U.S. Department of Education

Institute of Education Sciences

NCES 2006-031

Teacher Qualifications, 

Instructional Practices, 

and Reading and 

Mathematics Gains of

Kindergartners

Research and Development 

Report
 
U.S. Department of Education

Institute of Education Sciences

NCES 2006-031

Teacher Qualifications, 

Instructional Practices, 

and Reading and 

Mathematics Gains of

Kindergartners

Research and Development 

Report

March 2006

Cassandra M. Guarino

Laura S. Hamilton

J.R. Lockwood

RAND Corporation

Amy H. Rathbun

Education Statistics Services Institute

Elvira Germino Hausken

Project Officer

Institute of Education Sciences

National Center for 

Education Statistics
U.S. Department of Education 

Margaret Spellings 

Secretary

Institute of Education Sciences 

Grover J. Whitehurst 

Director

National Center for Education Statistics

Mark Schneider 

Commissioner

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March 2006 

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Suggested Citation 

Guarino, C.M., Hamilton, L.S., Lockwood, J.R., and Rathbun, A.H. (2006). Teacher Qualifications, 

Instructional Practices, and Reading and Mathematics Gains of Kindergartners (NCES 2006-031). U.S. 

Department of Education. Washington, DC: National Center for Education Statistics. 

For ordering information on this report, write to 

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Content Contact

Elvira Germino Hausken 

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elvira.hausken@ed.gov
iii 

Executive Summary 

There is increasing interest among educators, policymakers, and researchers in understanding the 

factors that make some teachers more effective than others, particularly in light of the current 

focus on educational accountability at the local, state, and national levels. Thus far, only a small 

body of research exists, however, that links specific teacher qualifications to student 

achievement. The lack of research is due primarily to the scarcity of data that link student test 

scores to the characteristics of their teachers. Furthermore, although scholars and policymakers 

agree that children’s early school and family experiences are pivotal, relatively little research 

exists on the effects of teachers on the educational outcomes of young children. 

This study fills a gap in the current research base on the relationship among teacher 

characteristics, instructional practices, and the achievement of young children through an 

analysis of data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 

(ECLS-K). These data were collected by the National Center for Education Statistics (NCES), 

within the U.S. Department of Education’s Institute of Education Sciences, from a nationally 

representative sample of the nation’s 1998–99 kindergarten class. The students were assessed in 

reading and mathematics in both the fall and the spring of their kindergarten year, and detailed 

information was gathered from their parents, teachers, and school administrators. In particular, 

the teachers were surveyed with regard to their background qualifications and the instructional 

practices they use in the classroom. As a result, ECLS-K data may provide information relevant 

to the relationships between teacher-reported qualifications and instructional practices and 

student achievement during the kindergarten year.

Data from ECLS-K were used to estimate the degree to which specific aspects of teacher 

training—the teaching credential and coursework in pedagogy—and teaching experience were 

associated with student achievement. In addition, the study identified teacher-reported 

instructional practices associated with student achievement gains and examined the qualifications 

of teachers and aspects of teacher training that were related to the use of these practices. Thus, 

the study addressed the following research questions: 

• To what extent are kindergarten teachers’ qualifications and instructional practices 

associated with gains in reading and mathematics of their students over the course of the 

kindergarten year? 

• How are the instructional practices of kindergarten teachers related to their 

qualifications? 

Using two-level hierarchical linear modeling (HLM), the first set of analyses estimated the 

relationship between student gains in reading and mathematics and teachers’ reports of their 

qualifications and the specific instructional practices they used in their classrooms. The second 

set of analyses, also using two-level HLM, estimated the relationship between teachers’ reports 

of their use of specific instructional practices and their qualifications. Comparisons in the text 

were tested for statistical significance to ensure that the differences were larger than might be 
iv 

expected due to sampling. Only coefficients with a p value of .05 or less were identified as being 

statistically significant.1

Spending more time on subject and working within a full-day kindergarten structure were found 

to be associated with relatively large gains in achievement. Teacher-reported instructional 

practice measures designed to emphasize reading and writing skills, didactic instruction, phonics, 

and reading and writing activities were positively associated with reading achievement gains. 

Instructional emphasis on traditional practices and computation, measurement and advanced 

topics, advanced numbers and operations, and student-centered instruction were positively 

associated with mathematics achievement gains. The study provided no evidence of direct 

relationships between the self-reported qualifications of teachers and student achievement except 

for employment status. Children whose kindergarten teachers were employed part time made 

smaller gains in reading than those whose teachers were employed full time. 

The analyses conducted in response to the second research question found evidence that certain 

teacher background variables—particularly the self-reported amount of coursework in methods 

of teaching reading and mathematics—were positively related to the teacher-reported frequency 

of various instructional practices that, in turn, were associated with higher student achievement. 

The completion of coursework in methods of teaching reading was positively associated with the 

use of phonics instruction, mixed-achievement grouping, student-centered instruction, and 

reading and writing activities. Coursework in methods of teaching mathematics was positively 

associated with the use of practices that emphasized numbers and geometry, advanced numbers 

and operations, traditional practices and computation, student-centered instruction, and mixedachievement grouping. In addition, kindergarten teaching experience was negatively related to 

the use of student-centered instruction in reading and positively related to the use of mixedachievement grouping in mathematics. Teacher certification appeared unrelated to reported 

instructional practices, with the exception of a positive association with an emphasis on concepts 

of measurement and advanced topics in mathematics. 

Certain caveats should be noted. Since teachers are not randomly assigned to schools and 

students are not randomly assigned to teachers or schools, the relationships found in this study 

cannot be interpreted as causal. They are instead to be interpreted as a description of existing 

relationships that is reflective of the de facto distribution of teachers and children within the 

education system. Despite these limitations, this study utilizes a full set of control variables that 

help mitigate selection bias and provide valuable new information regarding the relationships 

between student achievement, teacher-reported instructional practices, and teacher-reported 

qualifications for the kindergarten population. The rich data, their nested structure, and the 

longitudinal nature of the assessments permit analyses that provide new information regarding 

existing relationships between student achievement, instructional practices, and teacher 

qualifications for the kindergarten population.

 

1

Standard t test values were used to determine whether individual regression coefficients were greater than zero. 
v 

Foreword 

The Research and Development (R&D) series of reports at NCES has been initiated to 

1. share studies and research that are developmental in nature. The results of such studies 

may be revised as the work continues and additional data become available. 

2. share the results of studies that are, to some extent, on the “cutting edge” of 

methodological developments. Emerging analytic approaches and new computer software 

development often permit new and sometimes controversial analyses to be done. By 

participating in “frontier research,” we hope to contribute to the resolution of issues and 

improved analysis. 

3. participate in discussions of emerging issues of interest to education researchers, 

statisticians, and the federal statistical community in general. R&D reports may 

document workshops and symposia sponsored by NCES that address methodological and 

analytical issues or may share and discuss issues regarding NCES practices, procedures, 

and standards. 

The common theme in all three goals is that these reports present results or discussions that do 

not reach definitive conclusions at this point in time, either because the data are tentative, the 

methodology is new and developing, or the topic is one on which there are divergent views. 

Therefore, the techniques and inferences made from the data are tentative and subject to revision. 

To facilitate the process of closure on the issues, we invite comment, criticism, and alternatives 

to what we have done. Such responses should be directed to 

Marilyn Seastrom 

Chief Statistician 

Statistical Standards Program 

National Center for Education Statistics 

1990 K Street NW 

Washington, DC 20006-5651 

vii 

Acknowledgments 

The authors wish to thank Sandy Eyster of the Education Statistics Services Institute (ESSI) and 

Jerry West, formerly the Program Director of the Early Childhood and Household Studies 

(ECHS) Program of the National Center for Education Statistics (NCES) and currently with 

Mathematica Policy Research, Inc., for their helpful comments and assistance with the 

development of this report. We thank Lizeth Bejarano of the RAND Corporation for her clerical 

support and Greg Ridgeway, also with RAND, for his statistical support. We also appreciate the 

support provided by Elvira Germino Hausken, NCES project officer for the Early Childhood 

Longitudinal Study, Kindergarten Class of 1998–99 (ECLS-K), and Chris Chapman, NCES 

Program Director for ECLS-K. In addition, we appreciate the technical review comments 

provided by Marilyn Seastrom, Val Plisko, Kashka Kubzdela, and John Ralph of NCES; Lisa 

Bridges of the Institute of Education Sciences (IES); and Rachel Dinkes, Devin Carlson, Heather 

Freilich, and Stephen Mistler of ESSI. Special thanks also go to Mike Rollins of ESSI for his 

graphical support for the report. 

ix 

Contents 

 Page 

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

Foreword......................................................................................................................................... v 

Acknowledgments......................................................................................................................... vii 

List of Tables .................................................................................................................................. x 

1. Introduction................................................................................................................................. 1 

2. Background................................................................................................................................. 3 

Characteristics of Effective Teachers ................................................................................. 3 

Instructional Practices and Student Achievement............................................................... 4 

3. Data............................................................................................................................................. 7 

Achievement Assessments.................................................................................................. 7 

Student Characteristics........................................................................................................ 8 

Teacher Qualifications........................................................................................................ 9

Instructional Practices......................................................................................................... 9 

School Characteristics....................................................................................................... 12

4. Methods..................................................................................................................................... 13 

Statistical Models.............................................................................................................. 13 

Data Transformations and Sample Sizes .......................................................................... 15 

5. Findings..................................................................................................................................... 17 

Reading Achievement Gain Regressions.......................................................................... 17 

Instructional Practice Scale Regressions for Reading ...................................................... 23 

Mathematics Achievement Gain Regressions .................................................................. 26 

Instructional Practice Scale Regressions for Mathematics ............................................... 32 

Sensitivity Analyses.......................................................................................................... 33 

6. Summary................................................................................................................................... 35 

Limitations ........................................................................................................................ 35 

Discussion......................................................................................................................... 37 

Future Research Using ECLS-K Data .............................................................................. 38 

References..................................................................................................................................... 39 

Appendix A: ECLS-K Direct Cognitive Assessment Measures................................................. A-1 

Appendix B: Methodology Used in the Development of the Instructional Practice Scales ....... B-1 

Appendix C: Methodology Used in the Regression Analyses.................................................... C-1 

Appendix D: Sample Statistics for Variables Used in Analyses ................................................ D-1 

Appendix E: Standard Errors From Regression Models..............................................................E-1 
x 

List of Tables 

Table Page 

1. Standardized regression coefficients for the regression of kindergarten student 

achievement gains in reading on instructional practice scales: School year 

1998–99..............................................................................................................................19 

2. Standardized regression coefficients for the regression of kindergarten student 

achievement gains in reading on teacher qualifications: School year 1998–99 ................21 

3. Standardized regression coefficients for the regressions of kindergarten teachers’ 

reading instructional practice scales on selected teacher qualifications and school 

characteristics: School year 1998–1999.............................................................................25 

4. Standardized regression coefficients for the regressions of kindergarten student 

achievement gains in mathematics on instructional practice scales: School year 

1998–99..............................................................................................................................28 

5. Standardized regression coefficients for the regression of kindergarten student 

achievement gains in mathematics on teacher qualifications: School year 

1998–99..............................................................................................................................30 

6. Standardized regression coefficients for the regressions of kindergarten teachers’ 

mathematics instructional practice scales on selected teacher qualifications and 

school characteristics: School year 1998–1999 .................................................................34 

A-1. Means, standard deviations, and ranges of values for the ECLS-K base-year 

(kindergarten) reading and mathematics assessments: Fall 1998 and spring 1999 ........ A-4 

B-1. Kindergarten teacher reading instructional practice scales and item means: Spring 

1999..................................................................................................................................B-3 

B-2. Kindergarten teacher mathematics instructional practice scales and item means: 

Spring 1999......................................................................................................................B-4 

B-3. Reliabilities and correlations for kindergarten teacher reading instructional 

practice sum scores and IRT scores: Spring 1999 ...........................................................B-5 

B-4. Coefficient alpha reliabilities for kindergarten teacher mathematics instructional 

practice scales: Spring 1999.............................................................................................B-5 

B-5. Bivariate correlations of the kindergarten teacher reading instructional practice 

scales: Spring 1999 ..........................................................................................................B-5 

B-6. Bivariate correlations of the kindergarten teacher mathematics instructional 

practice scales: Spring 1999.............................................................................................B-6 

D-1. Unweighted sample statistics for variables used in child-level analyses: School 

year 1998–99................................................................................................................... D-1 

D-2. Unweighted sample statistics for variables used in teacher-level analyses: School 

year 1998–99................................................................................................................... D-3 

D-3. Bivariate correlations of the kindergarten teacher qualification variables: School 

year 1998–99................................................................................................................... D-4 
xi 

E-1. Standard errors of the standardized regression coefficients for the regressions of 

kindergarten student achievement gains in reading on instructional practice scales: 

School year 1998–99........................................................................................................E-1 

E-2. Standard errors of the standardized regression coefficients for the regressions of 

kindergarten student achievement gains in reading on teacher qualifications: 

School year 1998–99........................................................................................................E-3 

E-3. Standard errors of the standardized regression coefficients for the regressions of 

kindergarten teachers’ reading instructional practice scales on selected teacher 

qualifications and school characteristics: School year 1998–99......................................E-5 

E-4. Standard errors of the standardized regression coefficients for the regressions of 

kindergarten student achievement gains in mathematics on instructional practice 

scales: School year 1998–99............................................................................................E-6 

E-5. Standard errors of the standardized regression coefficients for the regression of 

kindergarten student achievement gains in mathematics on teacher qualifications: 

School year 1998–99........................................................................................................E-8 

E-6. Standard errors of the standardized regression coefficients for the regressions of 

kindergarten teachers’ mathematics instructional practice scales on selected 

teacher qualifications and school characteristics: School year 1998–99.......................E-10 

1 

1. Introduction 

There is increasing interest among educators, policymakers, and researchers in understanding the 

factors that may make some teachers more effective than others. The current focus on 

educational accountability at the local, state, and national levels underscores the importance of 

understanding these factors. Only a limited body of research exists that links specific 

qualifications of teachers to student achievement. The evidence that teachers with credentials 

promote student achievement more effectively than those without credentials is somewhat 

tenuous and mixed (Fetler 1999; Goldhaber and Brewer 2000). Some research finds small 

relationships between teachers’ subject-matter expertise and the achievement of their students 

(Goldhaber and Brewer 2000; Monk 1994). One of the primary reasons for the lack of a large 

body of definitive research on the topic of teacher effectiveness is the paucity of data that link 

student test scores to the characteristics of their teachers. Furthermore, although scholars and 

policymakers agree that children’s early school and family experiences are pivotal, relatively 

little research exists on the effects of teachers on the educational outcomes of young children. 

This study aims to fill a gap in the existing body of research on relationships linking teacher 

qualifications and teaching practices to the achievement of young children through an analysis of 

data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 (ECLS-K). 

These data were collected by the National Center for Education Statistics (NCES), within the 

U.S. Department of Education’s Institute of Education Sciences, from a nationally representative 

sample of the nation’s 1998–99 kindergarten class. Students were assessed in reading and 

mathematics in both the fall and the spring of the kindergarten year. Their parents were 

interviewed extensively about family circumstances and demographics. Children’s teachers were 

surveyed regarding their qualifications and the instructional practices they use in the classroom. 

Also, children’s school administrators were surveyed with regard to school characteristics. As a 

result, ECLS-K data may provide information relevant to the relationships linking self-reported 

teacher qualifications and instructional practices to student achievement during the kindergarten 

year.

In this study, data from ECLS-K are used to estimate the degree to which specific aspects of 

teacher training—the teaching credential and coursework in pedagogy—and teaching experience 

are associated with student achievement. In addition, the study identifies the teacher-reported 

instructional practices associated with student achievement gains and examines the types of 

training that are related to the use of these practices. Specifically, the study addresses the 

following research questions: 

• To what extent are kindergarten teachers’ qualifications and instructional practices 

associated with gains in reading and mathematics of their students over the course of the 

kindergarten year? 

• How are the instructional practices of kindergarten teachers related to their 

qualifications? 

The relationships revealed in this study cannot be interpreted as causal due to the lack of random 

assignment of children to teachers and schools. However, this study addresses unanswered 
2 

questions regarding the relationships linking the qualifications and instructional practices of 

kindergarten teachers to achievement outcomes. This report is organized as follows. Section 2 

discusses the existing research on teacher effectiveness and instructional practices. Section 3 

describes the data, and section 4 presents the methods used in this study. Section 5 presents the 

findings. Section 6 discusses the findings as well as possibilities for extending this research. 

In addition, the report contains five appendixes. Appendix A provides a description of the ECLSK direct cognitive assessment measures. Appendix B provides a description of the methodology 

used to create the instructional practice measures used in this study. Appendix C provides a 

description of the methodology used in the regression analyses. Appendix D presents sample 

statistics for variables used in this study. Appendix E presents the standard errors associated with 

the coefficients in the regression analyses included in the main text of the report. 
3 

2. Background 

Recent studies have suggested that teachers exert a significant influence on student learning. In 

particular, studies with elementary school students using value-added modeling approaches 

report that the overall effects of teachers may be large (Rowan, Correnti, and Miller 2002; 

Wright, Horn, and Sanders 1997). If the findings of large teacher effects are accurate, they 

suggest that efforts to improve education for all students must seek to identify the characteristics 

that distinguish effective from ineffective teachers. However, the research literature devoted to 

detecting the effects of specific teacher qualifications is inconsistent and sparse. Furthermore, 

few nationally representative studies have focused on relationships between teacher 

qualifications, instructional practices, and children’s achievement in kindergarten. This section 

provides a brief discussion of existing research on the effects of teacher qualifications on student 

achievement. This discussion is followed by a summary of the literature that has examined 

relationships between specific instructional practices and student achievement. 

Characteristics of Effective Teachers 

Studies that have examined available indicators of teacher preparation or quality—such as 

academic ability, certification status, subject-matter expertise, and experience—offer mixed 

findings, suggesting that there is not yet a consensus as to what characteristics influence 

achievement. Prior research focusing on the impact of credentials and preservice training (e.g., 

studies to obtain a teaching credential) on the quality of instruction has found inconsistent results 

regarding the impact of the teaching credential and small positive effects regarding subjectmatter preparation. Hawk, Coble, and Swanson (1985) found that for secondary school students, 

mathematics achievement was positively associated with having a teacher who was fully 

certified in mathematics. Fetler (1999) found a negative correlation at the school level between 

mathematics scores and the percentage of teachers with emergency credentials. In an analysis 

using individual student data, however, Goldhaber and Brewer (2000) found that the 

performance of high school students on standardized mathematics and science tests did not differ 

according to whether their teachers held standard or emergency credentials. They found, 

however, that students of teachers who were uncertified or who held a private school 

certification in mathematics had somewhat lower achievement levels than students of teachers 

with a standard, probationary, or emergency certification. Rowan, Correnti, and Miller (2002) 

found no effect of certification status on achievement growth at the elementary level. One caveat 

to be applied to studies dealing with teaching credentials is that the credential is not a standard 

measure of preparation, because requirements vary widely from state to state. Thus, the type of 

credential a teacher holds is a somewhat imperfect measure of preservice training. 

With regard to subject-matter preparation, Monk (1994), in a study of secondary high school 

students that controlled for prior test scores, found a positive effect of teacher coursework in both 

college mathematics and mathematics pedagogy on mathematics test scores. Goldhaber and 

Brewer (2000) found a weak positive association between high school achievement gains in 

mathematics and teachers with a master’s degree in mathematics versus those without a master’s 

degree or a mathematics-related bachelor’s degree. A recent study focusing on elementary school 
4 

students found no significant evidence of an impact of advanced degrees on achievement gains 

(Rowan, Correnti, and Miller 2002). 

With regard to teaching experience, Fetler (1999) found a positive relationship between the 

average number of years of teaching experience of mathematics teachers and high school 

mathematics scores at the school level. Rowan, Correnti, and Miller (2002) found a positive 

relationship between teaching experience and growth in mathematics achievement for students as 

they progressed from third to sixth grade. Murnane and Phillips (1981), in a study of the 

achievement of Black inner-city elementary school students that controlled for prior-year test 

scores, found a nonlinear relationship between achievement and teaching experience. For 

students in grades three, four, and six, having teachers with 15 or more years of experience was 

positively associated with gains. For fourth- and sixth-grade students, having teachers with 7 or 

fewer years of experience was also positively associated with gains. For students in the third 

grade, having teachers with 8 to 14 years of experience was negatively associated with gains. 

ECLS-K data provide information on several aspects of teacher training and qualifications, 

including teachers’ reports of their certification status, years of kindergarten teaching experience, 

and advanced degree status. In addition, the data provide valuable information not normally 

collected by other surveys, such as the amount of training teachers have received in methods of 

teaching reading and mathematics and the categories of instructional practices they use. Thus, 

this study was able to follow, in many cases, and extend the approaches used in prior studies 

with older children. In addition, ECLS-K data provide an opportunity to explore the relationship 

between teachers’ self-reported qualifications and instructional practices, as well as the links 

between each of these categories of factors and student achievement. 

Instructional Practices and Student Achievement 

To the extent that any of the characteristics explored in the previous section influence student 

learning, it is likely that they exert their effect in large part via the instructional practices that 

teachers use in the classroom. Early childhood reading researchers recommend that attention be 

given in every primary-grade classroom to a wide array of early reading skills including the 

alphabetic principle, reading sight words, reading words by mapping speech sounds to parts of 

words, achieving fluency, and comprehension (Snow, Burns, and Griffin 1998). In kindergarten, 

Ball and Blachman (1991) found that children who received instruction in phonemic 

segmentation and letter-sound combinations had higher reading and spelling scores than children 

who did not receive such instruction. While there is general agreement on the skills that should 

be taught, approaches on how best to teach reading are often debated. Some research with 

primary-grade children has shown that no single approach to teaching reading is superior to the 

rest, but that balanced or integrated early literacy instruction (i.e., instruction that includes an 

emphasis on both phonetics and meaning) is more effective in learning to read (Adams 1990; 

Chall 1992; Snow, Burns, and Griffin 1998). Certain teaching strategies and methods have also 

been found to be associated with greater gains in early mathematics learning. A meta-analysis of 

studies including kindergarten research found that the use of concrete materials or manipulatives, 

compared with more abstract instruction, was related to improved achievement and attitudes 

toward mathematics (Sowell 1989), especially during initial exposure to a skill (Baroody 1989). 

Also, problem-solving activities and opportunities to practice what is learned have been shown to 
5 

contribute to learning mathematics concepts and skills in the first years of school (National 

Research Council 2001). 

The measurement of instructional practices, however, is less straightforward. Most studies that 

examine classroom practices and the links between these practices and achievement have relied 

exclusively, or primarily, on teacher self-reports of the frequency with which teachers use 

specific practices such as cooperative learning groups, inquiry-based activities, manipulatives, 

and open-ended assessment techniques. 

Several of the studies that have used this method of measuring practices have examined links 

between student achievement and teacher-reported use of practices that emphasize problem 

solving and inquiry. These practices are often called “reform based” or “standards based” and 

include such activities as cooperative learning groups, student-led discussions, and open-ended 

assessment techniques that are intended to promote the development of complex cognitive skills 

and processes (Cohen and Hill 2000; Hamilton et al. 2003). Cohen and Hill’s (2000) study of 

teacher-reported use of reform-based practices found that frequency of use was positively related 

to mathematics test scores among fourth-graders. D’Agostino (2000) found that in first and 

second grades, teacher-directed basic skill orientation was associated with greater reading and 

mathematics achievement, while in fourth grade, a combination of basic skill instruction and 

student-centered advanced skill activities was associated with greater mathematics achievement.

A synthesis of data from 11 National Science Foundation-funded Systemic Reform Initiatives 

found a mixture of null and small positive results on both multiple-choice and open-response 

assessments for upper elementary and middle school teachers and students (Hamilton et al. 

2003). Several studies have attempted to examine whether the relationship between achievement 

and reform-based practices is different from the relationship between achievement and more 

traditional forms of instruction, such as the use of textbooks, lectures, and multiple-choice tests 

(Cohen and Hill 2000; Hamilton et al. 2003). Most of the differences in the relationships 

between student achievement and each of these types of practice have been found to be small. 

The small magnitudes of observed relationships may be attributable in part to measurement 

problems. Limited evidence exists regarding the extent to which survey-based measures of 

practices accurately capture what teachers do in the classroom. Stipek and Byler (2004) recently 

compared observational data of teacher instructional practices in kindergarten and first-grade 

classrooms with teachers’ self-reported practices, using instructional practice items that were 

similar in content to the ECLS-K item set, and found that teachers’ reports of their instructional 

practices were significantly correlated with observations of their practices. Mayer (1999) reports 

results of a study that compared information obtained from survey responses to information 

collected from classroom observations of middle school and high school algebra teachers. 

Results from his study indicated that a composite of teachers’ emphasis on reform-based 

mathematics teaching practices based on survey data was strongly correlated (r = .85) with a 

parallel composite based on classroom observations of the teachers’ mathematics instruction. He 

found that the survey data could be used to distinguish teachers who engaged in low levels of 

reform-based practices from those who relied heavily on such practices, but his study also 

suggested that survey results masked potentially important differences among teachers in how 

they implemented various practices. However, Mayer (1998) noted that when composites of 

individual teacher practice variables from one-time teacher surveys were grouped together to 

describe teachers’ pedagogical style, the reliability of the resulting composites was quite high. As 
6 

a result of these measurement issues, the observed weak effects between instructional practices 

and achievement may result from superficial implementation by teachers (which is not captured 

by frequency-based survey responses) rather than from the practices’ ineffectiveness. In addition, 

the kinds of instructional practices measured by most surveys constitute only a small part of the 

classroom instructional environment. Other aspects, such as the specific curriculum materials 

used and the pacing of instruction, are often not measured. 

Despite the limitations of paper-and-pencil frequency-based measures of practice, they currently 

provide one of the best sources of information about the distributions of instructional practices 

used by teachers across the nation. Surveys provide a cost-effective and reliable method for 

gathering data on practices across different state and district contexts. 

Most of the existing research on practices has focused on teachers at the higher elementary and 

secondary grades. Because of the growing recognition of the importance of developing literacy 

and quantitative skills from the earliest grades, there is a need to extend the work on instructional 

practices to include kindergarten and other early elementary grade levels. ECLS-K data on the 

instructional approaches used by kindergarten teachers permit this type of exploration. Xue and 

Meisels (2004) used these data to examine several classroom-level predictors of reading 

achievement and found that teachers’ reported use of a phonics-based approach, in particular, 

was related to achievement in reading (effect size of 0.06). The research described in this report 

builds on this work and extends it to mathematics. 
7 

3. Data 

ECLS-K data provide detailed information on a nationally representative sample of 22,000 

children enrolled in approximately 1,000 kindergarten programs, both public and private, in the 

United States during the 1998–99 school year. The two waves of data utilized in this study were 

collected in the fall and spring of the 1998–99 kindergarten year. This study uses five categories 

of data: achievement assessments, student characteristics, teacher qualifications, instructional 

practices, and school characteristics. 

Achievement Assessments 

Assessments that included cognitive, psychomotor, and physical components were conducted 

with the sampled kindergarten children through one-on-one tests administered by trained 

individuals both at the beginning and at the end of the school year.1

 Having both fall and spring 

measures is one of the features that distinguishes ECLS-K data from other longitudinal study 

data and makes them uniquely suited for an investigation of teacher effects over the course of the 

kindergarten year. 

The full achievement assessment used a computer-assisted personal interview (CAPI) and took 

approximately 50–70 minutes to complete. It included tests of reading, mathematics, and general 

knowledge. The test was untimed and required children to respond verbally or through pointing; 

no writing was required. Each test was conducted using a two-stage design, known as adaptive 

testing. The first stage consisted of a routing section that was administered to all students, and 

the second stage consisted of one of several alternative forms, the choice of which depended on 

(i.e., was adapted to) the child’s performance on the first stage. Although the assessments 

included a general knowledge test, only the assessments in reading and mathematics were used 

in this study. The reading and mathematics assessments had low-, middle-, and high-difficulty 

second-stage adaptive options. The purpose of this adaptive design was to maximize accuracy of 

measurement and minimize administration time.2

The content of the reading and mathematics assessments was selected to represent cognitive 

skills that are typically taught in kindergarten and that are thought to be important for the 

development of later proficiency (Rock and Pollack 2002). The reading test consisted of items 

measuring basic skills (e.g., letter recognition), vocabulary, and comprehension. The 

mathematics test covered five content strands: number sense, properties, and operations; 

measurement; geometry and spatial sense; data analysis, statistics, and probability; and patterns, 

functions, and algebra. Items tapping all five content strands are included in the kindergarten 

assessment, although the first strand (number sense, properties, and operations) is most heavily 

 

1

More detail about the ECLS-K achievement assessments is provided in appendix A of this report. 

2

See the ECLS-K Base-Year Public-Use Data Files and Electronic Codebook: User’s Manual (Tourangeau et al. 

2001) or the Early Childhood Longitudinal Study—Kindergarten Class of 1998–99 (ECLS-K), Psychometric Report 

for Kindergarten through First Grade (Rock and Pollack 2002) for a more complete description of the assessment 

procedures. 
8 

represented. Examples of the types of skills involved in this strand at the kindergarten level 

include counting sets of objects and solving simple addition problems using pictures. Examples 

of skills included in the measurement strand include comparing the length of two objects and 

identifying the value of different coins. Examples of skills in the geometry and spatial sense 

strand include naming simple shapes and identifying lines of symmetry. Skills in the data 

analysis, statistics, and probability strand include reading information from a bar graph. 

Examples of skills in the patterns, functions, and algebra strand in the kindergarten assessment 

include recognizing and extending patterns and sequences. 

Efforts were made to include children who spoke a language other than English in the 

assessments. Prior to administering the assessments, a language-screening test—the Oral 

Language Development Scale (OLDS)—was administered to those children identified from their 

school records (or by their teachers if no school records were available) as coming from homes 

in which the primary language spoken was not English. Children whose performance exceeded 

an established cut score on the OLDS received the full English direct assessment in both reading 

and mathematics. Those who did not pass the OLDS were not given the reading assessment. 

Students who did not pass the OLDS but who spoke Spanish were given a translated form of the 

mathematics assessment. Thus, the size of the sample of children who took the mathematics 

assessment was larger than that of children who took the reading assessment. Various methods 

were used to confirm that the psychometric properties of the Spanish mathematics assessment 

were comparable to those of the English version (Rock and Pollack 2002). 

This report uses children’s fall and spring kindergarten overall achievement scores in reading 

and mathematics, which are Item Response Theory (IRT) scale scores. Children’s IRT scale 

score values are a reflection of the number of items they would have answered correctly on the 

assessment if they had been administered all items in the battery. The IRT scale scores may be 

used to calculate longitudinal measures of gains because the scores from each round of data 

collection are set on a common scale. From the IRT scores, gain scores were created (in the form 

of a simple difference) to represent the change in relative achievement of the child over the 

course of the kindergarten year. All student-level models controlled for the time lapse between 

fall and spring test administrations, since not all children were assessed on the same day. 

Student Characteristics 

Parent interviews were the source of the demographic information utilized in this study. 

Approximately 18,950 parent interviews were completed. Parents reported the race, ethnicity, 

age, and sex of each child and indicated whether the child was repeating kindergarten in the 

1998–99 school year. Parents also provided information about their household income, the 

mother’s (or female guardian’s) educational attainment and occupation, and the father’s (or male 

guardian’s) educational attainment and occupation. NCES used the information from these 

variables to create a socioeconomic status (SES) composite variable, which is standardized with 

a mean of 0 and a standard deviation of 1. Details on the construction of this variable are 

available in the user’s manual for the ECLS-K base-year public-use data file (Tourangeau et al. 

2001). In addition, parents identified the primary language spoken in the home. 
9 

Teacher Qualifications 

Information on 3,305 kindergarten teachers was gathered in a set of self-administered paper-andpencil questionnaires that included questions on their qualifications and instructional practices. 

Measures of qualifications used in this study were years of kindergarten teaching experience, 

employment status (i.e., part time or full time), level of certification, educational attainment (i.e., 

receipt of a master’s degree), and the number of courses completed in methods of teaching 

reading and mathematics. 

With regard to certification, ECLS-K data include information about the type of teaching 

certificate teachers reported they possessed (none; temporary, probational, provisional, or 

emergency; alternative; regular but less than the highest available; and the highest available—

permanent or long term). The analyses in this study distinguish between teachers who have a 

regular or the highest certification available and those who do not. These categories were chosen 

on the basis of the distribution of certifications among teachers given that the vast majority of 

kindergarten teachers in the sample were certified and few teachers fell into the alternatively 

credentialed or noncertified categories (only 2 percent of teachers held alternative credentials and 

another 2 percent were uncertified). 

One of the difficulties inherent in research on national samples is the state-specific nature of 

many education programs and policies. It is important to note here that requirements for teacher 

certification often differ by state. Paths for attaining each type of certification vary across states 

in a number of respects, including the standards for admission into certification programs and the 

amount of in-classroom experience required. Therefore, ambiguities associated with certification 

status must be kept in mind when interpreting results from this study. 

ECLS-K data also include teacher-reported information on the area in which teachers are 

certified (elementary, early childhood, or other). The nature of early childhood and elementary 

certification is particularly variable across states, and it is common for teachers to possess both 

(e.g., by supplementing a standard elementary certification with a special early childhood 

certification). Because of this variation and the lack of clear definitions of early childhood and 

elementary certification, this information is not used in this study. As a result, readers are 

cautioned about the conclusions that can be drawn from results of the relationships between 

certification status and achievement gains. 

Instructional Practices 

The spring teacher questionnaire included a set of items that addressed instructional activities 

and skill emphasis in reading, mathematics, science, and social studies. The first two subjects are 

the focus of this study. The items address a wide range of instructional practices that may occur 

in classrooms in the early grades, not just practices considered to be developmentally appropriate 

for kindergarten.3

 Both the mathematics and reading practice items were selected to be aligned 

 

3

NCES and the authors do not speculate on whether certain types of practices are developmentally appropriate or 

inappropriate for kindergarten children. Instead, this report describes how frequently teachers use different types of 

instructional practices in their classrooms. 
10 

with the skills tested by ECLS-K achievement assessments. Many of the ECLS-K instructional 

practice items are similar in content to other research that uses teacher questionnaires to collect 

data on instructional practices in kindergarten classrooms (Stipek and Byler 2004). 

The items included in the analysis are of two types. One set of items asked teachers, “How often 

do children in this class do each of the following READING and LANGUAGE ARTS 

activities?” Teachers were asked to rate the frequency of each activity, using a scale that ranged 

from 1 (“never”) to 6 (“daily”). Intermediate scale points were 2 (“once a month or less”), 3 

(“two or three times a month”), 4 (“once or twice a week”), and 5 (“three or four times a week”). 

The other set asked, “For this school year as a whole, please indicate how each of the following 

READING and LANGUAGE ARTS skills is taught in your class(es).” For each specified skill, 

teachers could indicate that the skill was not taught, by selecting either “taught at a higher grade 

level” or “children should already know,” or could indicate the frequency with which the skill 

was taught, using a 5-point scale that ranged from “once a month or less” to “daily.” 

Intermediate scale points were the same as for the activities items. Similar sets of questions were 

asked about mathematics instruction. 

As discussed above, for the items that addressed skills taught in reading and mathematics, 

teachers could report that a particular skill was not taught by choosing either “taught at a higher 

grade level” or “children should already know.” For the analyses discussed in this report, which 

focus on the frequency with which teachers emphasize particular skills or topics, these two 

options were combined into a single “not taught” category. The numerical values for all of the 

options were then recoded so that the scale for the “skills” items was similar to that for the 

“activities” items (i.e., the category representing the greatest frequency received a score of 6, and 

the “not taught” category received a score of 1). This procedure enabled the two sets of items to 

be combined into a single factor analysis. Although the difference between the two “not taught” 

options may be of substantive interest for some purposes, because the focus of this research was 

on the amount of exposure students received, combining these categories was appropriate. 

Therefore, item means and factor analyses are based on sets of items with response options 

ranging from 1 to 6. The development of instructional practice scales from these items relies on 

prior work conducted for NCES (Hamilton and Guarino 2005). That study used factor analyses 

to create several scales similar to those used in Cohen and Hill (2000) and Hamilton et al. 

(2003). 

As a result of the factor analyses, seven scales were derived for reading and six scales were 

derived for mathematics. The seven reading scales were phonics; reading and writing skills;

reading and writing activities; didactic instruction; comprehension; student-centered 

instruction; and mixed-achievement grouping. The phonics scale includes items addressing 

teachers’ emphasis on activities such as learning and practicing letters and the importance 

teachers place on skills such as matching letters to sounds and recognizing letters. It is similar to 

the phonics scale used by Xue and Meisels (2004). The reading and writing skills scale measures 

teachers’ reported emphasis on promoting students’ ability to read fluently and to write using 

standard conventions (e.g., capitalization, punctuation, and conventional spelling). The reading 

and writing activities scale focuses on specific activities in which students engage to promote 

reading and writing ability, including reading aloud and writing in journals. Didactic instruction

includes three items that appear to measure more traditional language arts instructional activities 

that students probably do as seatwork—reading from basal texts, working in workbooks or on 
11 

worksheets, and writing words from dictation to improve spelling. Comprehension covers skills 

involved in understanding what is read (e.g., identifying main ideas, making predictions, and 

using context cues). Student-centered instruction appears to address activities in which students 

are responsible for producing something and sharing it with the class (e.g., publishing their own 

writing, performing plays, and doing an activity or project related to a book or story). The final 

scale, mixed-achievement grouping, consists of two items that assess the frequency of mixedachievement grouping and peer tutoring. Internal consistency reliability for the seven reading 

practices scales ranged from .69 to .83, with two exceptions. The reliability of the three-item 

didactic instruction scale was .50, and the reliability of the two-item mixed-achievement 

grouping scale was .48. 

The six mathematics instructional practice scales were numbers and geometry; advanced 

numbers and operations; traditional practices and computation; student-centered mathematics 

instruction; mixed-achievement grouping; and measurement and advanced topics. Some of the 

scales focused on particular content, whereas others related more to the structure of classroom 

instruction. The first scale, numbers and geometry, consists of 11 items, 3 of which address 

classroom activities designed to promote understanding of numbers, operations, and geometry. 

The other eight items in this scale address instructional objectives related to numbers and 

geometry. The second scale, advanced numbers and operations, contains five items from the 

“skills” item set. In contrast to the first scale, these items emphasize skills related to somewhat 

advanced numeracy concepts (e.g., reading two- and three-digit numbers). Traditional practices 

and computation appears to identify teachers who take a fairly didactic, teacher-directed 

approach to instruction and who emphasize computational facility. It includes the use of 

worksheets, textbooks, and problems on the chalkboard and emphasizes computational skills 

such as adding and subtracting single-digit numbers. The fourth scale, student-centered 

mathematics instruction, is similar to the corresponding scale identified for reading, and consists 

of six items that emphasize having students take an active role in their own learning (e.g., 

explaining how a mathematics problem is solved, working on problems that reflect real-life 

situations, and using creative movement or creative drama to understand mathematics concepts). 

The fifth scale, mixed-achievement grouping, consists of two items: use of mixed-achievement 

groups and peer tutoring. Finally, measurement and advanced topics includes one item from the 

“activities” set—work with rulers, measuring cups, spoons, or other measuring instruments—and 

eight “skills” items emphasizing topics other than the basic numbers and geometry topics 

addressed by the first and second scales. These include fractions, data collection, probability, and 

estimation, along with measurement-specific skills such as “using measuring instruments 

accurately.” Internal consistency reliability for the six mathematics practices scales ranged from 

.73 to .83, with one exception. The reliability of the two-item mixed-achievement grouping scale 

was .56. 

After identifying satisfactory factor solutions in reading and mathematics, scales for each teacher 

were created to represent the resulting set of factors. A number of methods may be used to 

combine information from a set of items into a single scale. The most common method for 

combining items that use Likert scales is to add the scores on the individual items, a process that 

is typically referred to as summative scoring (or sum scoring). When the resulting scales are 

based on a factor analysis, a common approach is to identify the factor on which each item has 

its highest loading and include that item in the calculation of a score for that factor. For this 

report, because some scales are constructed from more items than others, scores on individual 
12 

items composing the scale were averaged, rather than totaled, for each teacher. For teachers who 

answered some, but not all, items on a given scale, the average score was calculated based on 

those items that they did answer. For teachers who did not respond to any of the items used to 

create a particular scale, the imputation was carried out at the scale level. For these teachers, an 

imputation procedure that tried to reconstruct the item-level data prior to scale creation would be 

difficult to implement because of the potentially large number of individual items that would 

have to be imputed. Imputation on the aggregate scale reduces the missing information down to a 

missing scalar rather than an entirely missing vector. 

A summary of the methodology used in the development of the instructional practice scales and 

a list of items included in the scales is presented in appendix B. Descriptive statistics for the 

scales are presented in table D-2 of appendix D. It is important to note that these instructional 

practice scales provide information about teacher-reported frequency and do not address 

variations in intensity of instruction, total time spent in a given day, or overall quality of 

instruction. Therefore, there are important differences among teachers and their instructional 

practices that these scales cannot capture and that should be the focus of future research. 

School Characteristics 

Data were collected from school administrators through a self-administered questionnaire that 

provided information on the fiscal, organizational, and instructional environment of the school. 

For the purposes of this study, information was included on the size of the school, its percentage 

of minority students, its percentage of free-lunch-eligible students,4 and whether it is public or 

private. The study also utilized geographic information relating to region and urbanicity. 

 

4

The variable for percentage of free-lunch-eligible students in the school has a relatively high number of cases with 

missing data (26 percent at the school level). The variable was imputed for the missing cases, as were all variables in 

the analyses. 
13 

4. Methods 

The research presented in this study was conducted in two stages. The first stage consisted of 

using hierarchical linear modeling (HLM) to estimate the relationship between student gains in 

reading and mathematics achievement over the course of the kindergarten year and teachers’ 

reports of their qualifications and the specific instructional practices they used in their 

classrooms. The second stage involved using HLM to estimate the relationship between teachers’ 

reports of their use of particular instructional practices and their qualifications. 

To allow for the interpretation of HLM regression coefficients as effect sizes, certain 

transformations of the data were carried out. To maximize the number of cases included in the 

analyses and to reduce bias and increase the efficiency of parameter estimates, missing data 

items were imputed. The modeling of the two stages of the analysis and the transformation and 

imputation procedures are discussed below. 

Statistical Models 

The modeling of the relationship between the achievement gains of kindergarten students and the 

characteristics and instructional practices of their teachers is aided by four characteristics of the 

dataset. First, ECLS-K assesses children at the time when they enter the formal K–12 education 

system and follows them through their early school experiences, thus allowing the researcher to 

measure changes over time. The achievement regressions use a gain score consisting of the 

difference in scores on the fall and spring assessments (as described in section 3) as the 

dependent variable. This approach allows for an analysis of change during the time the student 

was with the teacher, controlling for student background characteristics. The ability to use an 

achievement gain score rather than a static one-time score improves the modeling considerably 

by controlling for initial differences in achievement. Gain scores “difference out” unobserved 

child-level characteristics that have time-invariant effects on achievement. Unobserved childlevel characteristics might be, for example, innate intelligence, attention span, or “enthusiasm for 

learning.” Second, the contextual variables provided in the dataset provide a fairly 

comprehensive set of controls, including age, socioeconomic status, and race/ethnicity. Third, the 

dataset includes a set of teacher-reported qualifications and practice variables that allow 

researchers to explore the relative contributions of a larger number of factors that might 

influence student outcomes. Finally, the data are collected in a nested structure, with children 

nested within teachers and teachers nested within schools. The nested structure of the data allows 

researchers to relate student outcomes to observable features of the higher level units to which 

they are linked, but it is important to note that this structure can also induce spurious positive 

correlations among outcomes from students sharing a teacher or school. These correlations, if not 

properly accounted for, can reduce the efficiency of the estimates and also introduce bias into the 

estimated standard errors for these estimates. Thus, this study uses HLM to account for these 

correlations and improve the validity of inferences. In addition to accounting properly for 

clustering at the school and teacher levels, HLM also allows for the modeling of effects at 

various levels. 
14 

In the first stage of the analysis, a two-level hierarchical linear model is used to estimate 

relationships between students’ achievement gains in reading and mathematics and teachers’ 

reports of their qualifications and use of specific instructional practices, taking into account the 

clustering of students within particular teachers and schools. The dependent variables in the 

achievement analyses are gain scores that represent the differences between the IRT fall and 

spring achievement scale scores for the reading and mathematics assessments. These analyses 

therefore estimate the association of various factors with the amount of learning children 

demonstrated during the kindergarten year.5

 Mean achievement gain scores were estimated as 

conditional upon a set of child-, teacher-, and school-level characteristics. These analyses permit 

inferences regarding the association of teaching practices and teacher qualifications with 

achievement gains. These models include random teacher effects, which capture both the 

teacher- and school-level variability. Since the number of teachers per school in the data is 

relatively small, computational constraints permit estimating only two levels (the child and 

teacher levels), rather than three levels (including the school level). Accounting for clustering at 

the teacher level facilitates valid inferences about the variables contained in the model, which is 

the primary goal in the conditional means models. A number of child-level control variables and 

teacher and school characteristics are also included in the model, mitigating the problem of 

selection bias to some degree. Selection bias can occur if the choices that parents make—such as 

the choice of a public or private school, full- or half-day kindergarten, or a particular 

neighborhood based on accessibility to a certain school—result from family characteristics that 

are not observed but are correlated with the observed factors influencing achievement. Again, it 

is important to bear in mind that none of these models can produce estimates that can be 

interpreted as truly causal effects due to the lack of random assignment at any level. A more 

complete description of the hierarchical linear models can be found in appendix C. 

The teacher is the unit of analysis in the second part of the analysis, which uses a similar twolevel hierarchical linear model to estimate the relationship of teacher scores on the specific 

instructional practice scale with their self-reported qualifications, taking into account the 

clustering of teachers within schools. In these models, the random intercept picks up school-level 

effects. The type of two-level model described above applies, with the substitution of teachers 

for children and schools for teachers. The characteristics of teachers used as covariates in the 

analysis are years of experience in teaching kindergarten; the number of courses completed in 

methods of teaching reading or mathematics; and whether they hold full teaching certification, 

possess a master’s degree, and work full or part time.6

 All HLM analyses applied survey weights 

to the level 1 variables.7

 

5

An alternative approach would be to estimate the conditional expectation of spring IRT scale scores and include fall 

scores as independent (predictor) variables. The interpretation of the results of this type of specification differs 

slightly from the interpretation of the gain-score model in that it represents the status of children’s learning adjusted 

by their fall status rather than by gains in learning. See appendix C for a discussion of studies supporting the use of 

gain scores. 

6

The part-time employment indicator variable was created directly from a variable called YKFULL provided in the 

ECLS-K restricted-use salary and benefits data file (NCES 2001-014). 

7

The child-level analyses used the weight BYCW0, and the teacher-level analyses used the weight B2TW0. 
15 

Data Transformations and Sample Sizes 

Transformations of the data were made to facilitate the interpretation of coefficients. All 

continuous variables, both dependent and predictor (independent), that were not percentages 

were standardized (i.e., were scaled to have a mean of 0 and a variance equal to 1). The 

regression coefficients for continuous predictors may be interpreted as effect sizes and represent 

the number of standard deviations of the dependent variable associated with one standard 

deviation change in the predictor, after controlling for the other variables in the regression. All 

percentages (i.e., the percentage of minority students in the school and the percentage of students 

eligible for free lunch in the school) were on the scale of 0 to 1, so the regression coefficients 

represent standardized changes in the dependent variable associated with moving from 0 to 100 

percent on the predictor. Dichotomous variables were not standardized and were coded with the 

usual 0/1 values, so that coefficients for such variables can be interpreted as the number of 

standard deviations of the dependent variable associated with moving from 0 to 1 on the 

dichotomous predictor. 

The initial ECLS-K sample contained approximately 22,000 kindergarten children. The weighted 

response rate for schools in the base year (i.e., kindergarten) was 74 percent, with 944 of the 

1,277 originally sampled schools participating. The base-year survey completion rates for 

children, parents, and teachers were 92, 89, and 94 percent, respectively.8 This study retains only 

the subset of children that have the data requisite for the analyses: 16,308 students linked to 

teachers and schools who had observed achievement gain scores for at least one of the two 

subject assessments and who did not change teachers or schools during the course of the 

kindergarten year. Of these students, 15,494 had observed reading gain scores and 16,284 had 

observed mathematics gain scores. The difference in the size of the two samples stems from the 

fact that children from non-English-speaking homes who did not meet the cutoff score on the 

OLDS screening test but spoke Spanish were given a mathematics test in Spanish but no reading 

test. Rock and Pollack (2002) present results of analyses that demonstrate the equivalence of the 

Spanish and English versions of the mathematics test. An earlier report revealed that estimates of 

the average reading achievement of kindergartners are not significantly affected by the exclusion 

of the students who could not be tested in English (Denton and West 2002). 

The teacher-level dataset contains 3,305 teachers. In the teacher-level regressions, the numbers 

of teachers with nonmissing values on the various reading and mathematics instructional practice 

scales were as follows: phonics (3,084), reading and writing skills (3,068), reading and writing 

activities (3,084), didactic reading instruction (3,078), reading comprehension (3,061), studentcentered reading instruction (3,082), mixed-achievement reading grouping (3,066), numbers and 

geometry (3,073), advanced numbers and operations (3,057), traditional practices and 

computation (3,075), student-centered mathematics instruction (3,062), mixed-achievement 

mathematics grouping (3,050), and measurement and advanced topics (3,073).

 

8

A nonresponse bias analysis was conducted to determine if substantial bias had been introduced due to school 

nonresponse. Details on the nonresponse bias analysis are included in the NCES report Kindergarten Teachers: 

Public and Private School Teachers of the Kindergarten Class of 1998–99 (Germino Hausken, Walston, and 

Rathbun 2004). Overall findings from the analysis indicated no strong biases due to school nonresponse. 
16 

In order to minimize the impact of missing values in the covariates, missing data were imputed 

for the independent variables. The dependent variables were not imputed. The imputation 

procedures are described in appendix C. The set of sample means and other statistics for the 

child- and teacher-level datasets can be found in appendix D. 
17 

5. Findings 

This section provides a description of the hierarchical linear modeling (HLM) regression 

findings for reading and mathematics. The results of the student-level achievement regressions 

provide evidence regarding the relationships between the achievement gains made by 

kindergarteners and teachers’ reports of their qualifications and the instructional practices they 

used in their classrooms. The results of the teacher-level instructional practice scale regressions 

explore the relationship between instructional practices and teacher characteristics. In 

interpreting the regression results, alpha = .05 is the criterion for statistical significance. 

Therefore, only coefficients with a p value of .05 or less are interpreted.9 These are marked in the 

tables with an asterisk. 

Reading Achievement Gain Regressions 

The regressions of fall-to-spring gains in reading achievement revealed several significant 

relationships with teacher-, school-, and child-level characteristics. Teacher-level variables 

present in every regression include an indicator for whether the kindergarten class was a full-day 

class and a measure of the time the teacher reported spending each day on reading or 

mathematics (tables 1 and 2). School-level variables present in every regression include school 

locale, control, enrollment size, percentage of minority students and percentage of free-luncheligible students, and region. Child-level variables present in every regression include gender, 

race/ethnicity, age at fall kindergarten assessment, days elapsed between assessments, 

kindergarten repeater status, and primary home language. 

Separate regression models were run for each of the individual instructional practice scales 

described in section 3 of this report to gain a sense of the relationship of each of these types of 

practices to achievement gains (table 1). An alternative specification that included all of the 

teacher practice variables simultaneously is presented in the last column of table 1. A final 

specification excluded the instructional practice scales and instead included several variables 

related to the self-reported qualifications of teachers: years of total kindergarten teaching 

experience (with a squared term to detect nonlinear effects), certification level (i.e., full vs. less 

than full), employment status (i.e., full vs. part time),10 degree status (i.e., receipt of a master’s 

degree), and the number of courses taken in methods of teaching reading or mathematics (0 to 6 

or more courses) (table 2). 

Teacher-Level Variables: Kindergartners’ reading gains were related to the amount of time spent 

in school, on subject, and on teachers’ reports of their use of various instructional approaches 

and were unrelated to the types of self-reported teacher qualifications examined in this study. 

Students in full-day kindergarten programs and students whose teachers reported spending 90 

minutes or more per day teaching reading exhibited significantly higher gains than those in part-

 

9

Standard t test values were used to determine whether individual regression coefficients were greater than zero. 10Part-time employment status does not necessarily provide the same information as the indicator for full-day 

kindergarten. Teachers might work full time and teach two half-day kindergarten classes, for example. 
18 

day kindergartens and those whose teachers spent less time each day on reading instruction, with 

effect sizes ranging from 0.07 to 0.10 for reading instruction time and 0.16 to 0.19 for full-day 

kindergarten.11 Students whose teachers reported a greater emphasis on reading and writing 

skills, a didactic approach, phonics, and reading and writing activities exhibited greater 

achievement gains than those whose teachers spent less time on such practices, with effect sizes 

of 0.10, 0.09, 0.07, and 0.05, respectively. Teacher use of comprehension, mixed-achievement 

grouping, and student-centered instruction were each unrelated to achievement gains. The 

alternative regression analysis that included all of the teacher practice variables simultaneously 

did not substantively affect any of the positive relationships (see the last column in table 1). 

However, the comprehension variable, which had a null relationship to achievement in the 

marginal model, showed a negative relationship in the full model, with an effect size of –0.05. 

Given high levels of correlation across some of the scales (see table B-5 in appendix B), and the 

difficulty of interpreting the coefficients in the full model, the reader is cautioned against 

interpreting this negative relationship as evidence that student achievement is harmed by an 

emphasis on comprehension. 

Table 2 presents the results of the specification in which the achievement gain in reading was 

regressed on teacher characteristics rather than on instructional practice scale scores. In this 

specification, no relationships were found for teacher-reported certification,12 coursework, or 

kindergarten teaching experience. Part-time employment status, however, was negatively 

associated with gains, with an effect size of –0.13.13

 

11The questionnaire included information about the number of days reading was taught each week and the number of 

minutes each day devoted to reading. The vast majority of teachers reported teaching at least some reading each day, 

and the cutoff of 90 minutes for the analyses described here was intended to provide a coarse indicator of exposure 

and to create roughly balanced group sizes. 

12Readers are reminded that the nature of early childhood and elementary certification is variable across states; thus, 

results of the relationships between certification status and achievement gains exhibited in a nationally 

representative sample should be interpreted with caution. 

13A sensitivity analysis was conducted that included all reading instructional practice scale scores in the regression 

in table 2. No change was found in the significance levels of the teacher qualifications. 
19 

Table 1. Standardized regression coefficients for the regression of kindergarten student achievement gains in reading on 

instructional practice scales: School year 1998–99

Instructional practice scales (standardized regression coefficients) 

Characteristic 

Analysis 

including 

phonics 

Analysis 

including 

didactic 

instruction

Analysis 

including 

reading 

and

writing 

skills

Analysis 

including 

reading and

writing 

activities

Analysis 

including 

comprehension

Analysis 

including 

mixedachievement 

grouping 

Analysis 

including 

studentcentered

instruction

Full 

analysis

Intercept -0.32 * -0.29 * -0.30 * -0.35 * -0.36 * -0.36 * -0.36 * -0.30*

Teacher-level variables 

90 minutes or more reading 

instruction per day 0.08 * 0.08 * 0.06 * 0.07 * 0.09 * 0.09 * 0.10 * 0.05

Full-day kindergarten 0.17 * 0.18 * 0.16 * 0.17 * 0.19 * 0.19 * 0.19 * 0.16*

Instructional practice scales 

Phonics 0.07 * † † † † † † 0.07* 

Didactic instruction † 0.09 * † † † † † 0.06*

Reading and writing skills † † 0.10 * † † † † 0.09*

Reading and writing 

activities † † † 0.05 * † † † 0.05*

Comprehension † † † † 0.01 † † -0.05*

Mixed-achievement 

grouping † † † † † 0.01 † #

Student-centered 

instruction † † † † † † -0.01 -0.07*

School-level variables 

School locale1 

Suburban 0.03 0.02 0.04 0.04 0.03 0.03 0.03 0.02 

Rural -0.04 -0.07 -0.02 -0.01 -0.04 -0.04 -0.05 -0.06 

School control2 

Private 0.03 -0.04 0.01 0.04 0.02 0.02 # -0.03 

Enrollment3 

150-299 students 0.09 0.12 0.12 0.11 0.11 0.11 0.11 0.12 

300-499 students 0.09 0.11 0.11 0.12 0.11 0.11 0.11 0.10 

500-749 students 0.07 0.10 0.10 0.10 0.10 0.10 0.10 0.08 

750 or more students 0.06 0.08 0.08 0.08 0.08 0.09 0.09 0.06 

Percent minority enrollment -0.05 -0.07 -0.09 -0.04 -0.04 -0.03 -0.03 -0.11 

Percent free-lunch-eligible 

enrollment # -0.02 0.02 0.02 # # # #

Region4 

West 0.20 * 0.17 * 0.19 * 0.20 * 0.20 * 0.20 * 0.20 * 0.16*

Midwest 0.08 * 0.06 0.08 * 0.08 * 0.07 * 0.07 * 0.07 * 0.07*

South 0.11 * 0.08 * 0.08 * 0.10 * 0.11 * 0.11 * 0.11 * 0.06 

See notes at end of table. 
20 

Table 1. Standardized regression coefficients for the regression of kindergarten student achievement gains in reading 

on instructional practice scales: School year 1998–99—Continued 

Instructional practice scales (standardized regression coefficients) 

Characteristic 

Analysis 

including 

phonics 

Analysis

including

didactic 

instruction

Analysis 

including 

reading 

and

writing 

skills

Analysis 

including 

reading 

and 

writing 

activities

Analysis 

including 

comprehension

Analysis 

including 

mixedachievement 

grouping 

Analysis 

including 

studentcentered

instruction

Full 

analysis

Child-level variables 

Female 0.10 * 0.10 * 0.10 * 0.10 * 0.10 * 0.10 * 0.10 * 0.10*

Race/ethnicity 

Asian/Pacific Islander5 0.08 0.08 0.07 0.08 0.08 0.08 0.08 0.08 

Black, non-Hispanic -0.18 * -0.19 * -0.18 * -0.18 * -0.18 * -0.18 * -0.18 * -0.18*

Hispanic # # # # # # # # 

Other, non-Hispanic race -0.03 -0.03 -0.03 -0.03 -0.03 -0.03 -0.03 -0.03 

Socioeconomic status 0.05 * 0.05 * 0.05 * 0.05 * 0.05 * 0.05 * 0.05 * 0.05*

Age at fall assessment # # # # # # # # 

Days between tests 0.17 * 0.16 * 0.16 * 0.16 * 0.17 * 0.17 * 0.17 * 0.16*

Kindergarten repeater -0.33 * -0.33 * -0.34 * -0.33 * -0.33 * -0.33 * -0.33 * -0.33*

Non-English primary home 

language 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.08

† Not applicable. 

# Rounds to zero. 

* p < 05. 1

The reference group for school locale is urban. 

2

The reference group for school control is public. 

3

The reference group for school size is less than 150 students. 

4

The reference group for school region is Northeast. 

5

The reference group for race/ethnicity is White, non-Hispanic. 

NOTE: Standard errors are presented in table E-1 of appendix E. The instructional practice scales, percent minority 

enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days between tests 

were analyzed as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal 

Study, Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999. 
21 

Table 2. Standardized regression coefficients for the regression of kindergarten student achievement gains 

in reading on teacher qualifications: School year 1998–99

Characteristic 

Teacher characteristics 

(standardized regression coefficients)

Intercept -0.24 *

Teacher-level variables 

90 minutes or more reading instruction per day 0.09 *

Full-day kindergarten 0.18 *

Years of kindergarten teaching experience 0.02 

Experience squared -0.01 

Part-time employment status -0.13 *

Full certification -0.05 

Master’s degree -0.01 

Coursework in methods of teaching reading1 

1 course -0.01 

2 courses -0.03 

3 courses -0.07 

4 courses -0.06 

5 courses -0.04 

6 or more courses -0.03 

School-level variables 

School locale2

Suburban 0.03 

Rural -0.04 

School control3

Private 0.01 

Enrollment4

150-299 students 0.10 

300-499 students 0.11 

500-749 students 0.10 

750 or more students 0.08 

Percent minority enrollment -0.04 

Percent free-lunch-eligible enrollment -0.01 

Region5

West 0.20 *

Midwest 0.07 *

South 0.10 *

See notes at end of table. 
22 

Table 2. Standardized regression coefficients for the regression of kindergarten student achievement gains in 

reading on teacher qualifications: School year 1998–99—Continued

Characteristic 

Teacher characteristics 

(standardized regression coefficients)

Child-level variables 

Female 0.10 *

Race/ethnicity6

Asian/Pacific Islander 0.08 

Black, non-Hispanic -0.18 *

Hispanic # 

Other, non-Hispanic race -0.03 

Socioeconomic status 0.05 *

Age at fall assessment # 

Days between tests 0.17 *

Kindergarten repeater -0.33 *

Non-English primary home language 0.06 

# Rounds to zero. 

* p < 05. 1

Courses are in methods of teaching reading; the reference group is zero courses. 2

The reference group for school locale is urban. 

3

The reference group for school control is public. 

4

The reference group for school size is less than 150 students. 

5

The reference group for school region is Northeast. 

6

The reference group for race/ethnicity is White, non-Hispanic. 

NOTE: Standard errors are presented in table E-2 of appendix E. The instructional practice scales, percent minority 

enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days between tests 

were analyzed as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal 

Study, Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999. 
23 

School-Level Variables: As shown in tables 1 and 2, kindergartners’ reading gains were related 

to the region in which the school was located. Students in the West and South showed higher 

gains than those in the Northeast, with effect sizes ranging from 0.16 to 0.20 in the West and 

from 0.08 to 0.11 in the South. Students in the Midwest also showed higher gains in all 

specifications except those that included the didactic scale (effect sizes range from 0.07 to 0.08). 

No other school-level characteristics were associated with achievement gains. 

Child-Level Variables: Several characteristics of the children were related to reading 

achievement gains. Girls showed higher gains than boys, with an effect size of 0.10 for all scales. 

Black kindergartners showed smaller gains than White kindergartners (effect sizes range from 

–0.18 to –0.19).14 Socioeconomic status was positively associated with gains (effect size of 0.05 

for all scales). Children who were repeating kindergarten showed gains that were lower than 

those of first-time kindergartners (effect sizes range from –0.33 to –0.34). 

Instructional Practice Scale Regressions for Reading 

The results of the teacher-level reading instructional practice regressions are presented in table 3. 

As explained in section 3, the instructional practice scales were based on the frequency with 

which teachers reported performing the instructional practices identified in the items that 

composed each scale. 

Teacher-Level Variables: Teaching reading for 90 minutes or more per day was positively 

associated with the emphasis teachers placed on each of the reading instructional practice scales, 

with effect sizes ranging from 0.13 to 0.35. This was to be expected since the scales were 

constructed on the basis of teacher reports of the frequency with which they used certain 

practices. In addition, and possibly for related reasons, the full-day kindergarten indicator was 

also positive in all of the reading scale regressions except those relating to phonics and 

comprehension (effect sizes range from 0.16 to 0.32). 

Coursework in methods of teaching reading was associated with several of the instructional 

practice scales, with effect sizes ranging from 0.33 to 0.66. Teachers who reported taking two, 

three, five, or six or more courses in pedagogy related to reading reported placing a greater 

emphasis on mixed-achievement grouping than teachers who did not take any reading methods 

coursework. Taking four or six or more such courses was also associated with a greater emphasis 

on student-centered instruction than taking no reading methods coursework. Taking six or more 

courses was associated with a greater emphasis on phonics and reading and writing activities

compared with no coursework. The amount of reading methods coursework was not related to 

 

14Throughout this report, White refers to White, non-Hispanic; Black refers to Black, non-Hispanic; and other, nonHispanic refers to American Indians, Alaska Natives, Pacific Islanders, and multiracial kindergartners. The reader is 

cautioned against interpreting the race coefficients as pure “race effects,” since they may be picking up familyrelated factors correlated with race. This report focuses on the relationships between teacher-level variables and 

student achievement; thus, the child-level variables serve only as controls and should not be overinterpreted. 

Studies that focus exclusively on the Black-White test score gap and study achievement levels rather than gains, 

such as Fryer and Levitt (2004), modify their model specifications to adjust for many of the types of family-related 

variables that are correlated with race. Thus, they are able to erase the Black-White test score gap in some 

specifications using ECLS-K. 
24 

the frequency with which teachers used didactic, comprehension, and reading and writing skills 

activities. 

Certification15 and possession of a master’s degree were unrelated to teachers’ emphases on any 

of the instructional practice scales. Kindergarten teaching experience was negatively associated 

with the reported use of student-centered instruction (effect size of –0.09). Part-time status was 

negatively related to the emphasis placed on phonics, didactic instruction, comprehension, and

reading and writing activities (effect sizes range from –0.23 to –0.52). 

School-Level Variables: School-level characteristics played a role in several reading instructional 

practice scale regressions, although the relationships varied depending upon the scale. Teachers 

in private schools reported less emphasis on phonics, comprehension, reading and writing 

activities, and mixed-achievement grouping than public school teachers (effect sizes range from 

–0.26 to –0.63) and greater emphasis on didactic instruction (effect size of 0.49). 

Rural teachers reported greater emphasis than urban teachers on a didactic approach (effect size 

of 0.31) but less emphasis on comprehension, reading and writing activities, reading and writing 

skills, and student-centered instruction (effect sizes range from –0.22 to –0.41). Suburban 

teachers reported less emphasis than urban teachers on student-centered instruction. 

School size was unrelated to all scales except phonics, in which teachers in schools with 500–

749 students reported a greater emphasis than those in schools with fewer than 150 students 

(effect size of 0.44). The percentage of minority students was positively associated with the 

frequency of instruction on the phonics, didactic, and reading and writing skills scales, with 

effect sizes of 0.42, 0.51, and 0.50, respectively. The percentage of free-lunch-eligible students 

was negatively associated with the frequency of instruction on the reading and writing activities 

scale (effect size of –0.34). 

Regional variables were related to two scales: teachers in the West and South reported a greater 

emphasis than those in the Northeast on a didactic approach (effect sizes of 0.28 and 0.32, 

respectively), and teachers in the West reported a lower emphasis than those in the Northeast on 

comprehension (effect size of –0.21). 

 

15Readers are reminded that the nature of early childhood and elementary certification is variable across states; thus, 

results of the relationships between certification status and instructional practices exhibited in a nationally 

representative sample should be interpreted with caution. 
25 

Table 3. Standardized regression coefficients for the regressions of kindergarten teachers’ reading instructional 

practice scales on selected teacher qualifications and school characteristics: School year 1998–99 

Instructional practice scales (standardized regression coefficients) 

Characteristic Phonics 

Didactic 

instruction

Comprehension

Reading 

and writing 

activities 

Reading 

and

writing 

skills 

Studentcentered

instruction

Mixedachievement

grouping

Intercept -1.08 * -0.69 * -0.41 * -0.38 -0.58 * -0.47 * -0.43 *

Teacher-level variables 

90 minutes or more reading 

instruction per day 0.22 * 0.13 * 0.35 * 0.31 * 0.31 * 0.22 * 0.30 *

Full-day kindergarten 0.14 0.17 * 0.08 0.29 * 0.18 * 0.32 * 0.16 *

Part-time employment status -0.52 * -0.24 * -0.23 * -0.24 * -0.09 -0.06 -0.21 

Years of kindergarten teaching 

experience 0.07 -0.01 0.01 -0.04 -0.03 -0.09 * 0.01

Experience squared -0.04 0.01 0.01 -0.02 -0.01 0.03 # 

Full certification -0.01 -0.01 0.02 0.03 0.03 0.10 0.02 

Master's degree -0.11 0.02 0.03 0.01 -0.03 0.06 0.07 

Coursework in methods of 

teaching reading1 

1 course 0.30 -0.01 0.02 0.14 -0.02 0.08 0.29 

2 courses 0.45 0.04 0.06 0.19 -0.03 0.29 0.35 *

3 courses 0.50 0.04 0.14 0.25 # 0.27 0.36 *

4 courses 0.59 0.16 0.23 0.29 0.16 0.42 * 0.30 

5 courses 0.51 0.08 0.07 0.29 -0.01 0.33 0.39 *

6 or more courses 0.66 * 0.15 0.24 0.33 * 0.17 0.43 * 0.38 *

School-level variables 

School locale2 

Suburban 0.07 0.05 -0.12 -0.12 -0.09 -0.20 * -0.11 

Rural 0.11 0.31 * -0.34 * -0.41 * -0.22 * -0.38 * -0.08 

School control3 

Private -0.26 * 0.49 * -0.29 * -0.63 * 0.03 -0.42 * -0.35 *

Enrollment4 

150-299 students 0.39 -0.09 0.23 -0.01 -0.07 0.02 -0.16 

300-499 students 0.41 -0.11 0.19 -0.07 # -0.04 -0.11 

500-749 students 0.44 * -0.12 0.25 -0.08 0.05 -0.06 -0.06 

750 or more students 0.41 -0.02 0.18 0.01 0.09 0.01 -0.24 

Percent minority enrollment 0.42 * 0.51 * 0.20 0.11 0.50 * 0.18 -0.09 

Percent free-lunch-eligible 

enrollment -0.18 0.05 -0.25 -0.34 * -0.17 -0.20 -0.07

Region5 

West -0.23 0.28 * -0.21 * 0.11 0.07 -0.14 0.06 

Midwest 0.03 0.14 -0.12 -0.04 -0.11 -0.14 -0.05 

South 0.01 0.32 * 0.01 0.12 0.27 -0.06 0.15 

# Rounds to zero. 

* p < .05. 1

Courses are in methods of teaching reading; the reference group is zero courses. 2

The reference group for school locale is urban. 

3

The reference group for school control is public. 

4

The reference group for school size is less than 150 students. 

5

The reference group for school region is Northeast. 

NOTE: Standard errors are presented in table E-3 of appendix E. The instructional practice scales, percent minority 

enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days between tests 

were analyzed as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal 

Study, Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999. 
26 

Mathematics Achievement Gain Regressions 

The regressions of gains in mathematics achievement also showed a number of relationships 

with teacher-, school-, and child-level characteristics. The regression results are presented in 

tables 4 and 5. 

Teacher-Level Variables: As was the case with reading achievement gains, kindergartners’ 

mathematics gains were related to the amount of time spent in school and on subject as well as 

on various teacher-reported instructional approaches but were unrelated to the qualifications of 

their teachers. Students in full-day kindergarten programs and students whose teachers reported 

spending more time on subject—in this case, 60 minutes or more per day teaching 

mathematics16—exhibited larger gains in mathematics achievement over the course of the 

kindergarten year than those who reportedly received less instruction, with effect sizes ranging 

from 0.06 to 0.10 for mathematics instruction time and from 0.14 to 0.18 for full-day 

kindergarten (table 4). Regarding the effects of different instructional practices, students of 

teachers who placed a greater emphasis on traditional practices and computation achieved 

greater gains than those whose teachers placed less emphasis on such practices (effect size of 

0.11). The advanced numbers and operations and measurement and advanced topics scales were 

also positively associated with achievement gains—the effect sizes for these were 0.05 and 0.06, 

respectively. Students of teachers who placed a greater emphasis on student-centered instruction

also showed higher gains than those who placed less emphasis on such practices (effect size of 

0.03). As with reading, the alternative specification that included all of the teacher practice 

variables simultaneously did not substantively affect any of the positive relationships (see the 

last column of table 4). However, the numbers and geometry variable, which had a null 

relationship to achievement in the marginal model, showed a negative relationship in the full 

model (effect size of –0.06). Again, given correlations across scales (see table B-6 in appendix 

B), and the difficulty of interpreting the coefficients in the full model, the reader is cautioned 

against interpreting this as evidence that student achievement is harmed by an emphasis on 

numbers and geometry. 

Table 5 displays the coefficients in the regression of mathematics achievement gains on teacherreported qualifications rather than instructional practice scale scores. No statistically significant 

relationships were found between achievement and teachers’ certification, coursework, 

kindergarten teaching experience, or part-time employment status.17 

School-Level Variables: Kindergartners’ gains in mathematics were related to region, school 

size, the percentage of minority students, and school type (public or private). As was found in the 

reading achievement gain regressions, students in the West, Midwest, and South showed greater 

mathematics gains than those in the Northeast (effect sizes range from 0.10 to 0.16) (table 4). In 

contrast to the results for reading gains, which showed no relationship to school size, students in 

schools with 500 or more students showed larger mathematics achievement gains than those in 

 

16A cut score of 60 minutes was chosen for mathematics (in contrast to the 90 minutes used for reading) because 

teachers reported spending less time on mathematics than on reading, and a cut score of 60 created a roughly 

balanced pair of groups. 

17A sensitivity analysis was conducted that included all mathematics instructional practice scale scores in the 

regression in table 5. No change was found in the significance levels of the teacher qualifications. 
27 

very small schools (i.e., those with fewer than 150 students) in all of the specified models (effect 

sizes range from 0.12 to 0.13). In addition, the mathematics achievement gains of children 

attending schools with 150–299 students were greater than those made by children in schools 

with fewer students in the specifications for the advanced numbers and operations and 

traditional practices and computation scales (effect sizes range from 0.11 to 0.12). Unlike the 

findings for reading achievement (table 1), the percentage of minority students was negatively 

associated with mathematics achievements gains in all of the specifications, with effect sizes 

ranging from –0.13 to –0.17 (table 4). In addition, students in private schools showed smaller 

mathematics achievement gains than those in public schools in the specifications for the 

traditional practices and computation scales (effect size of –0.08). 

Child-Level Variables: Several child-level characteristics were related to mathematics 

achievement gains, although these relationships were, in some cases, different from those 

obtained in the reading achievement regressions. Both Black and Hispanic kindergartners 

showed smaller gains than White kindergartners (effect sizes range from –0.24 to –0.25 for 

Black children and were –0.07 for Hispanic children for all scales). In the case of Hispanic 

kindergartners, the negative association with achievement gains was partially driven by the set of 

children who did not reach the cutoff score on the OLDS screening test. When children who took 

at least one of the two mathematics tests in Spanish were removed from the sample (798 out of 

the 16,284), the Hispanic coefficient was no longer significant in three of the specifications 

(those containing the traditional and the numbers and geometry scales and the specification 

containing qualifications) (data not shown in tables). Removing this group of children did not 

affect coefficients on any of the teacher variables. 

As was the case with the reading achievement gain regressions, children living in families with 

higher socioeconomic status exhibited greater gains than children from families with lower 

socioeconomic status (effect size of 0.06 for all scales), children who were repeating 

kindergarten showed smaller gains than first-time kindergartners (effect sizes range from –0.21 

to –0.22), and a larger time gap between the fall and spring tests was positively associated with 

gains (effect size of 0.13) for all scales. 
28 

Table 4. Standardized regression coefficients for the regressions of kindergarten student achievement gains in 

mathematics on instructional practice scales: School year 1998–99 

Instructional practice scales (standardized regression coefficients) 

Characteristic 

Analysis 

including 

numbers 

and 

geometry 

Analysis 

including 

advanced 

numbers 

and 

operations

Analysis 

including 

traditional 

practices and 

computation

Analysis 

including 

measurement 

and

advanced

topics

Analysis 

including 

mixedachievement

grouping 

Analysis 

including 

studentcentered

instruction

Full 

analysis

Intercept -0.28 * -0.27 * -0.19 * -0.27 * -0.28 * -0.27 * -0.19 *

Teacher-level variables 

60 minutes or more 

mathematics instruction 

per day 0.10 * 0.08 * 0.06 * 0.08 * 0.09 * 0.09 * 0.06 *

Full-day kindergarten 0.18 * 0.17 * 0.14 * 0.16 * 0.18 * 0.17 * 0.14 *

Instructional practice scales 

Numbers and geometry # † † † † † -0.06 *

Advanced numbers and 

operations † 0.05 * † † † † 0.02 *

Traditional practices and 

computation † † 0.11 *

† † †

 0.11 *

Measurement and advanced 

topics † † † 0.06 *

† †

 0.03 *

Mixed-achievement 

grouping † † † † 0.02 † 0.01

Student-centered instruction † † † † † 0.03 * #

School-level variables 

School locale1 

Suburban 0.03 0.04 0.02 0.04 0.03 0.04 0.02

Rural 0.03 0.04 # 0.04 0.03 0.03 0.01

School control2 

Private -0.01 # -0.08 * # # # -0.08 *

Enrollment3 

150-299 students 0.10 0.11 * 0.12 * 0.11 0.11 0.10 0.12 *

300-499 students 0.10 0.10 0.10 * 0.10 0.10 0.10 0.10 *

500-749 students 0.12 * 0.13 * 0.13 * 0.13 * 0.13 * 0.12 * 0.13 *

750 or more students 0.13 * 0.13 * 0.12 * 0.13 * 0.13 * 0.13 * 0.11 *

Percent minority enrollment -0.13 * -0.13 * -0.17 * -0.13 * -0.13 * -0.14 * -0.15 *

Percent free-lunch-eligible 

enrollment -0.01 0.01 -0.03 # # # -0.03

Region4 

West 0.16 * 0.15 * 0.16 * 0.17 * 0.16 * 0.16 * 0.15 *

Midwest 0.14 * 0.13 * 0.14 * 0.15 * 0.14 * 0.14 * 0.13 *

South 0.13 * 0.11 * 0.11 * 0.13 * 0.12 * 0.12 * 0.10 *

See notes at end of table. 
29 

Table 4. Standardized regression coefficients for the regressions of kindergarten student achievement gains in 

mathematics on instructional practice scales: School year 1998–99—Continued 

Instructional practice scales (standardized regression coefficients) 

Characteristic 

Analysis 

including 

numbers 

and 

geometry 

Analysis 

including 

advanced 

numbers and 

operations

Analysis 

including 

traditional 

practices 

and

computation

Analysis 

including 

measurement 

and advanced 

topics

Analysis 

including 

mixedachievement

grouping 

Analysis 

including 

studentcentered

instruction

Full 

analysis

Child-level variables 

Female -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02

Race/ethnicity5 

Asian/Pacific Islander 0.02 0.01 0.02 0.02 0.02 0.02 0.02

Black, non-Hispanic -0.24 * -0.24 * -0.25 * -0.24 * -0.24 * -0.24 * -0.25 *

Hispanic -0.07 * -0.07 * -0.07 * -0.07 * -0.07 * -0.07 * -0.07 *

Other, non-Hispanic race -0.03 -0.03 -0.02 -0.03 -0.03 -0.03 -0.02

Socioeconomic status 0.06 * 0.06 * 0.06 * 0.06 * 0.06 * 0.06 * 0.06 *

Age at fall assessment 0.01 0.01 0.01 0.01 0.01 0.01 0.01

Days between tests 0.13 * 0.13 * 0.13 * 0.13 * 0.13 * 0.13 * 0.13 *

Kindergarten repeater -0.22 * -0.22 * -0.21 * -0.22 * -0.22 * -0.22 * -0.21 *

Non-English primary home 

language -0.02 -0.02 -0.02 -0.02 -0.02 -0.02 -0.02

† Not applicable. 

# Rounds to zero. 

* p < .05. 1

The reference group for school locale is urban. 

2

The reference group for school control is public. 

3

The reference group for school size is less than 150 students. 

4

The reference group for school region is Northeast. 

5

The reference group for race/ethnicity is White, non-Hispanic. 

NOTE: Standard errors are presented in table E-4 of appendix E. The instructional practice scales, percent minority 

enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days between tests 

were analyzed as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal 

Study, Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999. 
30 

Table 5. Standardized regression coefficients for the regression of kindergarten student achievement gains 

in mathematics on teacher qualifications: School year 1998–99 

Characteristic 

Teacher characteristics

(standardized regression coefficients)

Intercept -0.22 *

Teacher-level variables 

60 minutes or more mathematics instruction per day 0.10 *

Full-day kindergarten 0.18 *

Years of kindergarten teaching experience 0.01 

Experience squared -0.01 

Part-time employment status -0.02 

Full certification -0.05 

Master’s degree 0.01 

Coursework in methods of teaching mathematics1 

1 course 0.01 

2 courses # 

3 courses -0.04 

4 courses -0.04 

5 courses -0.03 

6 or more courses 0.04 

School-level variables 

School locale2

Suburban 0.03 

Rural 0.03 

School control3

Private -0.02 

Enrollment4

150-299 students 0.11 

300-499 students 0.10 

500-749 students 0.13 *

750 or more students 0.13 *

Percent minority students -0.13 *

Percent free-lunch-eligible -0.01 

Region5

West 0.16 *

Midwest 0.14 *

South 0.13 *

See notes at end of table. 
31 

Table 5. Standardized regression coefficients for the regression of kindergarten student achievement gains 

in mathematics on teacher qualifications: School year 1998–99—Continued 

Characteristic 

Teacher characteristics

(standardized regression coefficients)

Child-level variables 

Female -0.02 

Race/ethnicity6

Asian/Pacific Islander 0.02 

Black, non-Hispanic -0.24 *

Hispanic -0.07 *

Other, non-Hispanic race -0.02 

Socioeconomic status 0.06 *

Age at fall assessment 0.01 

Days between tests 0.13 *

Kindergarten repeater -0.22 *

Non-English primary home language -0.03 

# Rounds to zero. 

* p <. 05. 1

Courses are in methods of teaching mathematics; the omitted category is zero courses. 2

The reference group for school locale is urban. 

3

The reference group for school control is public. 

4

The reference group for school size is less than 150 students. 

5

The reference group for school region is Northeast. 

6

The reference group for race/ethnicity is White, non-Hispanic.

NOTE: Standard errors are presented in table E-5 of appendix E. The instructional practice scales, percent minority 

enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days between tests 

were analyzed as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal 

Study, Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999. 
32 

Instructional Practice Scale Regressions for Mathematics 

The results for the mathematics instructional practice regressions are displayed in table 6. As 

explained in section 3, the instructional practice scales were based on the frequency with which 

teachers reported performing the instructional practices identified in the items that compose each 

scale. 

Teacher-Level Variables: Teaching mathematics for 60 minutes or more per day was positively 

associated with the emphasis teachers placed on each of the mathematics instructional practice 

scales, as expected, with effect sizes ranging from 0.23 to 0.30. In addition, the full-day indicator 

was also positive in all of the mathematics instructional practice scale regressions except that 

relating to advanced numbers and operations (effect sizes range from 0.15 to 0.30). 

The amount of coursework that teachers reported taking in methods of teaching mathematics was 

associated with scores on all instructional practice scales except the measurement and advanced 

topics scale, with effect sizes ranging from 0.08 to 0.37. Teachers who reported taking three, 

four, or six or more courses in pedagogy related to mathematics placed a greater emphasis on 

number and geometry and advanced numbers and operations than teachers who did not take any 

mathematics methods coursework. Taking four or six or more such courses was also associated 

with a greater emphasis on traditional practices and computation compared with no coursework. 

Taking three or more courses in mathematics methods was associated with a greater emphasis on 

student-centered instruction compared with no such coursework. Additionally, teachers who 

took two or more mathematics methods courses placed a greater emphasis on mixed-achievement 

grouping than teachers with no such coursework. 

Kindergartners whose teachers reported that they were fully certified participated more 

frequently in measurement and advanced topics than those whose teachers were not fully 

certified (effect size of 0.23). The possession of a master’s degree was not related to any scale 

score. Kindergarten teaching experience was positively associated with the reported frequency of 

the use of mixed-achievement grouping, with an effect size of 0.04. Part-time status was 

negatively associated with the emphasis placed on the traditional practices and computation

scale (effect size of –0.26). 

School-Level Variables: Certain school-level characteristics were related to the frequency with 

which teachers used particular instructional practices. Compared with teachers in public schools, 

teachers in private schools placed more emphasis on traditional practices and computation and 

less emphasis on mixed-achievement grouping, with effect sizes of 0.51 and –0.26, respectively. 

Teachers in rural schools placed less emphasis than those in urban schools on student-centered 

instruction and measurement and advanced topics (effect sizes of –0.25 and –0.26, respectively). 

School size was unrelated to any of the mathematics instructional practice scale scores. The 

higher the percentage of minority students in the school, the greater the teachers’ emphasis on 

numbers and geometry, traditional practices and computation, and student-centered instruction

(effect sizes of 0.27, 0.37, and 0.30, respectively). 

Regional differences varied. Teachers in the West reported spending more time than those in the 

Northeast on advanced numbers and operations but less time on numbers and geometry and 
33 

measurement and advanced topics (effect sizes of 0.20, –0.22, and –0.27, respectively). Teachers 

in the South and in the Midwest reported spending more time than those in the Northeast on 

advanced numbers and operations (effect sizes of 0.34 and 0.22, respectively). Teachers in the 

South also reported spending more time than those in the Northeast on mixed-achievement 

grouping, with an effect size of 0.19. 

Sensitivity Analyses 

In addition to the specifications presented above, a number of other specifications were used to 

test the sensitivity of results, particularly with respect to teacher certification. Teachers with 

temporary certification are often only a few months from earning full certification and may thus 

have similar levels of preservice training. A sensitivity analysis was run using a specification that 

substituted the full certification indicator with a variable indicating whether a teacher held a full 

or temporary certification in the achievement regressions. This variable behaved no differently 

than the full certification indicator. The achievement regressions that included teacher 

certification were also rerun without the variables indicating the number of courses completed in 

pedagogy to see if certification might then show a significant effect. The exclusion of these 

variables did not result in a change of significance for certification. 
34 

Table 6. Standardized regression coefficients for the regressions of kindergarten teachers’ mathematics instructional 

practice scales on selected teacher qualifications and school characteristics: School year 1998–99 

Instructional practice scales (standardized regression coefficients) 

Characteristic 

Numbers and 

geometry

Advanced

numbers 

and

operations

Traditional 

practices and

computation

Studentcentered

instruction 

Mixedachievement 

grouping

Measurement and

advanced

topics

Intercept -0.27 -0.19 -0.67 * -0.62 * -0.43 * -0.36 *

Teacher-level variables 

60 minutes or more mathematics instruction 

per day 0.25 * 0.24 * 0.28 * 0.30 * 0.23 * 0.29 *

Full-day kindergarten 0.15 * 0.04 0.30 * 0.19 * 0.24 * 0.25 *

Part-time employment status -0.16 -0.16 -0.26 * -0.12 -0.12 0.05 

Years of kindergarten teaching experience # -0.03 -0.03 # 0.04 * 0.02 

Experience squared 0.01 -0.02 # 0.01 -0.01 -0.02 

Full certification 0.03 -0.10 -0.10 -0.01 # 0.23 *

Master's degree -0.03 -0.03 -0.04 0.04 0.02 -0.01 

Coursework in methods of teaching 

mathematics1

 

1 course 0.03 0.17 0.04 0.08 0.10 0.04 

2 courses 0.14 0.13 0.01 0.14 0.08 * 0.07 

3 courses 0.27 * 0.22 * 0.17 0.33 * 0.17 * 0.16 

4 courses 0.40 * 0.25 * 0.25 * 0.31 * 0.18 * 0.17 

5 courses 0.25 0.17 0.10 0.41 * 0.28 * 0.15 

6 or more courses 0.37 * 0.29 * 0.27 * 0.35 * 0.16 * 0.18 

School-level variables 

School locale2 

Suburban -0.10 -0.01 0.09 -0.10 -0.04 -0.08 

Rural -0.16 -0.12 0.15 -0.25 * -0.06 -0.26 *

School control3 

Private -0.15 -0.16 0.51 * -0.18 -0.26 * -0.15 

Enrollment4 

150-299 students -0.24 -0.12 -0.18 0.16 -0.16 -0.08 

300-499 students -0.19 -0.21 -0.20 0.07 -0.08 -0.07 

500-749 students -0.14 -0.07 -0.16 0.12 -0.03 -0.11 

750 or more students -0.13 -0.06 -0.02 0.08 -0.08 -0.02 

Percent minority enrollment 0.27 * -0.05 0.37 * 0.30 * 0.10 0.05 

Percent free-lunch-eligible enrollment -0.10 -0.28 0.33 -0.22 # -0.05 

Region5 

West -0.22 * 0.20 * 0.10 -0.05 0.09 -0.27 *

Midwest -0.11 0.22 * 0.02 -0.06 0.03 -0.14 

South 0.09 0.34 * 0.18 0.17 0.19 * 0.01 

# Rounds to zero. 

* p < .05. 1

Courses are in methods of teaching mathematics; the reference group is zero courses. 2

The reference group for school locale is urban. 

3

The reference group for school control is public. 

4

The reference group for school size is less than 150 students. 

5

The reference group for school region is Northeast. 

NOTE: Standard errors are presented in table E-6 of appendix E. The instructional practice scales, percent minority 

enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days between tests 

were analyzed as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal 

Study, Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999. 
35 

6. Summary 

This study contributes to the research investigating the importance of teachers in promoting 

student achievement. The analyses presented examine the relationship between student 

achievement in the kindergarten year and the self-reported qualifications of teachers, as has been 

done in several studies of older populations of children. The analyses also make use of selfreported information on specific teaching practices provided in ECLS-K survey data to extend 

the approach generally followed in the literature by looking at the association of these 

instructional practices with achievement. In addition, this study investigates relationships 

between the propensity to use these practices and teacher qualifications. 

Limitations 

Several caveats apply in interpreting the findings of this study. Many of these have been noted 

throughout the preceding sections but are worth reiterating here. Despite the many strengths of 

ECLS-K data for addressing research questions about teachers’ effects on students, efforts to 

generalize from this study are hindered by limitations that are common to survey research. 

Understanding the factors that contribute to effective teaching is limited partially as a result of 

incomplete measurement of those factors. The data on instructional practices provide some 

evidence regarding the frequency of particular approaches, for example, but do not address 

variation in the quality of implementation of those practices or how they may change over the 

course of the year. Furthermore, the instructional practice scales are based on self-reported 

information, and teachers’ perceptions of what they do may not always match what they actually 

do in the classroom. Other data collection methods, such as classroom observations or teacher 

time logs, may yield more precise data about content coverage and instructional techniques at 

specific time periods than one-time teacher questionnaires; however, they are more costly to 

administer than questionnaires and they require much more frequent data collection to produce 

reliable estimates of instruction over the entire academic year (Rowan, Camburn, and Correnti 

2004). While teacher questionnaires administered on an annual basis are less expensive than 

observation or time log data collections, they are limited by concerns of teachers’ accuracy in 

recalling the curriculum topics emphasized over the entire school year. Furthermore, teachers 

may vary in the estimation techniques they use to report retrospectively on instructional activities 

over the entire year, resulting in different reports for teachers with similar teaching behaviors. 

However, by grouping multiple items that measure a common underlying characteristic, as is 

done in this study, the reliability of the composite variable will always be higher than the 

reliability of the individual items (Carmines and Zeller 1979). 

Some important aspects of instruction, such as the cognitive complexity of the work teachers 

assign and the kind of feedback teachers provide on written work, are especially difficult to 

measure with paper-and-pencil surveys. ECLS-K and all surveys are limited in their ability to 

adequately capture teaching practices information, as each of the practice types may encompass 

many different teaching activities. For example, an item such as doing an activity or project

related to a book or story could be interpreted and rated differently by teachers. Moreover, there 

is no information on the specific curriculum teachers are using. It is also important to keep in 
36 

mind that even if the scales used in this study accurately capture the instructional practice 

constructs they are designed to measure, the relationship between them and student achievement 

may not be fully captured in these assessments. For example, the assessments may not address 

all aspects of learning that are related to the instructional practices discussed. In addition, the 

instructional practices may affect later learning in ways that are not measurable in the 

kindergarten assessments. For example, teaching reading comprehension in kindergarten may 

prove crucial to future reading performance as well as science and analytic performance in later 

grades. The reader is therefore cautioned against interpreting the results of this study as clear 

signals for the adoption of policies that promote one instructional approach over another. 

In addition, reliability estimates for certain instructional practice scales were low due to the small 

numbers of items comprising these scales. In particular, the coefficient alpha reliability estimate 

for the didactic instruction scale in reading (which consisted of three items) was 0.50, and the 

alpha estimates for the mixed-achievement grouping scales in reading and mathematics (both of 

which consisted of two items) were 0.48 and 0.56, respectively. Therefore, the results obtained 

using these scales should be interpreted with a greater degree of caution than those that used the 

other scales, which had reliability estimates ranging from approximately 0.7 to approximately 

0.8.18

Measurement issues also arise when attempting to quantify or characterize teacher training. 

Teacher certification indicators may not measure consistent levels of preservice preparation, as 

this preparation varies from state to state. These inconsistencies may weaken the observable 

effects of these variables. Information on the numbers of relevant courses teachers completed 

during their preservice training is useful, but undoubtedly the quality and focus of those courses 

varies and there is no way to capture this variation in the models estimated in this study. 

Limitations in the outcome measure should also be considered. The student assessments may 

accurately evaluate particular elements of reading and mathematics learning but leave other 

elements unmeasured or less well measured. A related point is that because of the exclusion rules 

implemented in this study and the methods used for assessing students whose primary language 

is not English, the findings do not necessarily generalize to English language learners. 

A final caveat is that, since neither students nor teachers are randomly assigned to schools and 

students may not be randomly assigned to teachers, the analyses in this study may be subject to 

selection bias. This is a limitation shared by all studies using nonexperimental survey data. 

Although the presence of many control variables strengthens the model specifications used in 

this study, there may still be unobservable factors that systematically influence the matching of 

children to teachers and schools. It is therefore inadvisable to infer causal links between the 

teacher- and school-level variables examined and student outcomes. Despite these limitations, 

the rich data, their nested structure, and the longitudinal nature of the assessments in ECLS-K 

permit analyses that provide new information regarding existing relationships between student 

achievement, instructional practices, and teacher qualifications for the kindergarten population. 

 

18Adjusting the regression coefficients for attenuation due to low reliability would result in stronger measured 

relationships than are reported here. 
37 

Discussion 

The first research question addressed in this study asks how specific instructional approaches and 

teacher characteristics are related to achievement gains. With regard to this question, it was 

found that several teacher-reported variables describing instructional practices and organization 

were related to test-score gains. Among those factors that were more organizational than 

pedagogical, the results indicate that spending more time on subject and working within a fullday kindergarten structure were associated with relatively large gains in achievement compared 

with spending less time on subject or working in a part-day kindergarten setting. Among the 

instructional practices that teachers reported on in this study, those that emphasized reading and 

writing skills, didactic instruction, phonics, and reading and writing activities were positively 

associated with reading achievement gains. Instructional emphases on traditional practices and 

computation, measurement and advanced topics, advanced numbers and operations, and studentcentered instruction (e.g., having students explain how problems were solved) were positively 

associated with mathematics achievement gains. The study provided no evidence of a direct 

relationship between the self-reported qualifications of teachers and student achievement with 

the exception of teachers’ employment status. Kindergartners whose teachers were employed 

part time made smaller reading achievement gains than those whose teachers were employed full 

time. 

The analyses conducted in response to the second research question (i.e., the relationship 

between teacher qualifications and the use of specific instructional practices) found evidence that 

certain teacher-reported background variables were positively associated with the use of various 

practices that, in turn, were associated with higher achievement. In particular, the number of 

courses teachers reported taking in methods of teaching reading and mathematics was related to 

the emphasis placed on certain instructional approaches. The completion of coursework in 

methods of teaching reading was positively associated with the use of phonics instruction, 

mixed-achievement grouping, student-centered instruction, and reading and writing activities. 

Coursework in methods of teaching mathematics was positively associated with the use of 

practices that emphasized numbers and geometry, advanced numbers and operations, traditional 

practices and computation, student-centered instruction, and mixed-achievement grouping. In 

addition, kindergarten teaching experience was negatively related to the use of student-centered 

instruction in reading and positively related to the use of mixed-achievement grouping in 

mathematics. Teacher certification appeared unrelated to reported instructional practices, with 

the exception of a positive association with an emphasis on measurement and advanced topics in 

mathematics. 

Most of the effect sizes observed in this study are small. For example, the effect sizes for the 

instructional practice variables that showed significant relationships with achievement range 

from approximately 0.03 to 0.10. Although small, they are consistent with those found in other 

studies of relationships between instructional practice and achievement (e.g., Hamilton et al. 

2003; Xue and Meisels 2004). Moreover, it should be kept in mind that these effect sizes 

represent relationships for only a single academic year. If the same relationships were observed 

in subsequent grade levels, the cumulative effect sizes would be larger and more meaningful. As 

discussed below, the findings suggest the need to examine these relationships over a longer 

period of time. 
38 

Future Research Using ECLS-K Data 

This study focused on teacher qualifications, preservice training, and frequency-based measures 

of instructional practice as factors related to student achievement. Although these factors are 

likely to be important, ECLS-K data include several additional categories of information that 

may also be associated with student outcomes, including teachers’ assessments of the quality of 

their schools’ instructional climate, their philosophies about student learning, their evaluations of 

the adequacy of resources in their schools, and their levels of job satisfaction. Extensions of this 

study could incorporate these constructs. In addition, the data include information about 

teachers’ ongoing professional development opportunities, which may be as important as their 

preservice education. Incorporating these into the models would provide a more complete picture 

of the kinds of training associated with positive student outcomes. 

Another important feature of ECLS-K data is the tracking of students over the course of several 

years. The kinds of teacher qualifications and practices that are associated with positive 

kindergarten outcomes may differ from those that contribute to learning among older elementary 

students, so incorporating future waves of ECLS-K data would be informative. In addition, 

having multiple measures of student achievement throughout elementary school would facilitate 

the use of more complex longitudinal models, which would shed light on the nature of students’ 

achievement growth and the ways in which it is associated with teachers’ characteristics and 

classroom practices. 
39 

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 A-1 

Appendix A: 

ECLS-K Direct Cognitive Assessment Measures 

This appendix summarizes the direct cognitive assessments administered to ECLS-K sample 

children in the fall and spring of kindergarten. For more information about the ECLS-K 

cognitive assessments, please see the ECLS-K Base-Year Public-Use Data Files and Electronic 

Codebook: User’s Manual (Tourangeau et al. 2001) and the Early Childhood Longitudinal 

Study—Kindergarten Class of 1998–99 (ECLS-K), Psychometric Report for Kindergarten 

Through First Grade (Rock and Pollack 2002). In the fall of the base year, one-on-one child 

assessments were conducted with the sampled children. The assessment took approximately 50–

70 minutes and was designed to provide data on the developmental status of children in the 

United States at the start of their formal schooling. The ECLS-K cognitive assessment battery 

consisted of questions in three subject areas: language and literacy, mathematical thinking, and 

general knowledge. 

Instrument Development 

During the ECLS-K cognitive test development, an initial review of commercial assessments 

indicated that there were no “off-the-shelf” tests that met the domain requirements of ECLS-K, 

were both individually administered and adaptive, or provided items that could be used to 

measure children’s cognitive achievement longitudinally. The framework for ECLS-K drew 

from the National Assessment of Educational Progress (NAEP) fourth-grade test specifications. 

The NAEP assessment goals are similar to those of ECLS-K in that both projects assess 

cognitive skills typically emphasized in schools. For the grades in which the NAEP frameworks 

were inappropriate, ECLS-K solicited advice from early elementary school educators and 

curriculum specialists to articulate more suitable test specifications. The expertise of item writers 

from Educational Testing Service (ETS), elementary school curriculum specialists, and 

elementary school teachers was also used to develop new assessment items and select existing 

items to borrow or adapt, with permission, from published tests, including the Peabody 

Individual Achievement Test-Revised (PIAT-R), the Peabody Picture Vocabulary Test-Revised 

(PPVT-R), the Primary Test of Cognitive Skills (PTCS), the Test of Early Reading Ability 

(TERA-2), the Test of Early Mathematics Ability (TEMA-2), and the Woodcock-Johnson Tests 

of Achievement-Revised (WJ-R) (Rock and Pollack 2002). Across domains, test items were 

reviewed by elementary school curriculum and content area specialists for appropriateness of 

content and difficulty and for relevance to the assessment battery framework. In addition, items 

were reviewed for issues related to sensitivity to minority concerns. 

The Language Screener 

Prior to administering the cognitive assessment battery, a brief language-screening assessment 

was administered to those children identified from their school records (or by their teacher, if no 

school records were available) as coming from a language minority background (meaning that 

their primary home language was not English). The Oral Language Development Scale (OLDS) 

screening test was used to determine if a child was able to understand and respond to the ECLSK cognitive assessment items in English. Children who passed the language screener received 
 A-2 

the full ECLS-K direct assessment battery. Children who did not pass an established cut score on 

the language screener received a reduced version of the ECLS-K assessments. The OLDS, 

extrapolated from parts of the PreLAS 2000 Assessment (Duncan and De Avila 1998), measured 

children’s listening comprehension, vocabulary, and ability to understand and produce language. 

Children who passed the language screener received the full English direct assessment. Certain 

components of the direct child assessment could also be conducted in Spanish. If a child did not 

pass the language screener but spoke Spanish, he or she was administered a Spanish translated 

form of the mathematics assessment. Children who did not pass the established cut score on the 

language screener and whose native language was not Spanish were excluded from the cognitive 

assessment; however, assessors collected physical measurements of these children’s height and 

weight. Children who did not pass the OLDS in the fall of kindergarten were reassessed with the 

OLDS at subsequent data collection waves until they passed the OLDS language screener. In the 

fall of kindergarten, 1,567 children were not administered the English battery because of their 

performance on the OLDS. By the spring of first grade, this number had been reduced to 350. 

Two-Stage Assessment Design 

The direct cognitive assessment consisted of a set of two-stage assessments: a first-stage routing 

section for each subject area, followed by several alternative second-stage forms. The purpose of 

this adaptive assessment design was to maximize accuracy of measurement and minimize 

administration time. The same reading and mathematics sections, consisting of 12 to 20 items 

with a broad range of difficulty, were administered to all children. The routing section provided a 

rough estimate of each child’s achievement level, so that a second-stage form with items of the 

appropriate difficulty for maximizing measurement accuracy could be selected. A child’s 

performance on the routing section determined the second-stage form that was administered. The 

reading and mathematics assessments had low-, middle-, and high-difficulty second-stage 

options. The second-stage forms varied by level of difficulty so that a child would be 

administered questions appropriate to his or her current level of ability for each cognitive 

domain. The number of questions included in this assessment was limited in order to minimize 

the time and burden on the children. 

The cognitive assessment included both multiple-choice and open-ended items. For ease of 

administration, questions of similar format were grouped together in order of increasing 

difficulty within each group. When the question format changed, practice items were used to 

introduce children to the new format. Assessments were shortened or discontinued if the 

administrator perceived that the child was uncomfortable or distressed about responding to the 

assessment items. If no response was given to 10 questions in a row, assessors entered a “refuse” 

code into the computer for the remainder of the items in that subject area, without reading the 

questions, until reaching the next subject area, where he or she resumed reading the questions. 

This procedure was used to give children who did not want to respond to questions in one subject 

area (e.g., reading) a chance to respond to questions in another subject area (e.g., math). Scores 

in each subject area were computed only if at least 10 questions were answered in the combined 

first and second stages.
 A-3 

Cognitive Components 

The cognitive assessment focused on three general areas of competence: (1) language use and 

literacy (reading); (2) mathematics; and (3) knowledge of the social and physical world, referred 

to as “general knowledge.” The assessment did not ask the children to write anything or to 

explain their reasoning; rather, they used pointing or verbal responses to complete the tasks. The 

data were collected using a computer-assisted personal interviewing (CAPI) methodology. The 

assessment included the use of a small easel with pictures, letters of the alphabet, words, short 

sentences, numbers, or number problems. A brief description of the reading and mathematics 

cognitive assessments follows (the general knowledge assessment scores were not used in this 

report). 

Reading: The reading assessment included questions designed to measure basic skills (print 

familiarity, letter recognition, beginning and ending sounds, rhyming sounds, word recognition), 

vocabulary (receptive vocabulary), and comprehension (listening comprehension, words in 

context). Comprehension items were targeted to measure skills in initial understanding, 

developing interpretation, personal reflection, and demonstrating critical stance. 

Mathematics: The mathematics assessment items were designed to measure skills in conceptual 

knowledge, procedural knowledge, and problem solving. Approximately one-half of the 

mathematics assessment consisted of questions on number sense and number properties and 

operations. The remainder of the assessment included questions in measurement; geometry and 

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

of the mathematics assessment forms contained several items for which manipulatives were 

available for children to use in solving the problems. Paper and pencil were also offered to the 

children to use for the appropriate parts of the assessment. 

Reading and Mathematics Assessment Scores 

Scores based on the full set of test items were calculated using item response theory (IRT) 

procedures. IRT made it possible to calculate scores that could be compared regardless of which 

second-stage form a child took. IRT uses the pattern of right, wrong, and omitted responses to 

the items actually administered in a test and the difficulty, discriminating ability, and “guessability” of each item to place each child on a continuous ability scale. The items in the routing 

test, plus a core set of items shared among the different second-stage forms, made it possible to 

establish a common scale. It is then possible to estimate the score the child would have achieved 

if all of the items in all of the test forms had been administered. IRT scoring makes possible 

longitudinal measurement of gain in achievement over time, even though the tests administered 

are not identical at each point. The common items present in the routing test and in overlapping 

second-stage forms allow the test scores to be placed on the same scale, even as the two-stage 

test design adapts to children’s growth over time. Reliability statistics appropriate for each type 

of score were computed for each subject area, for the fall and spring kindergarten assessments. 

For the IRT-based scores, the reliability of the overall ability estimate, theta, is based on the 

variance of repeated estimates of theta. The fall and spring kindergarten reading and mathematics 

reliabilities range from 0.92 to 0.95. The IRT scale scores in the database represent estimates of 

the number of items students would have answered correctly if they had taken all of the 72 

questions in the first- and second-stage reading forms and all of the 64 questions in the 
 A-4 

mathematics forms. These scores are not integers because they are probabilities of correct 

answers, summed over all items in the pool. Gain scores may be obtained by subtracting the 

estimated number right at time 1 from the estimated number right at time 2. 

Table A-1 shows the types of scores, range of values, means, and standard deviations for the 

direct cognitive assessment. 

 

Table A-1. Means, standard deviations, and range of values for the ECLS-K base-year 

(kindergarten) reading and mathematics assessments: Fall 1998 and spring 1999 

Assessment score Mean 

Standard 

deviation 

Range of 

values 

Fall kindergarten reading IRT scale score 22 8.3 0-72 

Spring kindergarten reading IRT scale score 32 10.3 0-72 

 

Fall kindergarten mathematics IRT scale score 19 7.2 0-64 

Spring kindergarten mathematics IRT scale score 27 8.8 0-64 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, 

Kindergarten Class of 1998–99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999. 
 B-1 

Appendix B: Methodology Used in the Development 

of the Instructional Practice Scales 

The development of instructional practice scales relies on prior work for the National Center for 

Education Statistics (NCES) in which factor analyses of the instructional practice items were 

conducted to inform the development of scales measuring specific pedagogical constructs 

(Hamilton and Guarino 2005). This appendix describes the main procedures used for 

constructing the scales; additional details, including discussions of sensitivity analyses, are 

available from the authors upon request. 

Exploratory factor analysis was conducted to examine the structure of correlations among the 

instructional practice items in each subject. Each factor analysis was conducted on a random half 

sample of the data, which facilitated a cross-validation to test the stability of the solution. The 

initial analyses were conducted using one-half of the data. Once a reasonable solution was 

identified, the factor analysis was repeated using the second half of the data. The patterns of 

loadings across the two solutions were examined. The results were used to identify the number of 

items for which the highest loading occurred on different factors in the two half samples. In all 

cases, this number was small and was limited to those items that had relatively weak loadings on 

all factors in the original analysis. Thus, the cross-validation provided evidence regarding the 

stability of each solution. 

All analyses used principal components analysis with orthogonal (varimax) rotation. Other factor 

extraction methods were explored, and most of the results were relatively robust to choice of 

method.1

 This finding is consistent with other work that has compared results from different 

extraction methods (Thompson and Daniel 1996). Because some of the factors were expected to 

be correlated, solutions using various oblique rotations were also examined. Conclusions about 

which items clustered together were consistent with those from the orthogonal rotation, a finding 

that is also consistent with other research (e.g., Choi, Fuqua, and Griffin 2001). This report 

focuses on the orthogonal solutions to simplify reporting of results. Decisions about the number 

of factors to retain in each case were made based on a combination of empirical considerations 

(e.g., scree plots) and the need for scales that would be instructionally meaningful and 

informative. All analyses were weighted using the B2TW0 weights. 

Teachers who were missing data on one or more items were excluded from the initial factor 

analyses. A total of 3,243 teachers were administered the spring teacher questionnaires. The 

reading factor analysis was conducted on the 2,323 teachers who had complete data on all items. 

The mathematics analysis included 2,287 teachers. 

 

1

There were some exceptions in the reading analysis, discussed below. 
 B-2 

To create scales for use in subsequent modeling, simple sum scores were calculated using the 

items that had their highest loading on a given factor.2 This approach is consistent with the scale 

development used in other studies of instructional practice (see, e.g., Cohen and Hill 2000; 

Hamilton et al. 2003) and tends to produce results similar to those obtained through other 

methods of scale development. For teachers who answered some, but not all, items on a given 

scale, the average score of those items that they answered was used. 

Table B-1 lists the scales, the corresponding items, and the weighted item means for reading. 

Table B-2 lists the scales for mathematics. Tables B-3 and B-4 present the internal consistency 

(coefficient alpha) reliabilities of the reading and mathematics items, respectively. As expected, 

the reliabilities of the didactic instruction scale in reading and the grouping scales in both 

subjects are low due to the small numbers of items on these scales. This suggests that these 

scales should be used with caution. Some of these scales may be combined in ways that would 

enhance reliability without sacrificing information. However, the scales with particularly low 

reliability in these analyses seem to address constructs that are distinct from what is tapped by 

the other scales, so for some purposes they may be useful. Tables B-5 and B-6 present the 

bivariate correlations between the instructional practice scales used in this report. 

 

2

For a justification for using sum scores and a discussion of alternative methods, including IRT, see Hamilton and 

Guarino (2005). In particular, the correlations between corresponding IRT and sum scores in this study were all 

greater than 0.90, and for three of the seven scales the correlations were 0.99. 
 B-3 

Table B-1. Kindergarten teacher reading instructional practice scales and item means: Spring 1999 

Instructional scale 

Item 

number Variable name Description 

Mean

score

Standard 

deviation 

Reading and writing 29f A2SYLLAB Reading multi-syllable words, like adventure 2.7 1.84 

skills 29m A2PNCTUA Using capitalization and punctuation 4.1 1.91 

 29n A2COMPSE Composing and writing complete sentences 3.5 1.98 

 29o A2WRTSTO Composing and writing stories with an 

understandable beginning, middle, and end 2.2 1.57 

 29p A2SPELL Conventional spelling 2.9 2.01 

 29q A2VOCAB Vocabulary 4.3 1.94 

 29r A2ALPBTZ Alphabetizing 2.1 1.61 

 29s A2RDFLNT Reading aloud fluently 3.1 2.07 

Phonics 28a A2LRNLT Work on learning the names of letters 5.8 0.70 

 28b A2PRACLT Practice writing the letters of the alphabet 5.5 0.90 

 28c A2NEWVOC Discuss new or difficult vocabulary 5.4 0.92 

 28e A2PHONIC Work on phonics 5.7 0.77 

 29a A2CONVNT Conventions of print 5.4 1.17 

 29b A2RCGNZE Alphabet and letter recognition 5.8 0.70 

 29c A2MATCH Matching letters to sounds 5.7 0.73 

 29d A2WRTNME Writing own name (first and last) 5.5 1.15 

 29e A2RHYMNG Rhyming words and word families 4.6 1.11 

Didactic instruction 28j A2BASAL Read from basal reading texts 2.4 1.89 

28l A2WRKBK Work in a reading workbook or on a 

worksheet 4.1 1.84 

 28m A2WRTWRD Write words from dictation, to improve 

spelling 2.9 1.80 

Comprehension 29g A2PREPOS Common prepositions, such as over and 

under, up and down 3.9 1.57 

 29h A2MAINID Identifying the main idea and parts of a story 4.1 1.68 

 29i A2PREDIC Making predictions based on text 4.8 1.29 

 29j A2TEXTCU Using context cues for comprehension 4.4 1.67 

 29k A2ORALID Communicating complete ideas orally 5.3 1.15 

 

29l A2DRCTNS 

Remembering and following directions that 

include a series of actions 5.2 1.18 

28d A2DICTAT Dictate stories to a teacher, aide, or volunteer 3.9 1.37 

28h A2RETELL Retell stories 4.2 1.21 

Student-centered reading 

instruction 

28q A2DOPROJ Do an activity or project related to a book or 

story 4.0 1.35 

 28r A2PUBLSH Publish their own writing 2.4 1.41 

 28s A2SKITS Perform plays and skits 2.2 1.00 

Reading and writing 28i A2READLD Read aloud 4.7 1.46 

activities 28k A2SILENT Read silently 4.1 1.94 

 28n A2INVENT Write with encouragement to use invented 

spellings, if needed 4.6 1.57 

 28o A2CHSBK Read books they have chosen for themselves 5.0 1.34 

 28p A2COMPOS Compose and write stories or reports 3.3 1.72 

 28t A2JRNL Write stories in a journal 3.7 1.84 

28v A2MXDGRP Work in mixed-achievement groups on 

language arts activities 4.4 1.79 

Mixed-achievement 

grouping 

28w A2PRTUTR Peer tutoring 3.4 1.78 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, 

Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, spring 1999.
 B-4 

Table B-2. Kindergarten teacher mathematics instructional practice scales and item means: Spring 1999 

Instructional scale 

Item 

number Variable name Description 

Mean

score

Standard 

deviation 

Numbers and geometry 31a A2OUTLOU Count out loud 5.6 0.71 

31b A2GEOMET Work with geometric manipulatives 4.3 1.19 

 31c A2MANIPS Work with counting manipulatives to learn 

basic operations 4.8 1.04 

 32a A2QUANTI Correspondence between number and 

quantity 5.1 1.08 

 32b A21TO10 Writing all numbers between 1 and 10 4.6 1.29 

 32f A2SHAPES Recognizing and naming geometric shapes 4.1 1.39 

 32g A2IDQNTY Identifying relative quantity (e.g., equal, 

most, less, more) 4.3 1.26 

 32h A2SUBGRP Sorting objects into subgroups according to a 

rule 3.9 1.24 

 32i A2SZORDR Ordering objects by size or other properties 3.7 1.18 

 32j A2PTTRNS Making, copying, or extending patterns 4.3 1.29 

 32u A2ORDINL Ordinal numbers (e.g., first, second, third) 3.9 1.51 

32c A22S5S10 Counting by 2s, 5s, and 10s 4.1 1.68 

32d A2BYD100 Counting beyond 100 3.0 1.94 

Advanced numbers and 

operations 

32n A2PLACE Place value 3.0 2.13 

 32o A2TWODGT Reading two-digit numbers 4.6 1.66 

 32p A23DGT Reading three-digit numbers 2.7 2.02 

31k A2MTHSHT Do mathematics worksheets 4.2 1.54 

31l A2MTHTXT Do mathematics problems from their 

textbooks 2.1 1.87 

Traditional practices 

and computation 

31m A2CHLKBD Complete mathematics problems on the 

chalkboard 2.9 1.73 

 32e A2W12100 Writing all numbers between 1 and 100 2.3 1.55 

 32k A2REGZCN Recognizing the value of coins and currency 3.4 1.50 

 32l A2SNGDGT Adding single-digit numbers 4.0 1.48 

 32m A2SUBSDG Subtracting single-digit numbers 3.5 1.63 

31d A2MTHGME Play mathematics-related games 4.5 1.14 

31f A2MUSMTH Use music to understand mathematics 

concepts 2.7 1.52 

Student-centered 

mathematics 

instruction 

31g A2CRTIVE Use creative movement or creative drama to 

understand mathematics concepts 2.6 1.39 

 31i A2EXPMTH Explain how a mathematics problem is 

solved 3.9 1.58 

 31n A2PRTNRS Solve mathematics problems in small groups 

or with a partner 3.5 1.52 

 31o A2REALLI Work on mathematics problems that reflect 

real-life situations 3.9 1.46 

31p A2MXMATH Work in mixed achievement groups on 

mathematics activities 4.1 1.81 

Mixed-achievement 

grouping 

31q A2PEER Peer tutoring 3.1 1.80 

31h A2RULERS Work with rulers, measuring cups, spoons, or 

other measuring instruments 2.9 1.17 

Measurement and 

advanced topics 

32r A2GRAPHS Reading simple graphs 3.7 1.45 

 32s A2DATACO Performing simple data collection and 

graphing 3.2 1.38 

 32t A2FRCTNS Fractions (e.g., recognizing that 1/4 of a 

circle is colored) 2.0 1.17 

 32v A2ACCURA Using measuring instruments accurately 2.6 2.56 

 32w A2TELLTI Telling time 3.3 3.31 

 32x A2ESTQNT Estimating quantities 3.0 1.36 

 32bb A2PRBTY Estimating probability 1.7 1.15 

 32cc A2EQTN Writing mathematics equations to solve word 

problems 1.9 1.36 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, 

Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, spring 1999. 
 B-5 

Table B-3. Reliabilities and correlations for kindergarten teacher reading instructional practice sum scores and IRT 

scores: Spring 1999 

Instructional practices scale Number of items Alpha for sum score

Marginal reliability 

for IRT score

Correlation between 

sum and IRT score

Reading and writing skills 8 0.83 0.85 0.97

Phonics 9 0.75 0.68 0.90

Didactic instruction 3 0.50 0.53 0.99

Comprehension 6 0.77 0.82 0.94

Student-centered instruction 5 0.69 0.72 0.99

Reading and writing activities 6 0.77 0.82 0.96

Mixed-achievement grouping 2 0.48 0.51 0.99

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, 

Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, spring 1999. 

Table B-4. Coefficient alpha reliabilities for kindergarten teacher mathematics instructional practice scales: Spring 

1999 

Instructional practices scale Number of items Alpha for sum score

Numbers and geometry 11 0.83

Advanced numbers and operations 5 0.75

Traditional practices and computation 7 0.73

Student-centered mathematics instruction 6 0.74

Mixed-achievement grouping 2 0.56

Measurement and advanced topics 9 0.81

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, 

Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, spring 1999.

Table B-5. Bivariate correlations of the kindergarten teacher reading instructional practice scales: Spring 1999 

Instructional practices scale 

Reading 

and writing 

skills Phonics 

Didactic 

instruction 

Comprehension 

Studentcentered 

instruction 

Reading 

and 

writing 

activities 

Mixedachievement 

grouping 

Reading and writing skills 1.00 † † † † † † 

Phonics .32 1.00 † † † † † 

Didactic instruction .35 .21 1.00 † † † † 

Comprehension .52 .48 .17 1.00 † † † 

Student-centered instruction .41 .40 .11 .50 1.00 † † 

Reading and writing activities .52 .37 .16 .48 .61 1.00 † 

Mixed-achievement grouping .30 .28 .11 .35 .37 .41 1.00 

† Not applicable. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, 

Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, spring 1999. 
 B-6 

Table B-6. Bivariate correlations of kindergarten teacher mathematics instructional practice scales: Spring 1999 

Instructional practices scale 

Numbers and 

geometry 

Advanced 

numbers 

and 

operations 

Traditional 

practices 

and 

computation 

Studentcentered 

instruction 

Mixedachievement 

grouping 

Measurement and 

advanced 

topics 

Numbers and geometry 1.00 † † † † † 

Advanced numbers and operations .32 1.00 † † † † 

Traditional practices and 

computation .36 .32 1.00 † † † 

Student-centered instruction .59 .29 .39 1.00 † 

Mixed-achievement grouping .37 .23 .23 .51 1.00 † 

Measurement and advanced topics .55 .43 .42 .56 .36 1.00 

† Not applicable. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Kindergarten 

Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, spring 1999. 
C-1 

Appendix C: 

Methodology Used in the Regression Analyses 

Hierarchical linear modeling (HLM) was utilized to estimate the parameters in the gain score and 

teacher instructional practice scale score regressions. This appendix outlines the statistical 

models used in the analysis. In addition, it describes the imputation procedure used for the 

regression covariates and provides evidence supporting the use of gain scores as a dependent 

variable in achievement analyses. 

In the models in which mean achievement gain scores are estimated as conditional upon a set of 

child-, teacher-, and school-level characteristics, the indeterminacy in separating teacher and 

school variance components is addressed by including only teacher effects in the models, which 

capture both the teacher- and school-level variability. This provides an implicit definition of a 

“teacher effect” as a teacher effect plus any school effect. This two-level hierarchical conditional 

means model can be represented as follows, using notation commonly employed to describe 

hierarchical models of this type (e.g., Raudenbush and Bryk 2002; Singer 1998): 

Yij = α 0j + xij γ + ε ij

α0j = π 00 + zj β + ρ 0j 

where j = 1, . . . , J indexes teachers (and schools taken together), i = 1, . . . , N indexes children, 

Yij is the individual student gain score in reading or mathematics, α 0j is the mean achievement 

gain of students of teacher j, xij is a vector of child-level variables, γ is the associated vector of 

coefficients, εij is the random “child effect,” π 00 is the grand mean achievement gain, zj is a 

vector of teacher-level variables, β is the associated vector of coefficients, and ρ 0j is the random 

“teacher and school effect.” Substituting the second equation into the first yields the following 

equation that can be estimated: 

Yij = π 00 + zj β + xij γ + ρ 0j + ε ij

Statistical associations between Y and the teacher- and school-level variables contained in z, 

adjusted for the child-level variables contained in x, are reflected in β.

The teacher-level analysis employs a similar two-level hierarchical linear model to estimate the 

relationship of teacher scores on the specific instructional practice scales to their qualifications, 

taking into account the clustering of teachers within schools. A random intercept was included to 

pick up school-level effects. The two-level model described above applies, with the substitution 

of teachers for children and schools for teachers. The characteristics of teachers used as 

covariates in the analysis are years of kindergarten teaching experience, whether they hold a full 

teaching certification, whether they possess a master’s degree, the number of courses completed 

in methods of teaching reading or mathematics, and whether they work full or part time. 

All linear mixed models were estimated via restricted maximum likelihood using the HLM 

statistics package. Survey weights were applied to the level 1 variables, and multiple imputation 
C-2 

was used. The child-level analyses used the weight BYCW0, and the teacher-level analyses used 

the weight B2TW0. 

Imputation Procedures 

Missing data at the student, teacher, and school levels were imputed using the R package “norm” 

implementing the methods of Schafer (1997). A single imputed dataset was generated as follows. 

First, missing school-level data were imputed. Then, conditional on the complete school-level 

data, any missing teacher-level data were imputed. Finally, conditional on the complete teacherand school-level data, the missing student-level data were imputed. This resulted in one complete 

dataset at all levels. This procedure was carried out five times, resulting in five replicate datasets. 

In all cases, convergence diagnostics of the imputation models were carefully checked to ensure 

that the missing data were being sampled from the correct distributions. Also, in all cases, 

imputed discrete variables were renormalized to legitimate values of such variables. All key 

analyses were carried out on all of the five imputed datasets. The resulting estimates, standard 

errors, and significance calculations were based on combining quantities via the appropriate 

multiple imputation procedures (Rubin 1987), which account for the uncertainty due to missing 

values. 

The Use of Gain Scores 

The dependent variables in the achievement analyses are gain scores, which represent the 

differences between the IRT fall and spring scale scores for the reading and mathematics 

assessments. Using gain scores as the dependent variable, rather than spring scores with fall 

scores as a covariate, allows results to be presented in terms of progress made during the year, 

regardless of where along the continuum that progress is made. There are long-standing concerns 

about the unreliability of gain scores in the measurement literature, although these concerns have 

more recently been shown to be unfounded and based on faulty assumptions (e.g., Gottman and 

Rushe 1993; Williams and Zimmerman 1996). Rogosa and Willet (1983) show that gain-score 

reliabilities are strong when individual differences between pretest and posttest are substantial, as 

is the case in most longitudinal assessment applications (including the fall and spring 

kindergarten ECLS-K assessments). Maris (1998) argues that regression toward the mean is not a 

legitimate argument against using gain scores; nor is pretest measurement error a concern, unless 

assignment into independent variable groups is determined from pretest performance (which is 

not the case in ECLS-K). Additionally, the use of IRT scale scores and the adaptive testing 

approach used in ECLS-K limit the concern that gain scores may be unreliable due to floor and 

ceiling effects (Rock and Pollack 2002). 
D-1 

Appendix D: 

Sample Statistics for Variables Used in Analyses 

Table D-1. Unweighted sample statistics for variables used in child-level analyses: School year 1998–99 

Variable Sample size Mean

Standard 

deviation Minimum Maximum

Total Observations 16,308 † † † †

Child-level variables 

Mathematics achievement gain score 16,284 8.13 5.05 -26.76 31.60

Reading achievement gain score 15,494 10.00 6.17 -13.80 43.63

Female 16,307 0.49 0.50 0 1

Race/ethnicity 

Asian/Pacific Islander 15,665 0.06 0.23 0 1

Black, non-Hispanic 15,665 0.14 0.35 0 1

Hispanic 15,665 0.17 0.38 0 1

Other, non-Hispanic race 15,665 0.04 0.20 0 1

Socioeconomic status 15,711 0.04 0.79 -5 3

Age at fall assessment 16,301 68.49 4.46 45.77 96.50

Days between tests 16,308 185.95 21.08 115.00 262.00

Repeating kindergarten in 1998–99 15,242 0.04 0.21 0 1

Primary home language non-English 15,717 0.12 0.32 0 1

School-level variables 

School locale 

Suburban 16,308 0.47 0.50 0 1

Rural 16,308 0.12 0.33 0 1

School control 

Private 16,308 0.22 0.42 0 1

Enrollment 

0-149 students 16,143 0.07 0.25 0 1

150-299 students 16,143 0.20 0.40 0 1

300-499 students 16,143 0.28 0.45 0 1

500-749 students 16,143 0.29 0.46 0 1

750 or more students 16,143 0.16 0.36 0 1

Percent minority enrollment 15,879 37.26 34.86 0 100

Percent free-lunch-eligible enrollment 10,458 29.24 28.20 0 100

Region 

West 16,308 0.23 0.42 0 1

Midwest 16,308 0.26 0.44 0 1

South 16,308 0.32 0.47 0 1

See notes at end of table. 
D-2 

Table D-1. Unweighted sample statistics for variables used in child-level analyses: School year 1998–99—

Continued 

Variable Sample size Mean

Standard 

deviation Minimum Maximum

Teacher-level variables 

90 or more minutes reading instruction per day 15,256 0.49 0.50 0 1

60 or more minutes mathematics instruction per day 15,162 0.55 0.50 0 1

Full-day kindergarten 15,218 0.56 0.50 0 1

Years of kindergarten teaching experience 16,209 9.09 7.71 1 38

Part-time employment status 14,342 0.06 0.24 0 1

Full certification 15,650 0.86 0.35 0 1

Coursework in methods of teaching reading 

1 course 15,257 0.15 0.36 0 1

2 courses 15,257 0.25 0.43 0 1

3 courses 15,257 0.19 0.40 0 1

4 courses 15,257 0.10 0.30 0 1

5 courses 15,257 0.05 0.23 0 1

6 or more courses 15,257 0.23 0.42 0 1

Coursework in methods of teaching mathematics 

1 course 15,215 0.25 0.43 0 1

2 courses 15,215 0.26 0.44 0 1

3 courses 15,215 0.19 0.39 0 1

4 courses 15,215 0.08 0.28 0 1

5 courses 15,215 0.03 0.17 0 1

6 or more courses 15,215 0.13 0.33 0 1

† Not applicable. 

NOTE: Variables with a minimum of 0 and a maximum of 1 were coded as dummy variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal 

Study, Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999. 
D-3 

Table D-2. Unweighted sample statistics for variables used in teacher-level analyses: School year 1998–99 

Variable Sample Size Mean

Standard

Deviation Minimum Maximum

Total Observations 3,305 † † † †

Teacher-level variables 

Instructional practice scales 

Reading and writing skills 3,068 3.19 1.29 1 6

Phonics 3,084 5.53 0.50 1 6

Didactic instruction 3,078 3.10 1.31 1 6

Comprehension 3,061 4.69 0.96 1 6

Reading and writing activities 3,084 4.36 1.11 1 6

Student-centered reading instruction 3,082 3.42 0.85 1 6

Mixed-achievement reading grouping 3,066 3.98 1.42 1 6

Numbers and geometry 3,073 4.47 0.72 1 6

Advanced numbers and operations 3,057 3.48 1.35 1 6

Traditional practices and computation 3,075 3.19 0.99 1 6

Student-centered mathematics instruction 3,062 3.55 0.96 1 6

Mixed-achievement mathematics grouping 3,050 3.65 1.49 1 6

Measurement and advanced topics 3,073 2.72 0.84 1 6

Part-time employment status 2,769 0.06 0.23 0 1

Years of kindergarten teaching experience 3,280 8.20 7.46 0 38

Full certification 3,171 0.85 0.36 0 1

Master's degree 3,092 0.36 0.48 0 1

Coursework in methods of teaching reading 

1 course 3,098 0.16 0.37 0 1

2 courses 3,098 0.25 0.43 0 1

3 courses 3,098 0.19 0.39 0 1

4 courses 3,098 0.11 0.31 0 1

5 courses 3,098 0.05 0.22 0 1

6 or more courses 3,098 0.21 0.41 0 1

Coursework in methods of teaching mathematics 

1 course 3,081 0.27 0.44 0 1

2 courses 3,081 0.26 0.44 0 1

3 courses 3,081 0.18 0.38 0 1

4 courses 3,081 0.08 0.27 0 1

5 courses 3,081 0.03 0.18 0 1

6 or more courses 3,081 0.12 0.32 0 1

90 or more minutes reading instruction per day 2,983 0.54 0.50 0 1

60 or more minutes mathematics instruction per day 2,969 0.59 0.49 0 1

Full-day kindergarten 2,846 0.61 0.49 0 1

School-level variables 

School locale 

Suburban 3,305 0.49 0.50 0 1

Rural 3,305 0.09 0.29 0 1

School control 

Private 3,305 0.13 0.34 0 1

Enrollment 

0-149 students 3,286 0.05 0.23 0 1

150-299 students 3,286 0.11 0.32 0 1

300-499 students 3,286 0.24 0.43 0 1

500-749 students 3,286 0.32 0.47 0 1

750 or more students 3,286 0.27 0.45 0 1

Percent minority enrollment 3,242 44.65 35.83 0 100

Region 

West 3,305 0.27 0.44 0 1

Midwest 3,305 0.19 0.39 0 1

South 3,305 0.39 0.49 0 1

† Not applicable. 

NOTE: Variables with a minimum of 0 and a maximum of 1 were coded as dummy variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Kindergarten 

Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999. 
D-4 

Table D-3. Bivariate correlations of kindergarten teacher qualification variables: School year 1998-99 

Teacher qualifications 

Years of 

kindergarten 

teaching 

experience 

Part-time 

employment 

status 

Full 

certification 

Master’s 

degree 

Coursework 

in methods 

of teaching 

reading 

Coursework 

in methods 

of teaching 

mathematics 

Years of kindergarten teaching 

experience 1.00 † † † † † 

Part-time employment status -.10 1.00 † † † † 

Full certification .26 -.01 1.00 † † † 

Master’s degree .21 -.02 .17 1.00 † † 

Coursework in methods of 

teaching reading .20 .01 .21 .22 1.00 † 

Coursework in methods of 

teaching mathematics .25 .01 .22 .16 .75 1.00 

† Not applicable. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, 

Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999. 
E-1 

Appendix E: Standard Errors From Regression Models 

Table E-1. Standard errors of the standardized regression coefficients for the regressions of kindergarten student 

achievement gains in reading on instructional practice scales: School year 1998–99 

Instructional practice scales (standardized regression coefficients) 

Characteristic 

Analysis 

including 

phonics 

Analysis 

including 

didactic 

instruction

Analysis 

including 

reading and 

writing 

skills

Analysis 

including 

reading and 

writing 

activities

Analysis 

including 

comprehension

Analysis 

including 

mixedachievement 

grouping 

Analysis 

including 

studentcentered 

instruction

Full 

analysis

Intercept 0.075 0.076 0.076 0.077 0.078 0.079 0.079 0.071

Teacher-level variables 

90 minutes or more reading 

instruction per day 0.025 0.025 0.025 0.026 0.025 0.025 0.025 0.025

Full-day kindergarten 0.029 0.029 0.029 0.029 0.030 0.029 0.030 0.028

Instructional practice scales 

Phonics 0.014 † † † † † † 0.014

Didactic instruction † 0.013 † † † † † 0.014

Reading and writing skills † † 0.014 † † † † 0.017

Reading and writing 

activities † †

†

0.013 † † † 0.016

Comprehension † † † † 0.013 † † 0.016

Mixed-achievement 

grouping † †

†††

0.012 † 0.013

Student-centered 

instruction † † † † † † 0.014 0.016

School-level variables 

School locale1 

Suburban 0.027 0.027 0.027 0.028 0.028 0.028 0.028 0.027

Rural 0.041 0.041 0.041 0.042 0.042 0.042 0.042 0.041

School control2 

Private 0.043 0.042 0.042 0.045 0.043 0.044 0.043 0.042

Enrollment3 

150-299 students 0.067 0.066 0.067 0.069 0.069 0.070 0.070 0.060

300-499 students 0.066 0.065 0.066 0.068 0.069 0.069 0.069 0.060

500-749 students 0.066 0.066 0.066 0.068 0.069 0.069 0.069 0.060

750 or more students 0.069 0.068 0.069 0.071 0.071 0.072 0.072 0.062

Percent minority enrollment 0.059 0.059 0.059 0.059 0.060 0.059 0.060 0.057

Percent free-lunch-eligible 

enrollment 0.079 0.081 0.079 0.080 0.079 0.079 0.079 0.077

Region4 

West 0.039 0.038 0.038 0.039 0.039 0.039 0.039 0.037

Midwest 0.035 0.034 0.034 0.035 0.035 0.035 0.035 0.033

South 0.035 0.036 0.035 0.036 0.036 0.036 0.036 0.035

See notes at end of table. 
E-2 

Table E-1. Standard errors of the standardized regression coefficients for the regressions of kindergarten student 

achievement gains in reading on instructional practice scales: School year 1998–99—Continued 

Instructional practice scales (standardized regression coefficients) 

Characteristic 

Analysis 

including 

phonics 

Analysis 

including 

didactic 

instruction

Analysis 

including 

reading and 

writing 

skills

Analysis 

including 

reading and 

writing 

activities

Analysis 

including 

comprehension

Analysis 

including 

mixedachievement 

grouping 

Analysis 

including 

studentcentered 

instruction

Full 

analysis

Child-level variables 

Female 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.016

Race/ethnicity5 

Asian/Pacific Islander 0.047 0.046 0.046 0.047 0.047 0.047 0.047 0.046

Black, non-Hispanic 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032

Hispanic 0.033 0.033 0.033 0.033 0.033 0.033 0.033 0.033

Other, non-Hispanic race 0.044 0.044 0.044 0.044 0.044 0.044 0.044 0.043

Socioeconomic status 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010

Age at fall assessment 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009

Days between tests 0.011 0.011 0.011 0.011 0.011 0.011 0.011 0.011

Kindergarten repeater 0.047 0.046 0.047 0.047 0.046 0.046 0.046 0.047

Non-English primary home 

language 0.044 0.044 0.044 0.044 0.044 0.044 0.044 0.044

† Not applicable. 

1

The reference group for school locale is urban. 

2

The reference group for school control is public. 

3

The reference group for school size is less than 150 students. 

4

The reference group for school region is Northeast. 

5

The reference group for race/ethnicity is White, non-Hispanic. 

NOTE: Regression coefficients are presented in table 1 of the main report. The instructional practice scales, percent minority 

enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days between tests were analyzed 

as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, 

Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999. 
E-3 

Table E-2. Standard errors of the standardized regression coefficients for the regressions of kindergarten 

student achievement gains in reading on teacher qualifications: School year 1998–99 

Characteristic 

Teacher characteristics 

(standardized regression coefficients)

Intercept 0.118

Teacher-level variables 

90 minutes or more reading instruction per day 0.025

Full-day kindergarten 0.030

Years of kindergarten teaching experience 0.018

Experience squared 0.009

Part-time employment status 0.052

Full certification 0.043

Master’s degree 0.030

Coursework in methods of teaching reading1

1 course 0.102

2 courses 0.100

3 courses 0.099

4 courses 0.103

5 courses 0.114

6 or more courses 0.100

School-level variables 

School locale2

Suburban 0.027

Rural 0.042

School control3

Private 0.044

Enrollment4

150-299 students 0.068

300-499 students 0.068

500-749 students 0.067

750 or more students 0.070

Percent minority enrollment 0.059

Percent free-lunch-eligible enrollment 0.080

Region5

West 0.039

Midwest 0.035

South 0.036

See notes at end of table. 
E-4 

Table E-2. Standard errors of the standardized regression coefficients for the regressions of kindergarten 

student achievement gains in reading on teacher qualifications: School year 1998–99—

Continued 

Characteristic 

Teacher characteristics 

(standardized regression coefficients)

Child-level variables 

Female 0.016

Race/ethnicity6

Asian/Pacific Islander 0.047

Black, non-Hispanic 0.032

Hispanic 0.033

Other, non-Hispanic race 0.044

Socioeconomic status 0.010

Age at fall assessment 0.009

Days between tests 0.011

Kindergarten repeater 0.047

Non-English primary home language 0.044

1

Courses are in methods of teaching reading; the reference group is zero courses. 2

The reference group for school locale is urban. 

3

The reference group for school control is public. 

4

The reference group for school size is less than 150 students. 

5

The reference group for school region is Northeast. 

6

The reference group for race/ethnicity is White, non-Hispanic. 

NOTE: Regression coefficients are presented in table 2 of the main report. The instructional practice scales, percent 

minority enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days 

between tests were analyzed as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal 

Study, Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999.
E-5 

Table E-3. Standard errors of the standardized regression coefficients for the regressions of kindergarten teachers’ 

reading instructional practice scales on selected teacher qualifications and school characteristics: School 

year 1998–99 

Instructional practice scales (standardized regression coefficients) 

Characteristic Phonics 

Didactic 

instruction

Comprehension

Reading and 

writing 

activities

Reading and 

writing skills 

Studentcentered 

instruction

Mixedachievement 

grouping

Intercept 0.522 0.238 -0.405 0.277 0.195 0.234 0.218

Teacher-level variables 

90 minutes or more reading 

instruction per day 0.054 0.047 0.054 0.047 0.048 0.045 0.052

Full-day kindergarten 0.127 0.074 0.074 0.082 0.069 0.065 0.072

Part-time employment status 0.225 0.120 0.101 0.118 0.098 0.115 0.135

Years of kindergarten teaching 

experience 0.039 0.033 0.036 0.031 0.029 0.036 0.034

Experience squared 0.023 0.018 0.021 0.018 0.016 0.020 0.019

Full certification 0.117 0.074 0.078 0.066 0.065 0.068 0.075

Master's degree 0.060 0.045 0.056 0.045 0.046 0.050 0.051

Coursework in methods of 

teaching reading1

 

1 course 0.351 0.162 0.137 0.164 0.113 0.169 0.166

2 courses 0.337 0.164 0.130 0.164 0.112 0.171 0.156

3 courses 0.334 0.170 0.133 0.166 0.121 0.175 0.162

4 courses 0.337 0.167 0.139 0.165 0.120 0.169 0.169

5 courses 0.348 0.197 0.154 0.181 0.137 0.199 0.183

6 or more courses 0.336 0.169 0.144 0.168 0.119 0.181 0.164

School-level variables 

School locale2 

Suburban 0.141 0.076 0.065 0.082 0.062 0.067 0.064

Rural 0.166 0.112 0.113 0.117 0.101 0.101 0.097

School control3 

Private 0.118 0.109 0.114 0.100 0.098 0.099 0.105

Enrollment4 

150-299 students 0.216 0.141 0.144 0.140 0.117 0.130 0.133

300-499 students 0.215 0.135 0.151 0.137 0.121 0.119 0.129

500-749 students 0.225 0.138 0.150 0.140 0.118 0.120 0.132

750 or more students 0.230 0.140 0.159 0.143 0.127 0.129 0.137

Percent minority enrollment 0.148 0.156 0.143 0.116 0.110 0.107 0.138

Percent free-lunch-eligible 

enrollment 0.180 0.216 0.165 0.161 0.139 0.156 0.185

Region5 

West 0.144 0.100 0.103 0.113 0.092 0.088 0.091

Midwest 0.100 0.096 0.090 0.103 0.079 0.094 0.090

South 0.168 0.101 0.089 0.116 0.093 0.091 0.087

1

Courses are in methods of teaching reading; the reference group is zero courses. 2

The reference group for school locale is urban. 

3

The reference group for school control is public. 

4

The reference group for school size is less than 150 students. 

5

The reference group for school region is Northeast. 

NOTE: Regression coefficients are presented in table 3 of the main report. The instructional practice scales, percent minority 

enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days between tests were analyzed 

as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, 

Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999.
E-6 

Table E-4. Standard errors of the standardized regression coefficients for the regressions of kindergarten student 

achievement gains in mathematics on instructional practice scales: School year 1998–99 

Instructional practices scales (standardized regression coefficients) 

Characteristic 

 Analysis 

including 

numbers and 

geometry 

Analysis 

including 

advanced 

numbers and 

operations

Analysis 

including 

traditional 

practices and 

computation

Analysis 

including 

measurement and 

advanced 

topics

Analysis 

including 

mixedachievement 

grouping 

 Analysis 

including 

studentcentered 

instruction 

Full

analysis

Intercept 0.067 0.066 0.064 0.067 0.067 0.067 0.063

Teacher-level variables 

60 minutes or more 

mathematics instruction 

per day 0.025 0.025 0.024 0.025 0.024 0.024 0.025

Full-day kindergarten 0.028 0.028 0.028 0.029 0.028 0.028 0.028

Instructional practice scales 

Numbers and geometry 0.012 † † † † † 0.014

Advanced numbers and 

operations † 0.011 † † † † 0.012

Traditional practices and 

computation † † 0.012 † † † 0.013

Measurement and advanced 

topics † † † 0.013 †

†

0.016

Mixed-achievement 

grouping † † † † 0.013 

†

0.014

Student-centered instruction † † † † † 0.012 0.015

School-level variables 

School locale1 

Suburban 0.024 0.024 0.024 0.024 0.024 0.024 0.024

Rural 0.038 0.038 0.038 0.038 0.039 0.038 0.038

School control2 

Private 0.036 0.036 0.035 0.036 0.036 0.036 0.036

Enrollment3 

150-299 students 0.057 0.056 0.053 0.057 0.057 0.057 0.052

300-499 students 0.055 0.054 0.051 0.055 0.055 0.055 0.051

500-749 students 0.056 0.055 0.052 0.056 0.056 0.056 0.052

750 or more students 0.059 0.058 0.055 0.059 0.059 0.059 0.055

Percent minority enrollment 0.058 0.057 0.057 0.058 0.058 0.057 0.057

Percent free-lunch-eligible 

enrollment 0.076 0.076 0.075 0.077 0.077 0.076 0.077

Region4 

West 0.034 0.033 0.033 0.034 0.033 0.033 0.033

Midwest 0.029 0.029 0.029 0.029 0.029 0.029 0.029

South 0.033 0.033 0.032 0.033 0.033 0.033 0.033

See notes at end of table. 
E-7 

Table E-4. Standard errors of the standardized regression coefficients for the regressions of kindergarten student 

achievement gains in mathematics on instructional practice scales: School year 1998–99—Continued 

Instructional practices scales (standardized regression coefficients) 

Characteristic 

 Analysis 

including 

numbers and 

geometry 

Analysis 

including 

advanced 

numbers and 

operations

Analysis 

including 

traditional 

practices and 

computation

Analysis 

including 

measurement and 

advanced 

topics

Analysis 

including 

mixedachievement 

grouping 

 Analysis 

including 

studentcentered 

instruction 

Full

analysis

Child-level variables 

Female 0.017 0.017 0.017 0.017 0.017 0.017 0.017

Race/ethnicity5 

Asian/Pacific Islander 0.050 0.050 0.049 0.050 0.050 0.050 0.050

Black, non-Hispanic 0.031 0.031 0.030 0.031 0.031 0.031 0.030

Hispanic 0.031 0.031 0.031 0.032 0.032 0.031 0.031

Other, non-Hispanic race 0.046 0.046 0.046 0.046 0.046 0.046 0.046

Socioeconomic status 0.010 0.010 0.010 0.010 0.010 0.010 0.010

Age at fall assessment 0.009 0.009 0.009 0.009 0.009 0.009 0.009

Days between tests 0.010 0.010 0.010 0.010 0.010 0.010 0.010

Kindergarten repeater 0.046 0.046 0.046 0.046 0.046 0.046 0.046

Non-English primary home 

language 0.037 0.036 0.036 0.036 0.036 0.036 0.036

† Not applicable. 

1

The reference group for school locale is urban. 

2

The reference group for school control is public. 

3

The reference group for school size is less than 150 students. 

4

The reference group for school region is Northeast. 

5

The reference group for race/ethnicity is White, non-Hispanic. 

NOTE: Regression coefficients are presented in table 4 of the main report. The instructional practice scales, percent 

minority enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days 

between tests were analyzed as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal 

Study, Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-use Data File, fall 1998 and spring 1999. 
E-8 

Table E-5. Standard errors of the standardized regression coefficients for the regression of kindergarten 

student achievement gains in mathematics on teacher qualifications: School year 1998–99 

Characteristic 

Teacher characteristics 

(standardized regression coefficients)

Intercept 0.091

Teacher-level variables 

60 minutes or more mathematics enrollment per day 0.024

Full-day kindergarten 0.029

Years of kindergarten teaching experience 0.017

Experience squared 0.009

Part-time employment status 0.052

Full certification 0.038

Master’s degree 0.006

Coursework in methods of teaching mathematics1

1 course 0.061

2 courses 0.062

3 courses 0.064

4 courses 0.072

5 courses 0.104

6 or more courses 0.068

School-level variables 

School locale2

Suburban 0.024

Rural 0.038

School control3

Private 0.037

Enrollment4

150-299 students 0.057

300-499 students 0.054

500-749 students 0.056

750 or more students 0.059

Percent minority enrollment 0.057

Percent free-lunch-eligible enrollment 0.075

Region5

West 0.034

Midwest 0.029

South 0.034

See notes at end of table. 
E-9 

Table E-5. Standard errors of the standardized regression coefficients for the regression of kindergarten student 

achievement gains in mathematics on teacher qualifications: School year 1998–99—Continued 

Characteristic 

Teacher characteristics 

(standardized regression coefficients)

Child-level variables 

Female 0.017

Race/ethnicity6

Asian/Pacific Islander 0.050

Black, non-Hispanic 0.031

Hispanic 0.032

Other, non-Hispanic race 0.046

Socioeconomic status 0.010

Age at fall assessment 0.009

Days between tests 0.010

Kindergarten repeater 0.047

Non-English primary home language 0.036

1

Courses are in methods of teaching mathematics; the omitted category is zero courses. 2

The reference group for school locale is urban. 

3

The reference group for school control is public. 

4

The reference group for school size is less than 150 students. 

5

The reference group for school region is Northeast. 

6

The reference group for race/ethnicity is White, non-Hispanic.

NOTE: Regression coefficients are presented in table 5 of the main report. The instructional practice scales, percent 

minority enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days between 

tests were analyzed as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, 

Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999.
E-10 

Table E–6. Standard errors of the standardized regression coefficients for the regressions of kindergarten teachers’ 

mathematics instructional practice scales on selected teacher qualifications and school characteristics: 

School year 1998–99 

Instructional practice scales (standardized regression coefficients) 

Characteristic 

Numbers and 

geometry

Advanced 

numbers and 

operations

Traditional 

practices and 

computation

Studentcentered 

instruction

Mixedachievement 

grouping 

Measurement 

and advanced 

topics

 Intercept 0.216 0.187 0.246 0.214 0.208 0.189

Teacher-level variables 

60 minutes or more mathematics 

instruction per day 0.051 0.046 0.047 0.049 0.055 0.045

Full-day kindergarten 0.073 0.066 0.075 0.072 0.074 0.066

Part-time employment status 0.128 0.105 0.129 0.123 0.128 0.108

Years of kindergarten teaching 

experience 0.035 0.032 0.029 0.034 0.034 0.031

Experience squared 0.020 0.018 0.017 0.019 0.019 0.017

Full certification 0.078 0.071 0.069 0.082 0.080 0.063

Master's degree 0.052 0.050 0.044 0.055 0.053 0.046

Coursework in methods of 

teaching mathematics1

1 course 0.136 0.099 0.109 0.150 0.122 0.099

2 courses 0.132 0.102 0.108 0.141 0.121 0.101

3 courses 0.135 0.107 0.110 0.148 0.123 0.103

4 courses 0.137 0.117 0.119 0.153 0.136 0.111

5 courses 0.173 0.139 0.139 0.176 0.160 0.144

6 or more courses 0.143 0.109 0.118 0.160 0.133 0.117

School-level variables 

School locale2

Suburban 0.067 0.064 0.085 0.066 0.068 0.069

Rural 0.098 0.114 0.115 0.092 0.100 0.099

School control3

Private 0.104 0.103 0.115 0.094 0.110 0.099

Enrollment4

150-299 students 0.137 0.127 0.157 0.122 0.138 0.133

300-499 students 0.135 0.129 0.149 0.122 0.137 0.133

500-749 students 0.132 0.133 0.153 0.123 0.141 0.136

750 or more students 0.143 0.142 0.158 0.128 0.145 0.143

Percent minority enrollment 0.118 0.117 0.146 0.098 0.138 0.127

Percent free-lunch-eligible 

enrollment 0.173 0.142 0.183 0.127 0.183 0.160

Region5

West 0.100 0.096 0.114 0.086 0.095 0.100

Midwest 0.094 0.097 0.108 0.083 0.095 0.096

South 0.093 0.095 0.116 0.091 0.091 0.096

1

Courses are in methods of teaching mathematics; the reference group is zero courses. 2

The reference group for school locale is urban. 

3

The reference group for school control is public. 

4

The reference group for school size is less than 150 students. 

5

The reference group for school region is Northeast. 

NOTE: Regression coefficients are presented in table 6 of the main report. The instructional practice scales, percent minority 

enrollment, percent free-lunch eligible students, socioeconomic status, age at fall assessment, and days between tests were 

analyzed as continuous variables. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, 

Kindergarten Class of 1998-99 (ECLS-K), Base Year Restricted-Use Data File, fall 1998 and spring 1999.