell B students figured into the AYP 

determinations. For example, the pilot states differed in how they used safe-harbor provisions, 

such that the proportions of non-proficient but on-track students enrolled in safe-harbor schools 

may have varied from state to state. 
Evaluation of the Growth Model Pilot Project 45

Exhibit 26

Distribution of Students According to How Their Status and Growth Proficiency 

Classifications Compare, 2006–07

Pilot States

Proficient and 

On-Track (Cell A 

in Exhibit 25)

Not Proficient

but On-Track

(Cell B in 

Exhibit 25)

Proficient but 

Not On-Track

(Cell C in 

Exhibit 25)

Neither 

Proficient nor 

On-Track (Cell D 

in Exhibit 25)

Number of 

Students

Alaska 67% 20% 1% 11% 63,984

Arizona 52% 10% 10% 27% 283,434

Arkansas 39% 5% 12% 44% 156,722

Delaware 68% 25% N/A 7% 39,312

Florida 36% 8% 13% 43% 1,409,426

Iowa 69% 5% N/A 25% 119,104

North Carolina 54% 3% 14% 30% 392,549

Tennessee 85% 7% 0% 7% 352,945

Exhibit reads: Of the 63,984 students in the state of Alaska, 67 percent were proficient and on-track to 

remain at or above the proficiency cut point, 20 percent were not proficient but were on-track to reach 

proficiency, one percent were proficient but not on-track to remain at or above the proficiency cut 

point, and 11 percent were neither proficient nor on-track to proficiency.

Source: U.S. Department of Education, EDFacts, Alaska Department of Education, Arizona Department of 

Education, Arkansas Department of Education, Florida Department of Education, Tennessee Department of 

Education.

Comparisons of status and growth-only proficiency determinations for schools

As discussed in Chapter I, the pilot states had the option to apply growth criteria to school AYP 

determinations in a number of ways: after status and safe-harbor, before status and safe-harbor, 

without status or safe-harbor, etc. Of the eight pilot states in 2006–07, all but Delaware elected 

to apply growth criteria after status and safe-harbor. Delaware, in contrast, applied growth 

criteria first, followed by status and then safe-harbor. If all three criteria (status, safe-harbor, and 

growth) are applied, the total number of schools making AYP is not affected by changes in the 

order in which the criteria are applied. Nonetheless, the quality of the information about the 

schools provided by the AYP data is arguably affected by the order of application, depending on 

the manner in which the AYP data are reported.

Theoretically, schools that make AYP by growth-only are more likely to attain or maintain AYP 

in the future than schools that make AYP by status but not growth, and also more likely to attain 

or maintain AYP in the future than schools that make AYP by safe-harbor but not by status or 

growth. If the AYP results are reported in a way that shows the criteria under which a school 

first achieves the AMO benchmark, applying growth criteria before status and safe-harbor could

thus provide policymakers and the public with better information about school performance even 

though the overall numbers of schools making AYP would be the same. 

The results in Chapter II indicated that relatively few additional schools made AYP by growth 

after status and safe-harbor criteria were applied. Referring to the cells in Exhibit 27, the 

analysis in Chapter II focused on the number of schools that made AYP by growth (cells C plus 

G). However, those results do not provide a comprehensive account of the growth model data 
Evaluation of the Growth Model Pilot Project 46

collected through the GMPP. First, it was possible for the schools that made AYP by status or 

by safe-harbor to also have had sufficient numbers of students classified by the growth model as 

on-track to proficiency to also meet their AMOs strictly under the growth criteria. Those schools 

would be located in cells A and B in Exhibit 27. Second, it was also possible for the schools that 

were classified as having made AYP by status-plus-growth to either meet (cell C) or not meet 

(cell G) the AMO if the students’ on-track to proficiency data were exclusively used. 

Exhibit 27

How the Growth Model On-Track-to-Proficiency Designations Can Compare with AYP

Designations for Schools

School AMO Designations Under a 

Growth-Only Model

School AYP Designations in ESEA Reporting, Based on StatusPlus-Growth Determinations

Made AYP by 

Status

Made AYP by 

Safe-Harbor

Made AYP by 

Growth

Did not Make

AYP

Met AMO with growth-only A B C D

Did not meet AMO with growth-only E F G H

As noted in Chapter I, the EDFacts data classified schools in terms of AYP and reporting groups 

in terms of AMO with sets of mutually exclusive categories that do not allow one to address 

hypothetical questions of what would happen if the student growth model results were used 

differently. In order to assess the possible magnitude of the cells in Exhibit 27, the best resource 

is the status and growth proficiency data provided in the student files compiled by each of the 

pilot states. These data do not provide sufficient information to implement the states’

methodologies for determining whether schools made AYP, but they do contain information on 

the key dimensions of reading and mathematics proficiency and thus allow assessments of 

whether reporting groups and schools as wholes met their AMOs.

In Delaware and Iowa, all students who scored at proficiency or higher on the status criteria were 

also classified as “on-track” to proficiency per their growth models. The other six states, in 

contrast, applied their growth models to all students and identified some proficient students who 

were not on-track to continue to score at or above the proficiency levels in later grades. 

The results shown in Exhibit 28 indicate that for all eight states combined, 85 percent of the 

schools that made AYP by status also met their reading and mathematics AMOs using just the 

growth criteria. The states varied considerably, ranging from only 45 percent in Arizona and 67 

percent in Arkansas to over 90 percent in Alaska, Delaware, Florida, Iowa, North Carolina, and 

Tennessee.
Evaluation of the Growth Model Pilot Project 47

Exhibit 28

Number and Distribution of Schools That Made AYP Based on Status Criteria, by 

Whether They Met AMOs Based on Growth Criteria, 2006–07

Pilot States

Number Distribution

Number of 

Schools That 

Met AMO With

Status Criteria

Met AMO With

Growth-Only

Results (Cell A in 

Exhibit 27)

AMO Not Met by 

Growth-Only 

(Cell E in 

Exhibit 27)

Met AMO With

Growth-Only 

Results (Cell A in 

Exhibit 27)

AMO Not Met 

by Growth-Only 

(Cell E in 

Exhibit 27)

All Eight States 4,804 4,083 721 85% 15%

Alaska 319 301 18 94% 6%

Arizona 1,047 473 574 45% 55%

Arkansas 209 141 68 67% 33%

Delaware 96 96 0 100% 0

Florida 770 745 25 97% 3%

Iowa 780 780 0 100% 0

North Carolina 445 439 6 99% 1%

Tennessee 1,138 1,108 30 97% 3%

Exhibit reads: Of the 4,804 schools that made AYP based on status criteria, 4,083 schools (85 percent) met 

the state AMO under the growth criteria, while 721 schools (15 percent) did not.

Source: U.S. Department of Education, EDFacts, Alaska Department of Education, Arizona Department of Education, 

Arkansas Department of Education, Florida Department of Education, Iowa Department of Education, North Carolina 

Department of Education, and Tennessee Department of Education.

Taken at face value, these results indicate that very few schools that made AYP by status in 

Alaska, Delaware, Florida, Iowa, North Carolina, and Tennessee were not on-track to meet their 

AMO in the near term, whereas over half of the Arizona schools that made AYP by status were 

not on-track to maintain their AYP standing. 

These findings provide some evidence that the low rates of making AYP by growth found in 

some states (most notably Alaska, North Carolina, and Tennessee) and documented in Chapter II 

were not the result of low rates of students being on-track to proficiency and schools not having 

sufficient growth to meet their AMOs using growth-only. This, in turn, suggests that the low 

rates of making AYP by growth in these states with high rates of meeting AMOs by growth-only

was more a reflection of how their status models were designed rather than of an absence of 

growth. With status applied before growth, the large numbers of schools that could have met 

their AMOs by growth-only were obscured. 

Growth-only proficiency results of schools making AYP by safe-harbor

The safe-harbor provision of ESEA was designed to identify schools making progress toward 

meeting the AMO even though their reading or mathematics proficiency levels, or both, are still 

below the AMO. Specifically, safe-harbor recognizes schools and subgroups that have decreased 

the number of students scoring below proficiency thresholds by 10 percent or more from one 
Evaluation of the Growth Model Pilot Project 48

year to the next. Identifying progress among low-performing schools is, of course, also the 

intention of the growth models, but the growth models are distinguished by (1) basing progress 

estimates on longitudinal student-level data, and (2) evaluating progress in terms of whether it is 

sufficient to reach the AMO within a specific time frame (e.g., by the time the student completes 

grade 8).

By virtue of both these distinguishing features, schools meeting their AMOs by growth should be 

performing better than schools meeting their AMOs by safe-harbor but not by growth. 

Nonetheless, all of the pilot states except Delaware applied safe-harbor provisions before growth 

criteria in their AYP determinations. In order to estimate the number of safe-harbor schools that 

also met their AMOs using just the growth criteria, we used the student-level data to categorize 

the schools. 

The results in Exhibit 29 indicate that 87 percent of the safe-harbor schools in the six states that 

had any safe-harbor schools also met their AMO using the growth criteria. The percentages 

exceeded 70 percent in all states. Again, reasons for the differences among states will be 

explored in the final report, but the main point from this analysis is that the great majority of 

safe-harbor schools also met their AMOs by growth criteria.

Exhibit 29

Number and Distribution of Schools That Made AYP by Safe-Harbor Criteria, by 

Whether They Met AMOs Based on Growth Criteria, 2006–07

Pilot States

Number Distribution

Number of 

Schools That 

Met AMO With

Safe-Harbor

Met AMO With

Growth-Only

Results (Cell B in 

Exhibit 27)

AMO Not Met by 

Growth-Only 

(Cell F in 

Exhibit 27)

Met AMO With

Growth-Only 

Results (Cell B in 

Exhibit 27)

AMO Not Met 

by Growth-Only 

(Cell F in 

Exhibit 27)

All Six States 901 785 116 87% 13%

Arkansas 285 233 52 82% 18%

Delaware 22 20 2 91% 9%

Florida 155 140 15 90% 10%

Iowa 105 76 29 72% 28%

North Carolina 288 285 3 99% 1%

Tennessee 68 51 17 75% 25%

Exhibit reads: Of the 901 schools in the six states that made AYP by safe-harbor, 785 schools (87 percent) met 

the state AMO under the growth criteria while 116 schools (13 percent) did not meet the state AMO under the 

growth criteria.

Note: No schools from Alaska or Arizona made AYP by safe-harbor in 2006–07.

Source: U.S. Department of Education, EDFacts., Arkansas Department of Education, Delaware Department of 

Education, Florida Department of Education, Iowa Department of Education, North Carolina Department of Education, 

and Tennessee Department of Education.
Evaluation of the Growth Model Pilot Project 49

One implication of the overlap of safe-harbor and growth-only outcomes is that safe-harbor

appears to work largely as intended, in that it identifies schools that are improving. However, 

the growth-only percent of students on-track could be a better gauge of actual test score 

improvement than safe-harbor. This is because the growth-only measure relies on the 

longitudinal student records rather than the percentages proficient in each year. A second 

implication is thus that growth criteria could be usefully applied to AYP determinations before 

safe-harbor is applied and the information about school improvement would be enhanced.

Demographic characteristics of schools that made their AMO by status and growth criteria

As shown in Chapter III, schools enrolling higher proportions of low-income and minority 

students were more likely than more affluent and lower-minority schools to make AYP by 

growth in the status-plus-safe-harbor-plus growth system. It is also interesting to examine the 

demographic characteristics of schools that reached their AMOs with both the status and growth 

criteria. These schools are theoretically the most likely to continue to reach the accountability 

milestones leading to universal proficiency by 2014. 

To examine this relationship, the student data are used to determine both whether the school met 

the AMO by growth and by status. Using the student data for the status calculations has the 

advantage of clarifying the comparisons by removing schools that made AMOs by safe-harbor, 

confidence intervals, and multiyear averaging, all of which could produce different results than 

status-based AMO determinations built entirely from the student records.

The comparisons of status and growth proficiency results are restricted to six states because the 

Delaware and Iowa models defined all students proficient by status to also be on-track to 

proficiency by growth. The results in Exhibit 30 indicate that schools enrolling higher 

proportions of poverty students were less likely than schools with medium and low rates of 

poverty student enrollments to reach AMOs on both the status and growth criteria. The 

relationship of school poverty with meeting the AMOs on both criteria was stronger in Arizona 

and Arkansas than in Alaska, Florida, North Carolina, and Tennessee.
Evaluation of the Growth Model Pilot Project 50

Exhibit 30

Percentage of Schools That Met the AMO Under Status That Also Met the AMO Under

Growth-Only, by School Poverty Level, 2006–07

Pilot States

Number That Met AMO Under Status

Percent That Also Met AMO by GrowthOnly

Low 

Poverty

Medium 

Poverty

High 

Poverty

All 

Schools

Low 

Poverty

Medium 

Poverty

High 

Poverty

All 

Schools

All Six States 1,203 2,371 571 4,145 80% 87% 71% 83%

Alaska 90 183 50 323 96% 95% 92% 94%

Arizona 478 444 174 1,096 56% 45% 31% 48%

Arkansas 24 167 21 212 63% 72% 43% 68%

Florida 314 409 47 770 97% 98% 85% 97%

North Carolina 153 440 38 631 100% 100% 92% 99%

Tennessee 144 728 241 1,113 97% 100% 93% 98%

Exhibit reads: Of the 1,203 schools in the six states that met the AMO under status that had low enrollments 

of children from poverty-level households, 80 percent also met the AMO under growth in 2006–07.

Source: U.S. Department of Education, EDFacts, Alaska Department of Education, Arizona Department of Education, 

Arkansas Department of Education, Florida Department of Education, North Carolina Department of Education, 

Tennessee Department of Education.

The relationship between minority enrollment and making AMO by both criteria (not tabulated)

was in the same direction but somewhat weaker than the school poverty correlations. These 

results for high-poverty and high-minority schools show they were less likely to meet 

proficiency standards by both status and growth-only criteria. In contrast, the results in Chapter

III for poverty and minority enrollments showed that the less-advantaged schools were more 

likely to make AYP by growth in the status-plus-growth framework generally implemented 

under the GMPP. An implication of these contrasting results is that if the growth-only method 

were adopted for actual accountability purposes while retaining the current core GMPP 

principles, the number of less-advantaged schools making AYP would decrease. 

Extent of longitudinal matching

The final aspect of growth models examined here is the extent to which the state assessment 

systems were able to calculate growth indicators for their students. Growth indicators are 

generally based on at least two years of achievement data. However, some students in each 

school year will not have prior test score data because they transferred in from out of state or 

from a private school, were absent on the test dates, or were excluded from the prior year testing 

for one reason or another. The percentage of students with growth indicators is referred to as the 

match rate (all of the pilot states except Tennessee required two consecutive years of test scores 

in order to calculate growth indicators). 

The match rate has potentially important implications for the validity of a growth model: if a 

growth model is applied to all students in an ESEA reporting group in order to assess whether the 

AMO was met, then only the matched students are used to determine proficiency rates. Among 

the eight states examined here, only Delaware, Florida, and Tennessee applied their growth 

models to all students in ESEA reporting groups. In Delaware, growth model results were 
Evaluation of the Growth Model Pilot Project 51

considered first in making AYP decisions for each ESEA reporting group. Florida and 

Tennessee applied growth results after status and safe-harbor but used the growth model results 

for all students within ESEA reporting groups that did not make AYP by status or safe-harbor. 

The other states, in contrast, only used growth results for non-proficient students within reporting 

groups that did not make AYP by growth or safe-harbor.

In order to gain some information on how the results of growth models like the ones piloted in 

Delaware, Florida, and Tennessee might be affected by match rates, matched and non-matched 

students were compared in five of the states (Alaska, Arkansas, Florida, Iowa, and Tennessee; 

Arizona, Delaware, and North Carolina provided data only on matched students). Exhibit 31

presents the match rates and average test score differences among matched and non-matched 

students in the four states that provided scale-score data to the evaluation project. The match 

rates are the percentages of students who have the two years (2005–06 and 2006–07 school 

years) of test scores needed to calculate growth.

The five states generally had match rates of 90 percent or higher based on the supplied student 

data (Exhibit 31). Tennessee’s rate of 99 percent reflects the fact that the projection model it 

used is able to estimate projections even with missing data and almost all students thus have 

valid growth indicators. 

Exhibit 31

Differences Between Matched and Unmatched Grade-Standardized Student Scores for 

Reading and Math for Alaska, Arkansas, Florida, Iowa, and Tennessee, 2006–07

Pilot States

N Students in 

Grades 4–8

Percent With 

Test Scores 

From 2005–06

Difference 

(SDs) in 

Reading

Difference 

(SDs) in Math

Alaska 41,881 93% 0.10 0.09

Arkansas 175,051 90% 0.41 0.30

Florida 924,485 92% 0.43 0.47

Iowa 119,182 100% 0.65 0.73

Tennessee 356,496 a 99%

Exhibit reads: Of the 41,881 students in Alaska, 93 percent had matched scores. The mean achievement 

difference in scale scores between those who were matched and those who were unmatched was 0.1 

standard deviations in reading, and 0.09 standard deviations in mathematics.

a Tennessee did not provide the students’ scale scores in reading and mathematics.

Source: Alaska Department of Education, Arizona Department of Education, Arkansas Department of Education, 

Florida Department of Education, Iowa Department of Education, and Tennessee Department of Education
Evaluation of the Growth Model Pilot Project 52

In four of the states, reading and mathematics scale scores were available and the mean scores of 

matched and unmatched students could be compared. Unmatched students had substantially 

lower average test scores than matched students. Taken together, these results indicate that while 

the match rates were high, the matched population may have significantly higher levels of 

achievement than the unmatched group and thus be more likely to be proficient or on-track to 

proficiency. To that extent, reliance on growth-only data for AYP determinations may increase 

the likelihood a school will reach its AMO. While the match rates in the pilot states that 

provided the information were generally very high, the potential for a few exclusions to affect 

AYP results suggests that further study is needed to determine the validity of using non-matched 

status results rather than excluding them from the growth-only applications. 

Conclusions

This chapter addressed a number of hypothetical questions about the pilot growth models. The 

first question addressed was the extent to which the results of using only the growth models’ ontrack-to-proficiency results would diverge from the status model results among the schools that 

made AYP by the status model in 2006–07. This analysis identified the schools currently 

performing sufficiently well to make AYP by status criteria but, according to the state’s growth 

model, not making sufficient annual gains to reach the AMO by growth-only criteria. These 

schools would then be expected not to continue to make AYP if their pattern of low growth 

continued. For all eight states combined, 85 percent of the schools that made AYP by status also 

met their reading and mathematics AMOs using just the growth criteria. The states varied 

considerably, ranging from 45 percent in Arizona to over 90 percent in Alaska, Delaware, 

Florida, Iowa, and Tennessee. 

A similar analysis of the schools that made AYP by safe-harbor found that overall 87 percent of 

the safe-harbor schools in the six states that had any safe-harbor schools would have also met 

their AMO using the growth-only criteria. The results were more consistent across states, with

the great majority of safe-harbor schools in the pilot states also meeting their AMOs by growth 

criteria.

The relationship of school demographic characteristics with meeting AMOs both by status and 

growth-only criteria was examined to see whether divergence of the two indexes was 

concentrated in certain types of schools. The main finding here was that schools enrolling higher 

proportions of poverty students were less likely than schools with medium and low rates of 

poverty student enrollments to reach AMOs on both the status and growth-only criteria. 

The final aspect of growth models examined here was match rates. In this chapter we estimated 

the extent to which the pilot states had reading and mathematics test scores from both 2006–07 

and 2005–06 available, and whether the 2006–07 test scores differed for the students with and 

without the 2005–06 scores. The results indicate that while the match rates were high (90 

percent or greater in most states), the matched population may have significantly higher levels of 

achievement than the unmatched group and thus be more likely to be proficient. However, it is 

not necessarily the case that reliance on growth-only data for AYP determinations would

increase the likelihood a school will reach its AMO because the proficient students may not be 

on-track to maintain proficiency. But because proficient students are more likely than nonproficient students to be on-track, reliance on the matched cases would likely increase the odds 
Evaluation of the Growth Model Pilot Project 53

of reaching the AMO. If excluded students are concentrated in certain reporting groups, the 

impact of exclusions on school AYP determinations could be further increased. These points 

underscore the importance of maintaining high match rates if growth-only outcomes are applied 

to accountability decisions.
Evaluation of the Growth Model Pilot Project 54
Evaluation of the Growth Model Pilot Project 55

Conclusions

This interim report was designed to answer two main questions about the implementation of the 

Growth Model Pilot Project (GMPP) under the Elementary and Secondary Education Act as 

amended by the No Child Left Behind Act of 2001. The two questions and brief summaries of 

the study results based on analyses of data provided by eight pilot grantee states from 2006–07

that are the subject of this evaluation (Alaska, Arizona, Arkansas, Delaware, Florida, Iowa, 

North Carolina, and Tennessee) are as follows:

How have states in the pilot project implemented growth models?

While the models approved for the eight pilot grantee states that are the subject of this evaluation 

differ from one another in a number of important ways, all use state-specific assessment data to 

measure student progress and proficiency, and the method of incorporating growth outcomes in 

adequate yearly progress (AYP) determinations was generally the same. Seven of the eight pilot 

states applied growth criteria only after schools have failed to make AYP under the status and 

safe-harbor provisions, rather than determining AYP solely on the basis of student 

improvement—a “status plus growth” model. Delaware, in contrast, applied growth criteria first, 

and then applied the status model and safe-harbor provisions, respectively, to schools that did not 

make AYP under the growth model.

When a school is designated as “making AYP under growth,” this means that use of the growth 

model changed the designation for one or more targeted ESEA subgroups. Within the affected 

subgroup(s) for a given school, the growth criterion is usually applied only to the students who 

did not achieve at or above the proficiency level. Simply stated, “making AYP under growth,”

as defined by the GMPP, does not mean that all students are on-track to proficiency, and it can 

even mean only one non-proficient student is on-track if a sufficient number of others in the 

subgroup are proficient. Seven of the eight states whose 2006–07 school year data were 

available for analyses used the status-plus-growth model (Alaska, Arizona, Arkansas, Florida, 

Iowa, North Carolina, and Tennessee). Delaware used a growth-plus-status model for 

determining AYP. 

The models approved for the pilot study vary in how they (1) establish growth expectations for 

students, and (2) determine whether individual students are “on-track” to reach proficiency in the 

allotted time frame. We have identified three basic types of growth models being used in the 

GMPP: the transition matrix model (which evaluates student progress from year to year in terms 

of a relatively small set of discrete performance levels), the trajectory model (which uses the gap 

between a baseline test score and a performance standard several years out to calculate the 

amount of growth required to become proficient), and the projection model (which uses current 

and past test scores to statistically predict performance several years ahead, using new test scores 

to update projections of student performance).

There was little evidence that the type of model selected had an impact on the extent to which 

schools were identified as making AYP by growth within the GMPP framework. Further 

analyses of the strengths and weaknesses of the various models are planned for the final report, 

including side-by-side comparisons of generic versions of the three types of models using a 

common dataset. However, the results presented here suggest that impacts of differences in the 
Evaluation of the Growth Model Pilot Project 56

ways the models identify students as on-track to proficiency or not may be reduced by (a) the 

constraints of the GMPP guiding principles and particularly the requirement of universal 

proficiency by 2014, and (b) the various provisions within ESEA for recognizing AYP under the 

status model. The latter are generally designed to reduce the chance of incorrectly identifying 

schools as not making AYP, and the growth models were primarily adopted to further reduce that 

chance. But if the status provisions were already capturing most of the schools that might have 

been identified as making AYP by growth, then the numbers of schools identified as growth 

schools by the GMPP would be correspondingly reduced.

How did each pilot state’s growth model affect the number and kinds of schools that make 

AYP?

The eight pilot states in 2006–07 that are the subject of this evaluation provided both schoollevel (EDFacts) and the student-level data to the evaluation project and these data were used to 

address five subquestions. 

1. How many schools made AYP under the growth model that would not have made it under 

the ESEA status model?

The designs of the growth models in these states included only those students who (a) did not 

reach proficiency levels in reading or language arts and mathematics, and (b) were members 

of ESEA reporting groups that did not reach their Annual Measurable Objectives (AMOs) or 

obtain AYP via safe-harbor provisions. The pilot models simply added growth criteria to the 

traditional status plus safe-harbor model for determining AYP; thus growth criteria could 

only increase the number of schools making AYP. The number of schools identified as 

making AYP by growth under the GMPP in 2006–07 ranged from 1 percent or fewer of all

schools in Alaska, Arizona, North Carolina, and Tennessee, to 3 percent in Delaware, 5 

percent in Florida, 8 percent in Arkansas, and 11 percent of all schools in Iowa. The schools 

making AYP uniquely by growth represented percentage increases in the numbers of schools 

making AYP that ranged from highs of 16 percent in Florida, 14 percent in Arkansas, and 12

percent in Iowa to lows of 2 percent or fewer in Alaska, Arizona, North Carolina, and 

Tennessee. Expressed as percentages of the schools that did not make AYP under status or 

safe-harbor, the impact of the GMPP on identifying additional schools as making AYP 

ranged as high as 17 percent in Arkansas and 69 percent in Iowa.

2. Are AYP outcomes under the growth models related to school demographics and 

organizational characteristics?

Schools enrolling higher proportions of low-income and minority students were more likely 

to make AYP under growth in the status-plus-growth framework than were schools enrolling 

higher proportions of more affluent and nonminority students. However, if growth were the 

sole criterion for determining AYP, schools enrolling higher proportions of low-income and 

minority students would be more likely to move from making AYP to not making AYP.

3. How many schools that made AYP under the ESEA status model would also have made it 

if the growth criteria were used exclusively for assessing whether schools met their AMOs?

This question was addressed by drawing on the student data provided by the pilot states to 

calculate whether each school met its AMOs for reading and mathematics using the on-track

to proficiency indicators for each student. For all eight states combined, 85 percent of the 
Evaluation of the Growth Model Pilot Project 57

schools that made AYP by status also met their reading and mathematics AMOs using just 

the growth criteria. The states varied considerably, ranging from 45 percent in Arizona and 

67 percent in Arkansas to over 90 percent in Alaska, Delaware, Florida, Iowa, North 

Carolina, and Tennessee. 

4. What is the relationship between AYP status under the growth model and ESEA safeharbor provisions?

Six of the eight pilot states had at least one school classified in EDFacts as having made 

AYP by safe-harbor provisions. Overall, 87 percent of the schools making AYP by safeharbor provisions in the six states also met their states’ AMOs using the growth model 

criteria. Arkansas and Iowa each had about 80 percent of the total number of safe-harbor

schools make AYP by growth. Delaware and Florida had roughly 90 percent of the total 

number of safe-harbor schools that also met their AMO using the growth criteria.

5. To what extent are longitudinal student data required by the growth models available?

We estimated the extent to which the pilot states had reading and mathematics test scores 

from both 2006–07 and 2005–06 available, and whether the 2006–07 test scores differed for 

the students with and without the 2005–06 scores. While the match rates were high (90 

percent or greater in all states), the matched population may have significantly higher levels 

of achievement than the unmatched group and thus be more likely to be proficient or on-track

to proficiency. To that extent, reliance on growth data with their requirement for matched 

longitudinal records for AYP determinations may increase the likelihood a school will reach 

its AMO.

Implications for future policy

As used for school AYP purposes in all states except Delaware, the growth information for 

students was used only for reporting groups that did not make AYP under status criteria or safeharbor provisions. Consequently, it was generally not possible to determine from the official 

EDFacts reports the extent to which a school designated as making AYP by growth was actually 

realizing growth among its students. Delaware applied growth criteria before status and safeharbor criteria and all schools identified as making AYP by growth actually met their AMOs on 

the basis of Delaware’s growth model. An implication for future policy is that other states could 

clarify their schools’ progress by applying growth criteria before status and safe-harbor. Two 

general ways of doing that can be identified and each has advantages and disadvantages. Both of 

these options are methods for reporting of schools’ results related to AYP determinations, and do 

not suggest changes that would actually affect whether schools are determined to make AYP. As 

described here, neither of the methods would affect a school’s AYP status.

1. Applying growth criteria before status and safe-harbor criteria to all schools’ AYP 

determinations

A different possible ordering would involve first using the growth results to assess whether the 

reporting group reached the AMO, then, if not, using the union of growth and status results to 

estimate the percentage of students on-track or proficient. Safe-harbor might only then apply to 

reporting groups that did not reach the AMO through either of these calculations.
Evaluation of the Growth Model Pilot Project 58

The main advantage of applying growth before status and safe-harbor is that it would identify 

schools that are realizing adequate progress toward universal proficiency. This would clearly 

distinguish those schools from schools making AYP under status criteria but not realizing growth 

sufficient to continue meeting their AMOs. The latter are probably not a large number but 

identifying such schools would serve as an early warning mechanism of possible problems. The 

exploratory analyses in this report also indicate that applying growth criteria before safe-harbor

could usefully reclassify most of the current safe-harbor schools as making AYP by growth and 

would clearly identify the minority that are not on-track to proficiency and thus headed for 

sanctions in the near future. 

One disadvantage is that schools that are making AYP both by status and growth (arguably the 

strongest schools) would not be uniquely identified. Another possible disadvantage of applying 

growth first follows from the fact that the AYP-by-growth determination would be based on 

students with at least two consecutive years of test data. Matched students are likely to have 

higher test scores and thus make it more likely that their subgroups and school reaches the AMO. 

While the match rates in the pilot states that provided the information were generally very high, 

the potential of a few exclusions to affect AYP results suggests that states consider using nonmatched students’ status results rather than excluding them from otherwise growth-only 

applications.

2. Applying both growth and status criteria to all schools’ AYP determinations

The GMPP required states to compile student-level data on both status and growth criteria, and 

these data could be used to classify each school simultaneously on both criteria for AYPreporting purposes. That is, each school could be classified as making AYP by both growth and 

status, by growth-only, by status-only, by a mix of status and growth, or by safe-harbor only. 

This would have the advantage of uniquely identifying different sets of schools (those making 

AYP in terms of both growth and status). A possible hierarchy for reporting purposes would be:

• Met AMO by growth and by status (best)

• Met AMO by growth but not status

• Met AMO by status but not growth

• Met AMO by combining status and growth results, so that status results are used for 

students not on-track to proficiency

• Did not make AMO (worst)

A disadvantage is that some states (e.g., Delaware and Iowa) classified all students who were 

proficient using the status criterion as also being on-track to proficiency on the growth criterion, 

regardless of their prior year scores. This would have the effect of increasing the number of 

“met by growth and status” schools and would prevent comparisons with states that measured 

growth for proficient and non-proficient students.
Evaluation of the Growth Model Pilot Project 59

References

Booher-Jennings , J. (2005). “Below the Bubble: ‘Educational Triage’ and the Texas 

Accountability System.” American Educational Research Journal, 42: 231–268.

Chudowsky, N., Chudowsky, V., and Kober, N. (2009). Is the Emphasis on “Proficiency”

Shortchanging Higher- and Lower-Achieving Students? Center for Education Policy, 

Washington, D.C. Retrieved July 2009 from http://www.cepdc.org/index.cfm?fuseaction=document_ext.showDocumentByID&nodeID=1&Documen

tID=280.

Council of Chief State School Officers (CCSSO) (2008). Implementer’s Guide to Growth. 

Washington, D.C. Retrieved May 2008 from 

http://www.ccsso.org/content/pdfs/IGG%20Final%20AP.pdf.

Neal, D., and Schantenback, D. (2008). Left Behind By Design: Proficiency Counts and TestBased Accountability. Retrieved September 2008 from 

http://derek.a.neal.googlepages.com/restat_rev_final_200809.pdf.

U.S. Department of Education, Office of Elementary and Secondary Education (Jan. 15, 2009). 

Evaluation of the 2005-06 Growth Model Pilot Program. Washington, D.C. Retrieved 

Feb. 2009 from http://www.ed.gov/admins/lead/account/growthmodel/gmeval0109.doc.

U.S. Department of Education, Office of Elementary and Secondary Education (July 2007). No 

Child Left Behind Fact Sheet: “Growth Models: Ensuring Grade-Level Proficiency for 

All Students by 2014.” Washington, D.C. Retrieved May 2008 from 

http://www.ed.gov/admins/lead/account/growthmodel/proficiency.pdf.

U.S. Department of Education (Jan. 25, 2006).“Peer Review Guidance for the NCLB Growth 

Model Pilot Applications.” Washington, D.C. Retrieved May 2008 from 

http://www.ed.gov/policy/elsec/guid/growthmodelguidance.pdf.

U.S. Department of Education, Office of the Secretary, Office of Public Affairs (2003). No Child 

Left Behind: A Parent’s Guide. Washington, D.C. Retrieved May 2008 from 

http://www.ed.gov/parents/academic/involve/nclbguide/parentsguide.pdf.

U.S. Department of Education (2008). “U.S. Secretary of Education Margaret Spellings 

Approves Additional Growth Model Pilots for 2007–2008 School Year”, press release, 

June 10, 2008. Retrieved June 2008 from

http://www.ed.gov/news/pressreleases/2008/06/06102008.html. 

U.S. Department of Education, Office of Communications and Outreach (2009). “U.S. Secretary 

of Education Margaret Spellings Approves Additional Growth Model Pilots for 2008–

2009 School Year”, press release, Jan. 8, 2009. Retrieved January 2009 from

http://www.ed.gov/news/pressreleases/2009/01/01082009a.html.
Evaluation of the Growth Model Pilot Project 60

U.S. Department of Education, Office of Communications and Outreach (2006). “Secretary 

Spellings Approves Additional Growth Model Pilots for 2006–2007”, press release, Nov.

9, 2006. Retrieved June 2008 from

http://www.ed.gov/news/pressreleases/2006/11/11092006a.html. 

U.S. Department of Education, Office of Communications and Outreach (2005). “Secretary 

Spellings Announces Growth Model Pilot, Addresses Chief State School Officers’ 

Annual Policy Forum in Richmond”, press release, Nov. 18, 2005. Retrieved May 2008 

from http://www.ed.gov/news/pressreleases/2005/11/11182005.html.

U.S. Department of Education, Office of Planning, Evaluation and Policy Development, Policy 

and Program Studies Service (2007). State and Local Implementation of the No Child Left 

Behind Act, Volume III—Accountability Under NCLB: Interim Report, by K. LeFloch, 

F. Martinez, J. O’Day, B. Stecher, J. Taylor, and A. Cook. Washington, D.C.
Evaluation of the Growth Model Pilot Project 61

Appendix A.

Comparison of GMPP Growth Models with 

State Accountability Systems

Of the eight states approved for the GMPP for the 2006–07 school year, four already had 

implemented formal measures of student growth for state accountability purposes before their 

GMPP models were approved. A fifth state included growth as an optional measure, while the 

remaining two had begun developing growth models before joining the GMPP (one of which has 

since been implemented). In comparison, a 2007 survey by the Council of Chief State School 

Officer’s (CCSSO) Accountability Systems and Reporting State Collaborative on Assessment 

and Student Standards (ASR-SCASS) found that only six of the 23 responding states had fully 

operational non-AYP growth models and fewer than half calculated any form of growth at all.25

This suggests that states with growth modeling experience were better positioned to apply for 

and receive approval to participate in the federal program. In fact, the two states first approved 

for GMPP had the most prior experience using student progress to grade schools. Exhibit A.1 

provides brief descriptions of each state’s pre-GMPP growth model.

 25 See http://edmeasure.com/ASR/doku.php?id=asr:survey_results (retrieved May 2008). A GAO survey in March 

2006 found that 26 of 50 states were using growth models, of which seven measured individual student growth 

(GAO–06–948T). Three of those states are in the GMPP, and our review of documentation suggests that three other 

GMPP states were using (or about to use) student growth information for state accountability purposes.
Evaluation of the Growth Model Pilot Project 62

Exhibit A.1 Overview of Growth Components of State Accountability Systems

State

Non-AYP 

Growth 

Model

Year 

Implemented

Grades and 

Subjects 

Covered Growth Standards Applied School Progress Measured Other Features

Alaska School 

Performance 

Incentive 

Program

2007–08 3–10

Reading/Writing/ 

Math

Growth is measured using 

seven categories of 

performance

Points are awarded for 

student movement among 

performance categories and 

are averaged to create a 

school index score

Four performance levels are 

used to reward schools 

according to their growth index 

scores

Arizona Measure of 

Academic 

Progress 

(MAP)

1999–2000, 

revised 2005–

06

4–8

Reading/Math

Growth is measured using 

annual differences in scale 

scores and are averaged to 

calculate school growth

Points are awarded for 

meeting expected growth (by 

quartile) and are added to 

other measures of school 

performance (AZ LEARNS)

Expected growth is calculated 

using a value-added model 

adjusted to ensure proficiency 

by seventh grade and 

controlling for mobility/ceiling 

effects

Arkansas Act 35 Annual 

School 

Ratings 

System

2003–04, 

growth added 

in 2008–09

3–11

Reading/Writing/ 

Math

Student growth is based on 

changes in eight 

performance levels across 

adjacent years. 

Value points are added if a 

student moves up a 

performance category and 

are lost if a student moves 

down a category

School are evaluated using 

five performance levels for 

both “improvement” (Category 

One) and “status” (Category 

Two)

Delaware n/a n/a n/a n/a n/a n/a

Florida Grading 

Florida Public 

Schools

2001–02 3–10

Reading/Math/ 

Science/Writing

Growth is measured by 

movement among five 

performance levels

Grades schools by awarding 

points for the number of 

students meeting proficiency 

standards plus those making 

annual learning gains

Points also are awarded for 

students who maintain high 

performance, for the percent of 

students in the lowest quartile 

making gains, and if half or 

more of such students make 

gains

Iowa Optional n/a K–12

Reading/Math/

Social Studies/

Science

Growth for student profiles is 

measured using changes in 

ITBS and ITED scores

n/a n/a

Exhibit A.1 continues next page
Evaluation of the Growth Model Pilot Project 63

Exhibit A.1 Overview of Growth Components of State Accountability Systems

continued from previous page

State

Non-AYP 

Growth 

Model

Year 

Implemented

Grades and 

Subjects 

Covered Growth Standards Applied

School Progress 

Measured Other Features

North 

Carolina

ABCs Growth 

Model

1996–97, 

revised 2005–

06

K–8, HS

Reading/Math/ 

Science

Growth is the average of 

standardized scores from 

two previous years adjusted 

for regression to the mean 

and is expected to be “0” or 

above, indicating at least 

one year’s worth of gain

A mean growth score is 

calculated for the school, 

though schools can also 

meet expected growth if 60

percent or more of students 

test at grade-level 

proficiency 

Schools get credit for “high 

growth” if students who are 

stable or growing outnumber 

those declining by at least 

three to two [or a ratio of 3:2]

Ohio Value-Added

Assessment

2006–07 4–8, plans for 

K–10

Reading/Math

Growth is measured as 

mean NCE gains and is 

categorized as meeting or 

as being a standard error 

“above” or “below” the 

“expected” gain

LRC designations can be 

raised if schools are above 

expected growth for at least 

two years and lowered if 

below expectations for at 

least three years

Value-added is based on the 

2006–07 distribution of test 

scores and will be used for 

accountability beginning in 

2007–08

Tennessee Tennessee 

Value-Added 

Assessment 

System 

(TVAAS)

1992–93 3–8

Reading/Math/ 

Language/ 

Science/Social 

Science

Growth in TCAP results is 

measured as mean NCE 

gains relative to a state 

growth standard (1998 Terra 

Nova) or a state three-year 

average

School reports include 

average student gains by 

grade and whether 

achievement level meet 

growth standards or are 

within one, two, or more 

standard deviations 

Specific school effects also 

are estimated using up to five 

years of student data to 

predict scores for the average 

student in a given school; 

teacher effect data is 

restricted access
Evaluation of the Growth Model Pilot Project 64

However, these state accountability growth models had to be modified in significant ways for 

use in GMPP. One basic difference between models approved under ESEA and those used for 

state accountability purposes is the definition of expected growth. The seven core principles 

require that the ESEA growth models place limits on the amount of time students have to reach 

proficiency, usually by the last grade tested as applied, resulting in growth expectations that put a 

student “on-track” to meet grade-level standards in a few years. Most state growth models do 

not require students to be on-track to proficiency but, for example, simply expect students to 

exhibit a year’s worth of growth per year of instruction. The principle of universal proficiency 

by 2014 also translates into rising AMOs, a requirement that is absent from state accountability 

systems. The goal of states in most cases is to determine whether individual schools and the 

system as a whole are improving rather than to see if a given student will be proficient in a few 

years or if a school will have all students proficient by 2014. 

Another major difference is that growth components of state accountability systems typically 

calculate an average for the entire school instead of basing school performance on the results of 

each subgroup separately, and may average over subjects as well. This means that a school can 

still make adequate growth for state accountability purposes even if one or more subgroups fails 

to grow or if the school exhibits strong growth in one subject but not another. Of course this 

does not mean that growth results for subgroups and subjects are not reported, and states often

measure growth for more than reading and math. The goal is to create a composite growth score 

that can then be combined with other measures of school performance (including AYP) both for 

reporting purposes, such as a “grade” on school report cards, and for rewarding schools that meet 

or exceed state standards. 

The result of these differences is that more schools tend to make adequate growth for state 

accountability purposes than would make AYP under the GMPP. For example, 779 of the 1,298 

(or 60 percent) of the North Carolina schools that failed to make AYP in 2006–07 made expected 

growth under the state guidelines. Of these, 187 (or 14 percent) met the state standards for high 

academic growth. The federal growth model used by North Carolina sets the bar higher for both 

expected growth and percent proficient (AMO) than does the growth model used for state 

accountability, suggesting that the universal proficiency requirement is driving most if not all of 

this difference. Florida also drops the proficiency deadline in its grading system, although the 

transition matrix model used sets expectations that may differ from a single year’s worth of 

growth.26

Offsetting this tendency of the 2014 deadline to lower the number of schools making adequate 

growth is that state accountability systems do not give schools credit if enough students grow to 

push a subgroup or school over the proficiency threshold as is done in the status-plus-growth 

models implemented under the GMPP.

The school itself can make adequate growth if half or more of low achievers meet 

expected growth, which is a different standard than the AMO used for AYP purposes. Thus 

about 84 percent of Florida schools made adequate growth in both reading and math for 

2006–07, compared to the 34 percent of schools that made AYP under the GMPP. 

27

 26 Note that students who score in the two lowest FCAT achievement levels still can make expected growth if they 

make a year’s worth of growth as determined by FCAT developmental scores.

This means that schools classified as making AYP by 

27 Note that states often give growth credit to schools for maintaining proficiency, which is similar to a growth-plusstatus model, and may grade schools on proficiency status criteria as well.
Evaluation of the Growth Model Pilot Project 65

growth may not be showing much growth for the student body as a whole. Thus of the 12 North 

Carolina schools that made AYP by growth in 2006–07, only three met the state’s high growth 

standard and one did not make the lower standard of expected growth. Similarly, 10 of the 19 

Tennessee schools that made AYP by growth in 2006–07 grew at a rate below the state threeyear average for math, while 14 schools grew at a below average rate for reading. One school 

even experienced negative growth for both reading and math. Growth models are only one 

component of federal accountability under the GMPP and thus do not provide much information 

about whether a school is growing as currently reported. However, results from growth 

measures used for state accountability purposes suggest that many more schools would make 

AYP if the first of the seven core principles of the ESEA project was relaxed.
Evaluation of the Growth Model Pilot Project 66
Evaluation of the Growth Model Pilot Project 67

Appendix B: State GMPP Model Summaries

The core of each growth model is the method of determining whether a student is “on-track” to 

being proficient. While states’ methods can be categorized as one of three types of growth 

models (trajectory, transition matrix, or projection), each state’s method has unique features. 

This appendix offers additional details about the growth models used in Alaska, Arizona, 

Arkansas, Delaware, Florida, North Carolina, and Tennessee. All the relevant detail of Iowa’s 

growth model is included in the main text.

Alaska

Alaska uses a trajectory model that calculates growth for students in grades 4 through 6, grade 8 

and grade 9, using results of the Alaska Standards Based Assessment Test mathematics and 

language arts. 

Proficiency levels for these tests are scaled so that thresholds are 300 for math and 600 for 

literacy within each grade. The literacy score is cutoff at 600 because it is a combination of 

reading and writing, each of which has a cutoff of 300 points. For this summary we will 

consider a generic cutoff score of 300 for each grade. 

Students are always classified by the traditional status model in grades 3 and 7. In grades 4 

through 6 it is possible to use the growth model. In the Alaska growth model the first year a 

student is below proficient is considered their base year, and growth targets for subsequent years 

are calculated by evenly dividing the difference between the base year score and the cutoff in 

grade 7. In grades 8 and 9, the first year a student is below proficient is considered the base year, 

and growth targets for subsequent years are calculated by evenly dividing the difference between 

the base year score and the cutoff in grade 10. 

For example, if a student scores below proficient in some grade q (between grades 3 and 6), 

growth targets for each subsequent grade is a function of their base score in grade q, Yq, plus the 

difference between this score and 300 weighted fraction of the years that have elapsed between 

the previous grade and grade 7. Thus, a student in grades 4 through 6 is considered to be ontrack toward proficiency in grade k if their score, Yk

Y Y Y kq q kq q ≥+ − × − − (300 ) (( ) (7 ))

, is greater than or equal to this function,

, assuming k > q and Yq

For students who score below proficient in some grade q between grades 7 and 10, growth 

targets for each subsequent grade is a similar function of their base score in grade q, Y

< 300.

q, plus the 

difference between this score and 300 weighted fraction of the years that have elapsed between 

the previous grade and grade 10. Thus, a student in grades 8 or 9 is considered to be on-track

toward proficiency in grade k if their score, Yk

Y Y Y kq q kq q ≥+ − × − − (300 ) (( ) (10 ))

, is greater than or equal to this function, or, 

, assuming k > q and Yq

These targets, once established by the baseline year, remain the growth targets for subsequent 

years.

< 300.
Evaluation of the Growth Model Pilot Project 68

The illustration in exhibit B.1 below showcases this process. This figure shows the proficiency 

standard for each grade (300) along the solid line connecting points a to i. The shaded polygons 

illustrate the necessary growth between years to be on-track toward proficiency for a set of 

hypothetical students. 

Exhibit B.1

Illustration of Alaska’s Method for Determining Whether a Student Is On-Track Toward

Proficiency

Label a b c d e f g h i

Grade 3 3 4 5 6 7 8 9 10

Score 300 200 226 250 275 200 234 267 300

Student Z is below proficient in the third grade, he scored 200 (point b) instead of the proficiency 

standard of 300. In applying the formulas above, Alaska’s growth model would set a new target 

score of 226 in the fourth grade (point c), 250 in grade 5 (point d), and 275 in grade 6 (point e), 

to be considered on-track for those grades. While that student cannot be used for growth model 

AMO calculations in the third grade, that student will be expected to make those targets 

calculated for subsequent years to be considered as on-track in grades 4 through 6. Similarly, 

student X is below proficient in the seventh grade, he scored 200 (point f) instead of the 

proficiency standard of 300. In applying the formulas above, Alaska’s growth model would set 

new target scores of 234 in the eighth grade (point g), and 264 in grade 9 (point h), to be 

considered on-track for those grades. While that student cannot be used for growth model AMO 

calculations in the seventh grade, that student will be expected to make those targets calculated 

for subsequent years to be considered as on-track in grades 8 and 9. 
Evaluation of the Growth Model Pilot Project 69

Arizona

Arizona uses a trajectory model to set growth targets for students in grades 3 through 8 using 

Arizona’s Instrument to Measure Standards (AIMS) test. The score cutoffs for reading and math 

are presented in Exhibit B.2.

Arizona, like other states using trajectory models, sets growth targets for students who are not 

proficient based on a baseline score. Growth targets are set by determining the necessary 

improvement to reach proficiency and setting evenly spaced improvement targets over a given 

set of years. In Arizona, growth targets are set based on the first non-proficient score. Growth 

targets calculated from a baseline score in K through third grade require the student to reach 

proficiency by the sixth grade. Growth targets calculated based on a fourth grade score require 

the student to be proficient by seventh grade. Growth targets calculated based on scores in 

grades 5, 6, and 7 require the student to be proficient by the eighth grade. Growth targets are 

reset each year based on student performance and movement in and out of the Arizona public 

school system. However, the specific grade required to reach proficiency does not change when 

targets are reset. 

Exhibit B.2

Arizona Proficiency Standards Test Cutoffs for Grades 3 Through 8

Grade Reading Cutoff Math Cutoff

3 431 420

4 450 448

5 468 476

6 478 496

7 489 517

8 499 537

While each student is assigned growth targets based on actual performance, Arizona is unique 

compared to other growth model pilot states in that schools are evaluated on each student’s 

estimated score instead of students’ actual score. However, in calculating the proportion of 

students within a school who are considered to be on-track toward proficiency, students are 

classified based on the lower bound of their predicted scores. These predicted scores are 

generated from a statewide statistical model which fit current year scores to scores from the 

previous years. 
Evaluation of the Growth Model Pilot Project 70

Arizona estimates a regression model predicting the current year scores of all students by their 

previous year’s score. Let Yit

Yit = α + βYit−1 + ei

be the score from student i in grade k in school j at the current 

year t, . From this model, Arizona predicts each student’s current score, 

1

* Y Y it = + α β it− . There is a statewide standard error, *Y t

SE , associated with each year’s 

predicted score, which typically equals about 4 or 5 scale score points. The score used to 

evaluates a student’s growth, Yit

* , is then a lower bound of a confidence interval estimated 

around the predicted score, or * * 1.96 Lower

it it Y t

Y Y SE   =− ×    . As a result, each student is 

evaluated not on their actual score, but on this lower bound of an estimated predicted score. 

The illustration in exhibit B.3 below showcases this process. This figure shows the proficiency 

standards for grades 4, 5, 6, 7, and 8 along the solid line connecting points a, c, i, l, and m. The 

shaded polygons illustrate the necessary growth between years to be on-track toward proficiency 

for a of hypothetical student. 

Student Z is below proficient in the fourth grade, he scored 446 (point b) instead of the 

proficiency standard of 450 (point a). Arizona’s growth model would set a new target score of 

460 in the fifth grade (point e) to be considered on-track. Student Z then scored exactly 454 in 

the fifth grade (point f), which is below the necessary growth target. However, the student 

predicted score is 465 (point d), which is above the growth target. Yet, the school will be unable 

to count that student as on-track because the lower bound of the predicted confidence interval is 

457 (point d*), still better than the actual score, but also still below the growth target. The 

student actual fifth grade score is then used to estimate a new growth target of 469 in the sixth

grade (point j). 

Student Z then did well in the sixth grade, scoring 484 (point g), well above the normal cutoff of 

478 (point i). However, that student’s predicted score is 480 (point h) with a lower bound 472 

(point h*). Because the lower bound is still greater than the growth target, that student can then 

be counted as on-track. Under a growth-only model, that student’s growth target for seventh

grade would be higher than the normal cutoff (point k instead of point l) because that student’s 

actual sixth-grade score was greater than the normal cutoff as well. 
Evaluation of the Growth Model Pilot Project 71

Exhibit B.3

Illustration of Arizona’s Method for Determining Whether a Student Is On-Track

Toward Proficiency

Label a b c e d d* f g h h* i j k l m

Grade 4 4 5 5 5 5 5 6 6 6 6 6 7 7 8

Score 450 446 468 460 465 457 454 484 480 472 478 469 491 489 499

Arkansas

Arkansas uses a trajectory model that calculates growth for students in grades 4 through 7 using 

results of the Arkansas Benchmark Exams for mathematics and literacy, which are administered 

in grades 3 through 8 (plus grade 11 for literacy). 

Proficiency levels for these vertically scaled exams are set for each grade, and growth targets are 

based on the annual exam score increment needed to reach the proficiency standard in eighth

grade. These proficiency standards are presented in table B.4 below.
Evaluation of the Growth Model Pilot Project 72

Exhibit B.4

Arkansas Benchmark Exam Proficiency Standards for Grades 3 Through 8

Grade Proficiency Standard

3 500

4 559

5 604

6 641

7 673

8 700

If a student does not achieve proficiency in a base year, the growth targets necessary to be 

considered on-track toward proficiency are calculated based on the total increment between a 

student’s base score and the proficiency standard in eighth grade (700). However, instead of 

setting growth targets by evenly dividing the total increment between the base score and 700, the 

increments are proportioned so that the growth increments follow a curve that matches the 

concave nature of the typical proficiency standards. 

This means that, for example, instead of setting the growth increment from third to fourth grade 

to be a quarter (0.25) of the total necessary improvement to reach 700 by eighth grade, the 

growth increment for fourth grade is set to slightly more than a quarter (0.295) of the total 

necessary improvement to reach 700 by eighth grade. Thus, the annual increment that a student 

must attain in order to be classified as on-track to proficiency is calculated using grade-specific 

growth target multipliers. The multiplier for any grade “k” is simply a ratio of the difference 

between the current and previous year’s proficiency standards, Pk and Pk-1

Pk − P ( k −1 ) 700 − P ( k −1 )

, to the difference 

between the proficiency standard for eighth grade and the previous year, or, 

.

These multipliers are presented in Exhibit B.5.

Exhibit B.5

Arkansas Growth Target Multipliers for Grades 3 Through 7

Grade Multiplier

4 0.295

5 0.319

6 0.385

7 0.542

Another method of illustrating a specific growth increment is to use the following formula that 

calculates the minimum score necessary to be considered on-track toward proficiency. For any 

student in grade k, the minimum score necessary to be considered “on-track” is his or her

previous score, Yk-1,, plus the difference between 700 and his or her previous score, 700-Yk-1, 
Evaluation of the Growth Model Pilot Project 73

times the multipliers outlined above. Thus, if the current score, Yk

YY PP P Y kk kk ≥+ − − × − − −− − 1 11 1 ((( ) (700 700 k )) ( k ))

, is greater than or equal to 

this function, or, 

,

that student is considered to be on-track toward proficiency. From this formula, we see that this 

model resets the growth target every year rather than setting a series of annual targets based on 

the first below-proficient exam score. This formula can also determine minimum scores even for 

students who score above the proficiency threshold. Thus, students can be identified that are not 

improving toward the eighth grade standard of 700 even though they are currently proficient.

The illustration in exhibit B.3 below showcases each of these features. This figure shows the 

proficiency standards for each grade along the solid line connecting points a, c, g, k, m and n. 

The shaded polygons illustrate the necessary growth between years to be on-track toward

proficiency for a set of hypothetical students. 

Student Z is below proficient in the fourth grade, he scored 505 (point d) instead of the 

proficiency standard of 559 (point c). In applying the formulas above, Arkansas’ growth model 

would set a new target score of 567 in the fifth grade (point i) to be considered on-track. If 

student Z scored exactly 567 in the fifth grade, then his growth targets would follow the dotted 

line from point i to point n. In addition, imagine that student Z in fact did better than scoring 567 

in the fifth grade—let us say that he scored 575 (point h). Then, that student’s growth target for 

sixth grade would be reset and instead would be 623 (point l). Note that because student Z did 

better than his growth target in the fifth grade, his new growth target for the sixth grade is 

slightly higher—point l is above the dotted line from point i to point n. 

Another student, student X, scored well above the standard in fourth grade at 600 (point b). By 

applying the same formula, the Arkansas growth model would set a fifth-grade target score of 

632 (point e), which is likewise well above the proficiency standard of 604 (point g). Next, 

imagine that student X scored lower than his target score in fifth grade—let us say he scored 615 

(point f). Student X scored above proficient in fifth grade, but because is score is lower than his 

target score generated from fourth grade, he is not considered to be on-track toward proficiency. 

The Arkansas model does reset scores each year, and so we can see that his target for sixth grade 

is set at 648 (point j), which is closer to the proficiency standard of 641 (point k). Note that his 

sixth-grade target is below the dotted line from point e to point n. This shows that his new target 

score is reflecting that he did not score as high in the fifth grade as he did in the fourth grade. He 

would need to score at least 691 in the seventh grade (point k), which is more than the normal 

seventh-grade proficiency standard of 673 (point l). 
Evaluation of the Growth Model Pilot Project 74

Exhibit B.6

Illustration of Arkansas’ Method for Determining Whether a Student Is On-Track

Toward Proficiency

Label a b c d e f g h i j k l m n

Grade 3 4 4 4 5 5 5 5 5 6 6 6 7 8

Score 500 600 559 505 632 615 604 575 567 648 641 623 673 700

Delaware

Delaware’s transition matrix model uses a “value table” method for AYP determinations that 

assigns points for students depending on the type and extent of changes between the performance 

levels (see Exhibit 6 in the report). Points in the value table increase with both the magnitude of 

change in level of proficiency, and the overall level of proficiency. As a result, a student scoring 

toward the bottom during his previous grade receives fewer points for moving up one level than 

he would if he moved up several levels. All students who surpass their grade level cutoff receive 

the maximum points regardless of how high they scored or whether their underlying scores 

actually declined from the prior year. From these points assigned to students, schools meet their 

AMO if the average number of points per student meets or exceeds a target number of points set 

by Delaware for particular subjects and grades. 

Delaware’s point system is designed to be an analogue to the AMO system used for status 

models by giving partial weight to students who are below proficient but still making progress. 

In fact, the target number of points that Delaware sets is simply the standard AMO that is 

rescaled to the point system. 
Evaluation of the Growth Model Pilot Project 75

For example, in the 2006–2007 school year the status model AMO for reading was 68 percent

proficient. For that same year, the target number of points that a school’s students needed to 

gain on average was 204. If we divide the target points by the maximum number of points a 

student can receive, we return to the AMO (204/300 = 0.68). To illustrate how a school meeting 

the AMO under the status model would perform under the growth model, imagine two schools 

with 100 students, school Z and school X (see exhibit B.7 below) 

In the first school, school Z, exactly 68 out of 100 students (68 percent) were proficient in 

reading. That school meets the AMO of 68 percent exactly. Let us assume that in this school all 

students who were below proficient did not move up any categories from their previous grade. 

Then, under Delaware’s growth model, that school would receive 

68 × 300 = 20400 points,

out of a total possible 

100 × 300 = 30000 points.

The average number of points per student would be

20400

100 = 204 ,

which is exactly the target number of points a school needs to make their AMO under the growth 

model, and the number of achieved points, 20,400, is exactly 68 percent (the AMO) of the total 

possible 30,000 points. Thus school Z would make their AMO under both the status model and 

the growth model. 

To illustrate how a school that would not meet its AMO under the status model, but would make 

its AMO under the growth model, consider another school X which also has 100 students, but 

only 30 students are proficient. Under the status model, only 30 percent of the students are 

proficient, which is well below the target AMO of 68 percent. Yet, the school does have many 

students who are improving. Under the growth model, the proficient students account for only

30 × 300 = 9000 points,

which is only 30 percent of the total possible 30,000 points. Remember, though, school X has 

students who are improving, including 30 students who moved from PL 1A to PL 1B for 

30 × 150 = 4500 points,

and another 15 students moved from PL 1B to PL 2A for 

15 × 175 = 2625 points,

and another 15 students moved from PL 1B to PL 2B for 

15 × 225 = 3375 points,
Evaluation of the Growth Model Pilot Project 76

and 5 students who did not improve, who stayed at PL1A for 

5 × 0 = 0 points.

That school would total 20,500 points out of a possible 30,000 points. That would be 68.3

percent of the total possible points, greater than the AMO for reading that year. The average 

number of points per student would be 205, which is larger than the 204 points necessary to meet 

the AMO. Under the growth model, school X would meet the AMO.

This means that Delaware’s status model is actually like a simple transition matrix in which all 

students who are proficient are given the maximum number of points, and all student who are 

below proficient are given no points at all. The growth model, then, gives students who improve 

a partial number of points. The table in Exhibit B.7 can be used to estimate the proportion of the 

total points each improvement is worth. Another way to think about Delaware’s growth model is 

that a student who moves from the first level, PL 1A, to the second level, PL 1B, is given half 

(0.50) the weight of a student who is proficient when the percent proficient is calculated. This 

means that in Delaware’s transition matrix system, two students who move from the first to the 

second level equal one student who is proficient. 
Evaluation of the Growth Model Pilot Project 77

Exhibit B.7

Example Comparison of Two Hypothetical Schools in

Delaware to Illustrate Growth Model

School Z School X

Year 1 Year 2

Points Per 

Student

Proportion 

of Total 

Possible 

Points

Number of 

Students Per 

Cell

Points 

Per Cell

Number of 

Students 

Per Cell

Points 

Per 

Cell

PL 1A PL 1A 0 0.00 0 0 5 0

PL 1A PL 1B 150 0.50 0 0 30 4,500

PL 1A PL 2A 225 0.75 0 0 0 0

PL 1A PL 2B 250 0.83 0 0 0 0

PL 1A Proficient 300 1.00 0 0 0 0

PL 1B PL 1A 0 0.00 0 0 0 0

PL 1B PL 1B 0 0.00 0 0 0 0

PL 1B PL 2A 175 0.58 0 0 15 2,625

PL 1B PL 2B 225 0.75 0 0 15 3,375

PL 1B Proficient 300 1.00 0 0 0 0

PL 2A PL 1A 0 0.00 0 0 0 0

PL 2A PL 1B 0 0.00 0 0 0 0

PL 2A PL 2A 0 0.00 0 0 0 0

PL 2A PL 2B 200 0.67 0 0 5 1,000

PL 2A Proficient 300 1.00 0 0 0 0

PL 2B PL 1A 0 0.00 0 0 0 0

PL 2B PL 1B 0 0.00 0 0 0 0

PL 2B PL 2A 0 0.00 0 0 0 0

PL 2B PL 2B 0 0.00 32 0 0 0

PL 2B Proficient 300 1.00 0 0 0 0

Proficient PL 1A 0 0.00 0 0 0 0

Proficient PL 1B 0 0.00 0 0 0 0

Proficient PL 2A 0 0.00 0 0 0 0

Proficient PL 2B 0 0.00 0 0 0 0

Proficient Proficient 300 1.00 68 20,400 30 9,000

Total 100 20,400 100 20,500

Percent Proficient Year 2 68% 30%

Average Points 204 205

Meet AMO by Status (68% proficient)? Yes No

Meet AMO by Growth (204 Average Points)? Yes Yes
Evaluation of the Growth Model Pilot Project 78

Florida

Florida’s growth model applies to students in grades 3 through 10 using the Developmental Scale 

Scores (DSS) from the Florida Comprehensive Assessment Tests (FCAT) for mathematics and 

reading. The state uses a trajectory model that bases growth targets on the score required for 

proficiency three years after the first year tested (usually, grade 3). To be counted as proficient, 

a student who was not proficient at the baseline must close the gap between his baseline score 

and the proficiency cutoff three grades later by one-third each year. This means that a student 

can only make proficiency by growth for two years because the gap must be fully closed in the 

third year, (i.e., a student must meet or exceed the minimum proficiency score in year 3). A 

student first enrolled in grade 9 must close the gap by half to be counted as “on-track.” The 

cutoffs for grades 3 through 7 are presented in Exhibit B.8.

Exhibit B.8

Florida’s Cutoff Developmental Scale Scores to Be Considered Proficient 

on the FCAT for Grades 3 Through 7

Grade DSS Cutoffs for Reading DSS Cutoffs for Math

3 1198 1269

4 1456 1444

5 1510 1632

6 1622 1692

7 1715 1786

The illustration in exhibit B.9 below showcases this process for reading. The bold line 

connecting points a, c, f, i, and k represent the FCAT DSS score cutoffs for reading for grades 3 

through 7. The shaded polygons represent the growth increments necessary to be considered ontrack toward proficiency. To illustrate the properties of Florida’s growth model, let us revisit 

student Z and student X. 

Student Z is below proficient. He scored 1326 in fourth grade (point d), which is below the 

grade-specific cutoff of 1456. Florida’s growth model would then set growth targets for the 

following two years, fifth grade and sixth grade, by dividing the difference between his fourthgrade score and the seventh-grade cutoff into thirds. In other words, he would be expected to 

close the gap between his fourth-grade score and the seventh-grade cut-off by a third during the 

first year after he was not proficient (fifth grade). In turn, he would be expected to close the gap 

by two-thirds after two years of not being proficient (sixth grade). He would then be expected to 

be proficient after three years (seventh grade). Geometrically, this is drawing a straight line from 

point d at grade 4 to point k at grade 7. This line then sets growth targets at point g and point j 

for grades 5 and 6, respectively. Thus, the growth target for student Z in fifth grade is 1455 

(point g) and 1586 in sixth grade (point j). 
Evaluation of the Growth Model Pilot Project 79

Exhibit B.9

Illustration of Florida’s Method for Determining Whether a Student Is On-Track

Toward Proficiency in Reading

Label a b c d e f g h i j k

Grade 3 4 4 4 5 5 5 6 6 6 7

Score 1198 1548 1456 1326 1603 1510 1455 1659 1622 1586 1715

Unlike Arkansas’ trajectory model, Florida’s method is not intentionally designed as a method 

for tracking the progress of proficient students. Florida does not scale growth targets to match 

the pattern of cutoff scores. As a result, this method is very sensitive to the pattern of cutoffs set 

for each grade. This means that if this method were used to draw growth targets for proficient 

students, then the magnitude of the higher expectations would fluctuate each grade, depending 

on grade-by-grade standards. Furthermore, the problem of how far above the cutoff a growth 

target would be for any one grade would greatly depend on which grade was used for the base 

year. 

For example, imagine that student X scored 1548 (point b) in the fourth grade, which is 92 points 

above the cutoff of 1456 (point c). Let us further assume that for some reason, that score was 

used at a baseline for future growth targets. As a result, that student’s growth targets would be 

represented by the line from point b to point k. By following that line we see that student X 

would have to score 1603 points to be considered on-track (point e), which is 93 more points 

than the cutoff of 1510 in the fifth grade (point f). He would not be expected to score as many 

more points in sixth grade, however, because the cutoff scores increase by a large amount 

between the fifth and sixth grades. In the sixth grade, student X would have to score 1659 (point 
Evaluation of the Growth Model Pilot Project 80

h), or only 37 more points than the cutoff of 1622 (point i). This illustrates that students who 

score above proficient would be subject to inconsistent expectations because the pattern of cutoff 

scores in Florida is not linear, and the model is not designed to mimic the pattern of standards 

from grade to grade or reset expectations.

North Carolina

North Carolina uses a trajectory model to identify growth targets and both End-of-Grade (EOG) 

tests and End-of-Course (EOC) tests for assessing student progress. The state uses a 

Standardized Scale Approach (SSA) to growth which uses the normative distribution of student 

performance in the standard setting year of any test edition as a common basis to build a scale. 

State documents note that this approach is useful for measuring the growth in student 

performance from one year to the next and also adapts well to the changes in curriculum and 

subsequent changes in test editions.

The SSA system uses a time-locked modified z-scale termed a “change scale” or “c-scale.” 

Thus, the c-scale cut score for proficiency on any given test edition at an individual grade level 

remains constant for the life of the scale and test edition regardless of the changes in the 

distribution of test scores that might occur as schools change their instructional methods. The 

state means and standard deviations from the standard setting year are used indefinitely for any 

given test. 

The 2005–06 school year was the standard setting year for the Mathematics EOG tests at grades 

3–8 and the 2002–03 school year was the standard setting year for the Reading EOG tests in 

grades 3–8. NC performs an equating study to set the achievement level cut scores at the same 

time the c-scale is built. 

The trajectory is built based on the student’s performance either the previous year, or on the 

third- grade pretest, whichever is appropriate to the grade in which the student first enters the 

state. Therefore, the following table illustrates the basis for prediction, the targeted test for 

proficiency, the years of trajectory, and the percent of difference between baseline performance 

and proficiency expected by the trajectory based on the year the student is first enrolled in the 

state in a tested grade.

Exhibit B.10 Grades and Tests Used for Trajectory Growth in North Carolina and the 

Percent of Difference Expected to Be Closed Per Year

Grade of First 

Enrollment

Test Used as the 

Basis for 

Prediction

Test Used as Target for 

Proficiency

Years to 

Proficiency

Percent of 

Difference 

Closed Per 

Step

Steps to 

Proficiency

3 3rd grade pretest 6th grade EOG 4 25% 4

4 4th grade EOG 7th grade EOG 4 33% 3

5 5th grade EOG 8th grade EOG 4 33% 3

6 6th grade EOG Algebra I or English I EOC 4 33% 3

7 7th grade EOG Algebra I or English I EOC 4 50% 2

8 8th grade EOG Algebra I or English I EOC 3 100% 1
Evaluation of the Growth Model Pilot Project 81

The trajectories are built individually by student and separately for reading or mathematics. 

Therefore, a student will have a trajectory based on their baseline mathematics score and the 

proficiency cut score for mathematics separate from reading. In the upper grades, Algebra I is 

the AYP assessment for 10th-grade students and is the trajectory target for math while English I 

is the trajectory target for reading or language arts.

The following table displays the performance expected of students to be counted as on trajectory 

for inclusion in the proposed method of comparing school performance to AMO targets.

For a student who enters in third grade and has a grade 3 pretest:

Year in State-Tested Grade

Decrease From Baseline Assessment in Performance 

Discrepancy

1 25% of Original Gap

2 50% of Original Gap

3 75% of Original Gap

4 or more Student Must Be Proficient

For a student who enters in fourth, fifth, or sixth grade:

Year in State-Tested Grade

Decrease From Baseline Assessment in Performance 

Discrepancy

1 Baseline, Not On Trajectory

2 33% of Original Gap

3 66% of Original Gap

4 or more Student Must Be Proficient

Therefore, if a subgroup has met its 95 percent participation target but has not met its proficiency 

target, and the subgroup has met its other academic indicator, the process of incorporating the 

growth measure would be:

1) First identify if the student has been in membership the full academic year and is both 

tested and not proficient.

2) These three conditions being met, the number of years the student has been in the state 

will be determined using the historic files from the state’s accountability system.

3) If the student has been in the state (in a tested grade) for four years or more, the student 

will remain non-proficient for comparison to the annual measurable objectives (AMO). 

If the student has been in the state public schools three years or less, the correct baseline 

score will be located (using the table above).

4) The student’s performance on the baseline assessment in the subject of interest will be 

converted to the c-scale.

5) Based on the student’s baseline score and proficiency in the target year, a difference will 

be calculated.

6) The decrease in the difference will be compared against Table 4 above based on the 

number of years in the tested grades in North Carolina.
Evaluation of the Growth Model Pilot Project 82

7) If the student’s performance on the current assessment is equal to or better than the 

minimum from the previous step, include the student in the percent proficient calculation 

to compare against the state’s AMOs.

To illustrate, assume a student enters North Carolina in the fourth grade. The student scores 

below proficient in the current school year in reading. This child’s known test scores are listed 

below.

Grade 3 EOG 4 EOG 5 EOG

Developmental Score Not in NC 229 241

C-scale score -2.68 -1.98

Because the student’s first full year in the state is the fourth-grade year, the student will need to 

be on trajectory to be proficient by the end of the seventh grade and thus on the seventh-grade 

EOG for reading. The developmental score for seventh grade reading equivalent to proficient is 

252. The associated c-scale score is -1.00.

Because the student was not in the state for the third-grade test, the fourth-grade EOG score will 

be used as the baseline. The difference between the baseline and proficient on the seventh grade 

test in terms of c-scale scores is 1.68 (difference between 2.68 and 1.00). For the current year 

(fifth grade, the second year in the state), the student must perform well enough on the test to 

have 33 percent less difference between the c-scale score for proficiency and his baseline 

(fourth- grade EOG) c-scale score (divide 1.68 by 3 = 0.56). 

For this to be true, the child would need to score at least -2.12 (difference between 2.68 and 

0.56). The child’s actual c-scale score is -1.98 which means the child met the standard to be 

deemed on trajectory for the current year and thus will be included in the percent of students on 

trajectory or proficient for comparison to the AMO for the school as a whole and any subgroups 

to which the child may belong.

Tennessee

Adapted from “Evaluation of the 2005–06 Growth Model Pilot Program,” U.S. Department of 

Education, 2009.

Tennessee uses a projection model to assess student growth. The state uses a student’s history of 

test scores in an equation to project or predict that student’s future score. To complete this 

process, previous cohorts of student scores are used in generating a prediction equation that can 

be applied to the current cohort of students. For example, last year a cohort of sixth-graders in 

Tennessee were tested on the state reading exam. These same sixth-graders also had scores from 

the state reading exam for grades 3, 4, and 5. The scores on the sixth-grade reading test are 

placed in a matrix called Y. The reading scores for grades 3–5 are placed in a matrix called X. 

All the reading scores from grades 3–6 are combined into a design matrix called XY. The 

matrices are used in a statistical procedure to generate a covariance matrix called C with 

submatrices CXX and CXY (CYX = CXY

T

) and CYY. These submatrices are used for various 

statistical functions but primarily in calculations for b = CXX-1CYX to generate the regression 
Evaluation of the Growth Model Pilot Project 83

coefficients b1, b2, ... bN

Projected Score = M

. For example, the projected score is computed using variations of the 

following equation:

Y + b1(X1 – M1) + b2(X2 – M2) + ... + = MY + xi

T

b

where MY, M1, etc. are estimated mean scores for the “future test score” or response variable (Y). 

The previous test scores can also be referred to as the “predictor variables.” To complete 

projected scores in the equation you make the following substitutions:

MY

b

= estimated mean score on test

1, b2, ... bN

X

= regression coefficients used to predict performance

1, X2, ... XN

M

= previous reading scores

1, M2, ... MN = average school reading scores

The Tennessee model includes a statewide “average schooling effect,” which is obtained by 

calculating the mean scores for each grade of a particular school and then averaging those means 

over all schools within the state. It is intended to account for the fact that a current school has no 

control over the effectiveness of the schools that their students will attend in the future (thus 

potentially affecting the student’s growth). The average schooling effect assumes that each 

student will have the “average schooling experience” of all Tennessee schools. 

Tennessee’s model projects scores for all students, estimating each student’s performance in 

reading and math in three years. Each student’s projection is based upon his or her available test 

scores. For example, student A has reading scores for 2003, 2004, and 2005 whereas student B 

has reading scores for 2003 and 2005. In both cases, projected scores are computed using the 

equation described above using student-specific values.
Evaluation of the Growth Model Pilot Project 84

Exhibit B.11

Illustration of Tennessee’s Method for Determining Whether a Student Is On-Track

Toward Proficiency in Reading

In Exhibit B.11, student A is currently below proficient (year 1) but projected to be proficient in 

year 4. In Tennessee’s growth model, student A would be considered proficient in year 1 for 

AYP determinations and in each of the succeeding years if he or she continues to be on this 

trajectory to proficient. 

Student B is missing data for 2004. Tennessee addresses the issue of missing test scores by 

using the regression coefficients from (b = CXX-1CYX) and constants in the equation described 

above to fill in the missing test scores. Thus, all relevant student data are included in projecting 

score for a student. Using the available data for student B, a growth trajectory is developed that 

shows a projected decline in performance, though the student is projected to remain above 

proficient. Because student B is projected to remain above proficient by year 4, student B is 

proficient for the current year AYP determinations. If student B’s projection indicated he or she 

would fall below proficient, student B would be considered non-proficient in the current year 

AYP determinations.