Gender and Cognitive Skills Throughout Childhood Dissertation

Gender and Cognitive Skills throughout Childhood

Dissertation

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Benjamin Guild Gibbs, M.S.

Graduate Program in Sociology

The Ohio State University

2009

Dissertation Committee:

Douglas Downey, Advisor

Rachel Dwyer

Vincent Roscigno

Benjamin Guild Gibbs

2009

Abstract

When do gender gaps in math and reading skills emerge and why? I examine

gender gaps in math and reading from 9 months to 4 years of age with the Early

Childhood Longitudinal Study—Birth Cohort and from kindergarten to 5th grade with the

Early Childhood Longitudinal Study—Kindergarten Cohort. With standardized

assessments of cognitive skills, I find that girls excel in early math and reading skills in early childhood, before kindergarten begins. Although girls’ advantages in reading

continue, math advantages appear to reverse upon school entry. I show with item-level

assessments that this “reversal of fortunes” pattern is misleading. Girls maintain math

advantages in counting, identifying numbers, and shape recognition across childhood.

Boys’ advantages emerge with the onset of multiplication, division, place values, rate and

measurement, and fractions. I find that gender gaps in reading can be largely explained

by gender differences in classroom citizenship. For math, gender differences in parental

expectations and investments are largely the result of feedback effects rather than

parents’ gender-stereotypic behavior.

Dedication

To my girls, Abbey and Amelia.

iii

Acknowledgments

This work represents nearly a three year effort with support and guidance from

many individuals and institutions. My advisor, Doug Downey, provided constant

encouragement throughout the many iterations of this project. Without his direction,

constructive skepticism, and continued interest, this project would not have come to

fruition. An early collaborator, Anne McDaniel, was instrumental in shaping the initial

questions developed in this dissertation. Claudia Buchmann gave of her time on early

drafts and provided direction during the critical first stages of the project. Andrew

Penner gave generously of his time to read a portion of this work that lead to questions that quickly pushed this project further and sparked news lines or inquiry to explore.

Finally, anonymous reviewers of a portion of this work detailed how research seeking to

reconcile two competing literatures might be framed. I also benefited from the support of faculty and fellow graduate students who gave feedback in several forums on campus, including presentations in the Early Childhood working group, the Hayes Research

Forum, and a conference hosted by the Initiative in Population Research.

Research at this scale required extensive support from friends and family. Marcia

Gibbs, copy edited the manuscript several times during the final stages of this project

with narrow time constraints. Kevin Shafer was an instrumental friend and colleague in

the process who gave continued interest and encouragement throughout the projects

development, as did Jamie Lynch, Deniz Yucel and many others. The burden of time and

energy disproportionately placed in dissertation work was gracefully shouldered by my

wife, who kept two small girls busy while giving unwavering support throughout the

entirety of this process. She gently showed me how to balance family, work, and community obligations.

Finally, this research was supported by a grant from the American Educational

Research Association which receives funds for its “AERA Grants Program” from the

National Science Foundation and the National Center for Education Statistics of the

Institute of Educational Sciences (U.S. Department of Education) under the NSF Grant

#DRL-0634035. Opinions reflect those of the author and do not necessarily reflect those of the granting agencies.

Vita

May 2, 1977 ...... Born – Laconia, New Hampshire

2003...... B.S. Sociology, Brigham Young University

2005...... M.S. Sociology, Brigham Young University

2008 to present...... AERA Doctoral Fellow, The Ohio State University

Publications

Bahr, S., Armstrong, A., Gibbs, B., Harris, P., Fisher., J., 2005. The reentry process: how parolees adjust to release from prison. Fathering 3, 243–265.

Fields of Study

Major Field: Sociology

Table of Contents

Abstract...... ii

Dedication...... iii

Acknowledgements...... iv

Vita...... vi

List of Tables ...... vii

List of Figures...... x

Chapter 1: Introduction...... 1

Chapter 2: Literature Review...... 9

Chapter 3: Methods...... 42

Chapter 4: Results...... 64

Chapter 5: Conclusion and Discussion ...... 97

References...... 109

Appendix: Supplemental Material ...... 125

vii

List of Tables

Table 1: Descriptive Statistics including Comparisons of Female and Male Mean

Differences, ECLS-B ...... 71

Table 2: Descriptive Statistics including Comparisons of Female and Male Mean

Differences, ECLS-K...... 73

Table 3: Descriptive Statistics of Cognitive Skills including Comparisons of Female and

Male Mean Differences, ECLS-B...... 77

Table 4: Descriptive Statistics of Cognitive Skills including Comparisons of Female and

Male Mean Differences, ECLS-K...... 77

Table 5: Structural Equation Model of Bayley Scores at 9 months by Gender, Controlling

for Various Factors in the Model...... 90

Table 6: Structural Equation Model of Bayley Scores at 2 years by Gender, Controlling

for Various Factors in the Model...... 91

Table 7: Structural Equation Model of Early Math Skills by Gender at 4 Years of Age,

Controlling for Various Factors in the Model...... 92

viii

Table 8: Structural Equation Model of Early Reading Skills by Gender at 4 Years of Age,

Controlling for Various Factors in the Model...... 93

Table 9: Structural Equation Model of 5th Grade Math Skills by Gender, Controlling for

Various Factors in the Model...... 94

Table 10: Structural Equation Model of 5th Grade Reading Skills by Gender, Controlling

for Various Factors in the Model...... 96

Table 11: Descriptives including gender comparisons, Kindergarten-Fall ...... 128

Table 12: Descriptives including gender comparisons, Kindergarten-Spring...... 129

Table 13: Descriptives including gender comparisons, 1st Grade-Fall...... 130

Table 14: Descriptives including gender comparisons, 1st Grade-Spring...... 131

Table 15: Descriptives including gender comparisons, 3rd Grade-Spring ...... 132

Table 16: Descriptives including gender comparisons, 5th Grade-Spring ...... 134

Table 17: Subtest Level of Proficiency with Descriptions ...... 135

List of Figures

Figure 1: Conceptual Model of Gender-Role Socialization ...... 25

Figure 2: Autoregressive Latent Trajectory Model of Gender Differences in Cognitive

Skill...... 62

Figure 3: Cohen's d Calculation...... 62

Figure 4: Growth Curve (ALT) of Standardized Math Scores by Gender, ECLS-K ...... 78

Figure 5: Growth Curve (ALT) of Standardized Reading Scores by Gender, ECLS-K....78

Figure 6: Gender Differences in Bayley and Math Skills from 9 months to 5th Grade .....83

Figure 7: Gender Differences in Reading Skill from 2 years to 5th Grade ...... 83

Figure 8: Subtests of Math-Related Measures from Preschool to 5th Grade ...... 84

Figure 9: Subtests of Reading-Related Measures from Preschool to 5th Grade...... 85

Figure 10: Math Scores Distributions by Gender, Kindergarten-Fall ECLS-K...... 127

Figure 11: Reading Scores Distributions by Gender, Kindergarten-Fall ECLS-K...... 127

Figure 12: Math Scores Distributions by Gender, Kindergarten-Spring ECLS-K ...... 127

Figure 13: Reading Scores Distributions by Gender, Kindergarten-Spring ECLS-K .....127

Figure 14: Math Scores Distributions by Gender, 1st Grade-Spring ECLS-K...... 127

Figure 15: Reading Scores Distributions by Gender, 1st Grade-Spring ECLS-K...... 127

Figure 16: Math Scores Distributions by Gender, 3rd Grade-Spring ECLS-K ...... 127

Figure 17: Reading Scores Distributions by Gender, 3rd Grade-Spring ECLS-K ...... 127

Figure 18: Math Scores Distributions by Gender, 5th Grade-Spring ECLS-K ...... 127

Figure 19: Reading Scores Distributions by Gender, 5th Grade-Spring ECLS-K ...... 127

Chapter One: Introduction

In 2005, Larry Summers, then president of Harvard, suggested in an academic

forum that men are innately better at math and math-related skills than women. He

argued that supporting evidence can be found in early childhood and that these differences are a leading explanation for the overrepresentation of men in professions in

science, technology, engineering, and math (Summers, 2005). This speculation resulted

in an academic backlash that led to his removal. Since then, numerous publications have

debated the merits of Summers’s position (see Ceci and Williams, 2007). Research on

gender differences remains clearly controversial, stemming from competing views of when gender differences emerge and what they mean for gender stratification in adulthood.

Renewed attention on this debate has merit. Although in the last several decades women have made important strides in educational attainment, surpassing men on several indicators such as college entrance and graduation (Buchmann & DiPrete, 2006), gender stratification has not disappeared. Women’s political and economic power remains considerably behind that of men. Women on average earn far less than their equally skilled counterparts in the workplace while men are overrepresented in the highest paying occupations and in powerful political positions (see England, 2005). Although these gaps

have diminished in the past few decades, salary and occupation differences persist,

having changed little since 1990 (Blau and Kahn, 2007).

One explanation, similar to Summers’s claim, is that gender gaps in cognitive skill develop at a very young age and send boys and girls on different life trajectories.1

This line of inquiry is reasonable given recent trends. First, labor market returns to cognitive skills have grown in the past few decades (Murnane, Willett and Levy, 1995).

The link between gender differences in cognitive skills to wage inequality, albeit modest, has grown as well (Blau and Kahn, 2007; Bobbit-Zehar, 2008). Second, given that the relative size of gender discrimination via labor market queuing and the job devaluation may be more modest than previously expected (Reskin, 1993; Kilborne, Farkas, Beron,

Weir and England, 1994; see Tam 1997), some scholars have turned toward factors preceding job entry to explain labor market inequalities (Correll, 2001), specifically gender differences in cognitive skills (see Buchmann, DiPrete, McDaniel, 2008).

Summers’s claim was based on research examining early childhood, but what do we know about gender gaps in this period? Although it is well known that, on average, boys outperform girls on standardized tests of math whereas girls outperform boys on tests of reading and verbal skill in adolescence (Maccoby and Jacklin, 1974; Hedges and

Nowell, 1995; Nowell and Hedges, 1998; Voyer, Voyer, and Bryden, 1995; Lynn and

Irwing, 2004; Whitley, McHugh, and Frieze, 1986; Feingold, 1996; Friedman, 1989;

Penner and Paret, 2007; Hyde, Fennema, and Lamon, 1990; Hyde, 2005), research

1 Summers’s biological argument need not be made when observing gender differences in early childhood. Had he simply made the conjecture that early childhood differences may have lasting effects, his appointment as president may have been longer.

documenting gender gaps in early childhood has far less consensus (Halpern, 2000;

Gallagher and Kaufman, 2005; Geary, 1999; Feingold, 1996; Entwisle, Alexander, and

Olson, 1994). As a result, the link between what is known in adolescence is difficult to

reconcile with unclear findings in early childhood research.

In addition to exploring the origins of gender differences in cognitive skills, this

study will focus on one pattern in early childhood that is especially puzzling. Girls begin

to fall behind boys on standardized tests of math skills2 only after school begins (Leahey

and Guo, 2001; Penner and Paret, 2008; Entwisle, Alexander, and Olson, 1994),3 but by some accounts, girls show early math advantages over boys throughout the pre-school years (for reviews, see Halpern, 2000; Geary, 1998; Worell and Goodheart, 2006). As

Sadker and Sadker (1994) observe, “girls begin school looking like the favored sex” (p.

138), but the transition to school, the authors suggest, introduces structural and cultural constraints that work against girls’ early advantages in math. Do girls’ fortunes reverse, as Sadker and Sadker posit, when they begin formal schooling? If so, this would be important news for understanding the origin and explanation of gender differences in math-related skills. This disruption would have implications for research on life-course transitions. If girls’ “home child” experiences encourage girls’ math development, yet their “school child” experiences discourage girls from math, then the transition to school would mark a truly “critical period” for girls (see Entwistle, Alexander, and Olsen, 1997).

2 I use the term “math skill” to refer to both standardized scores of math skill as well as skills thought to be precursors to standardized math skill, referred here as either math-related skill or early math, where appropriate. 3 Penner and Paret (2008) find that average differences are found after school entry although extreme score differences can be found at school entry.

It is important to consider that women have recently passed men in college

attendance and other indicators of educational success (Buchmann and DiPrete, 2006).

As a result, the concern over girls’ disadvantage has come under closer scrutiny. Yet, the

notion that schools favor boys is a logically consistent explanation regarding the apparent

reversal from early-childhood female advantages to later male advantages in math skills.

This view is important to address because the argument that schools shortchange girls has

been an enduring line of inquiry (see Buchmann et al. 2008 for a review of the literature).

The aim of this dissertation is to examine the “schools as culprit” assumption as a means

to clarify the origins, trajectories, and explanations of gender gaps in math and reading

throughout childhood.

Only recently has data been available to examine the origins of gender differences

in cognitive skill at a national level or to explore the size of cognitive skill trajectories

over time. In addition, national data rich in cognitive assessments and parenting

interaction with children have been rare (Lytton and Romney, 1991). In a review of over

2,000 gender difference studies examining cognition, Hyde (2005) finds that less than 5% were nationally representative (author’s calculations). Of these studies, disparate

measures of cognition were utilized and few of these track a national sample of small

children over more then two points in time. The absence of large-scale, developmental

data in early childhood may partly explain why conflicting findings regarding gender

gaps in cognitive skill persist despite decades of research (Halpern, 2000; Feingold,

1996).

One corollary to the gender and cognitive skill literature is the reliance on global

math and reading scores from standardized tests. Many scholars of cognitive skills,

especially sociologists, rely on standardized measures of math and reading that are

constructed from multiple subtests (Leahey and Guo, 2001; Geary, 1998). If wide

variations in subtests of math and reading trajectories exist, then a singular focus on aggregated scores may obscure these underlying patterns. Subtests may reveal gender

gaps that simultaneously converge, diverge, and even show parity over time depending

on the type of skill assessed. By examining the more detailed components of global tests, an apparent reversal of fortunes may simply reflect a shift in the type of skills assessed.

Disregarding these more subtle patterns could lead to misplaced conclusions regarding the path of girls’ early math and reading trajectories.

To date, we know little about when these differences emerge, the effect of school transition on cognitive skill trajectories, and what factors explain these enduring differences. Child developmentists often argue that gender differences in math emerge early in childhood (for an exception, see Spelke, 2005) while educational sociologists often argue that gender differences diverge in earnest during the high school years (Leahy and Guo, 2001). A test of the gender-reversal hypothesis, requiring a comprehensive view of girls’ transition from “home child” to “school child,” and its effect on cognitive skill development, has yet to be undertaken. In addition, gender differences in assessments of specific math and reading skills and detailed documentation of parent- child interactions has yet to be documented across childhood.

This research is guided by the following three questions: (1) When do gender

gaps in math and reading emerge? (2) Do girls’ math fortunes reverse? and (3) Does

parent socialization explain gender gaps in cognitive skills during childhood? To address

these questions, this study utilizes two complementary data sets, the Early Childhood

Longitudinal Survey-Birth Cohort 2001 and the Early Longitudinal Survey-Kindergarten

Cohort 1998–99. The first spans infancy to early childhood and the second, early to

middle childhood. These data are uniquely suited to address these three questions. They

are comprehensive, utilizing multiple assessments of cognitive skill in standardized and

subtest forms, and contain an unprecedented level of detail regarding parent-child

interaction on a national-scale. The contribution of this study will be to provide a first-

of-its-kind national portrait of gender and cognitive skills throughout childhood.

This dissertation is organized into five chapters. Chapter Two reviews the

literature, separated into three sections—the first on the origins of gender gaps in math

and reading, the second on the “reversal of fortunes” argument regarding girls’ decline in math advantages from early to late childhood, and the third on gender differences in parent socialization and its relationship to cognitive skill development. Chapter Three details the methods and measures, including details on the samples and cognitive skill assessments used in the two data sets analyzed in this study. Chapter Four reports the results regarding the origins of math and reading skills, the “gender reversal” hypothesis, and the role of parent socialization on cognitive skill trajectories across childhood.

Conclusions are outlined with discussion in Chapter Five.

My findings document that math and reading gaps begin in early childhood and favor girls. Girls show advantages over boys throughout this period, but math gaps, on the surface, appear to reverse at the transition to school. With item-level assessments, I show that the “gender reversal” conclusion is misguided. There is no evidence of a

disruption in math or reading skills upon school entry for boys or girls. Rather, the

gender gap emerges due to a shift in content, supporting the argument that gender gaps in

math are the result of increasing item-complexity, rather than a reversing female math trajectory.

On the surface it appears that gaps—even for more complex math—stem partly from social indicators. Parents have higher expectations and invest more in tutoring for boys versus girls. These factors reduce boys’ math advantage by nearly a half. But when the child’s previous math skills in first and third grade are considered, gender expectations show only slight gender differences and the effect of tutoring becomes non- significant. The child’s skill level significantly alters the relationship between parents’ beliefs and behaviors and their children’s cognitive outcomes. This feedback effect has important implications for how parent-child interactions are conceptualized and examined. Without accounting for the child’s previous skill levels, parent effects can be overstated. Finally, citizenship in the classroom is linked to higher scores for both math and reading. Thus, when girls’ higher scores on teacher-rated classroom citizenship (or approaches to learning) are considered, the gender gap in reading skills becomes non- significant. For math, the size of the gender gap nearly doubles. This latter finding is disconcerting. It suggests that even if boys and girls were to have similar math scores

overall, gender parity is achieved through different mechanisms. In other words, girls appear to work harder than boys in the classroom (in terms of citizenship) to obtain similar results in standardized assessments in math.

Chapter Two: Literature Review

This review is guided by one principal question, why are there gender differences in cognitive skills? The answer to this question is complex, but not because explanations for math and reading skills have not been articulated or examined. Much of the research on this question depends on what is meant by “cognitive skills.” Thus, it seems fitting from the onset to first define what “cognition” is understood to be, what constitutes

“skill,” and what measurements seem best suited to capture the underlying assumption of these two concepts.

Cognition refers to the mental processes in the brain used to gain knowledge and comprehension of the outside world. This includes thinking, knowing, remembering, judging, and problem solving (Tomasello, 1999). Cognition is often distinguished from other skills, such as gross and fine motor skills as well as more general levels of functioning including attitudes and behaviors. Measurement of cognition becomes exceptionally difficult to assess in the earliest stages of life because infants are nonverbal.

Without language, assessing cognitive development requires creative techniques to gauge

learning.4 This study will use assessments of cognitive skill for children in nonverbal and

verbal stages of development.

In the literature, achievement or skill is conceptually distinct from ability although empirically difficult to separate. Skill is subject to learning through environmental

interaction, ranging from informal socialization to formal instruction. Conversely, ability is understood to be a propensity to learn, independent of instruction. The difficulty of this distinction is that ability, which suggests some innate characteristic that is hard- wired, is expressed through assessments that also capture achievement. This is especially problematic for gender where the only tests expressly designed to capture ability— intelligence quotient (IQ) testing—are normalized to eliminate gender differences

(Brody, 1992; Halpern et al., 2007). Thus, much of what is known about gender differences is through the rubric of achievement testing (e.g., curriculum-based assessments), not assessments expressly designed to capture ability. Due to this limitation, and the growing concern that innate ability (e.g., general intelligence or g) is an unsubstantiated assumption (see Mackintosh, 1996; 1998), this paper will use

“achievement” and “skill” rather than terms reflecting “ability.”

Gender gaps vary significantly by which assessments are used and how much emphasis is placed on some assessments over others when compiling aggregate measures of skill. For the purpose of this study, I focus on math and reading skill assessments for

4 One example is habituation. Habituation is the technique where a small child, usually an infant, is presented with various objects. Because only new stimulus illicit a reaction by most infants, when the objects are presented several times, the infant eventually will no longer react, having grown disinterested in a familiar object. If a second set of objects is presented, differing only slightly from the first, a reaction from the infant would signify that he or she can distinguish these objects from the former as different. The ability to distinguish subtle differences between objects is considered one aspect of cognitive skill (see McCall and Carriger, 1993).

two reasons. First, math and reading tests produce psychometrically distinct domains that

are statistically reliable and valid, as is the case for the two data sets assessed here (see

Mulligan, Flanagan, and Denton, 2006; Rock and Pollack, 2002). Second, these tests

have demonstrated linkages to academic and labor market outcomes (Heckman, Stixrud,

and Urzua, 2006).

Another cognitive domain that shows important linkages to labor market

outcomes, especially in well-paying professions such as engineering, architecture,

physics, and chemistry is visuospatial skills (Smith, 1964; Snow and Yalow, 1982; Sorby

and Baartmans, 2000). Visuospatial skills are associated with the ability to take a visual

image and mentally picture this image in another way, whether placed in another location or physically altered (Halpern et al., 2007).5 These skills are different from math and

reading because they are often not directly integrated into school curriculum or expressly

assessed in standardized testing. In addition, research has shown that visuospatial skills

seldom influence students’ educational and career plans directly (Halpern et al., 2007).

Even when visuospatial skills are assessed, they are strongly linked to quantitative skill.

As a result, it is often difficult to unravel distinct skills sets empirically (Tartre, 1990).6

The SAT and the ACT tests are critical tools for assessing cognitive skill. But unlike standardized assessments of math and reading designed to gauge cognitive skill for a whole population of test-takers, only a certain group of girls and boys will take the SAT and ACT. As a result, selection effects jeopardize the generalizability of SAT and ACT

5 However, this concept has little agreement about what assessments and cognitive domains define visuospatial skill (see Halpern, 2000 for a review). 6 Science is another area of proficiency thought to be a “skill.” As Halpern et al. (2007) note, science represents a line of inquiry, not a domain of cognition. In practice, science requires the use of both math and reading skills.

test scores (see Buchmann et al., 2008). This study relies on an assessment of cognitive

skills across a random sample of students, which allows inference to all males and females in the United States, not the just the group taking SAT or ACT examinations.

Overall, the examination of gender difference in cognitive skill via assessments of math and reading is warranted, given these measures have sound psychometric properties and are gauged to assess group-level differences in skill (Mulligan, Flanagan, and

Denton, 2006; Rock and Pollack, 2002). As will be detailed in Chapter Three, these assessments also have the advantage of capturing cognitive skill growth over time. In the following sections, gender gaps in math and reading skills will be reviewed regarding (1) the origins of gender differences, (2) the impact of formal schooling on these differences,

(3) and the role of parenting on gender differences in math and reading skill.

1. WHEN DO GENDER DIFFERENCES IN COGNITIVE SKILLS EMERGE?

Two separate literatures have debated the origins of gender differences in math skill (and to a lesser degree reading skill) in isolation, with little cross-fertilization. As their specializations imply, educational sociologists have primarily focused on gender gaps after school begins. In contrast, child developmentalists have focused on early childhood (see Entwisle, Alexander, and Olson, 1997) although more work in this field has begun to include outcomes in adolescence (see Halpern, 2000). As a result, despite considerable attention and empirical rigor, the origins and explanations of gender differences in math skills remain unclear (Halpern, 2000; Gallagher and Kaufman, 2005;

Geary, 1999; Feingold, 1996; Leahey and Guo, 2001; Buchmann et al., 2008).

This review will first cover what is conventionally understood as the origin of gender gaps in cognitive skills among educational sociologists, followed by the research of child developmentalists. Buchmann et al. (2008) and Halpern, Benbow, Geary, et al.

(2007) are prominent reviews and will provide a reference point for the following survey of the literature on gender differences in childhood and adolescence.

Childhood and Adolescence

There is broad consensus among educational sociologists that gender differences emerge sometime after formal schooling begins. On average, boys outperform girls on standardized tests of math, whereas girls outperform boys on tests of reading and verbal skill (Maccoby and Jacklin, 1974; Hedges and Nowell, 1995; Nowell and Hedges, 1998;

Feingold, 1996; Voyer, Voyer, and Bryden, 1995; Lynn and Irwing, 2004; Whitley,

McHugh, and Frieze, 1986; Friedman, 1989; Penner and Paret, 2008; Hyde, Fennema, and Lamon, 1990; Hyde, 2005). Several studies in the sociological tradition argue that the origins of these differences occur sometime in the middle school to high school years.

Using the National Longitudinal Survey of Youth (NLSY) and the National

Educational Longitudinal Study (NELS:88), Leahey and Guo (2001) posit that meaningful gender differences do not form until high school. Their work is novel in that they utilize growth curve modeling to account for previous gaps over time. By focusing on subsets of math skill in the NELS data, they find important variations in gender gaps in adolescence based on the type of math skill assessed. Although they note early female advantages from age 4 to about age 11, no explanation or further analysis is provided to

understand this puzzling finding. Despite extensive documentation of gender gaps in

math skill across development, they did not examine gender differences in reading skill.

In Entwisle et al.’s seminal work (1994) examining social influences on

educational outcomes, their study suggests that gender gaps in average math skills

emerge sometime in late middle school or early high school. They argue, however, that the examination of averages masks extreme score distributions. They examine the top distribution of math scores by gender and find that boys’ advantages emerge as early as middle school.7 Also, by examining extreme scores, Penner and Paret (2008) report that boys outperform girls on standardized math tests even sooner, as early as kindergarten.

With more extensive longitudinal data, Leahey and Guo’s find (2001) that from ages 4 to

7, higher-scoring girls do better than higher-scoring boys, but by ages 11 to 13, there is

no statistical difference. It appears that girls may have initially higher scores that quickly

reverse at school entry.

Although gender differences in extreme scores are an important consideration,

this study will focus on average score differences. For the most part, the average and

extreme score gender difference literatures reveal similar trends. In this study, the data

will show only slight extreme scores differences. A visual inspection of these differences

reveals only slight variation in the distribution of math and reading scores examined in this study (see Appendix).

7 Using neighbor-level conditions, they find that in middle school, out-of-school activities moderate gender gaps, specifically neighborhood effects (gender differences in play). Work by Downey and Vogt-Yuan (2005) support this argument—in middle school, boys’ and girls’ time spent outside of school contributes to gender differences in math and reading skill. See the parent socialization section for more discussion.

For reading, gender differences show a different pattern than math. Boys fall behind girls in reading in kindergarten (Tach and Farkas, 2006) and continue to struggle with reading in elementary school (Trzesniewski, Moffitt, Caspi, Maughan, 2006). In addition, boys are more likely than girls to have reading disabilities, such as stuttering and delayed speech throughout childhood (Halpern, 1997; Muter, 2003; Rutter, Caspi,

Fergusson, Horwood, et al., 2004).

Overall, the most critical limitation of the sociological inquiries is the near exclusion of early childhood. This oversight is understandable. Evidence of near gender parity (of average scores) at school entry does not provide a clear indication that gender gaps in adolescence have reversed from early childhood. But when the developmental period preceding kindergarten entry (early childhood) is considered, as Leahey and Guo

(2001) show, female advantages are found. What appears as an anomaly among the sociological literature is a pattern found throughout the early childhood literature.

If gender differences in math skills are thought to emerge in adolescence, what should educational sociologists make of gender differences in early childhood?

Early Childhood

Child developmentalists find that many early-math advantages favor girls. At ages before school entry, girls outperform boys on memory tests of spatial locations

(Kimura, 1999), simple arithmetic (Ginsberg and Russell, 1981), mathematical problem solving (Hyde et al., 1990), basic computation (Hyde et al., 1990), and standardized assessments of early math skill (i.e., Test of Early Mathematical Ability) (see Lachance

and Mazzocco, 2006) including less/more tests, counting, informal calculation, relationships between numbers, formal calculation, and decimal concepts (Ginsburg and

Baroody, 2003).8 Girls also excel in reading-related skills including vocabulary, speech production and general verbal skill (Hyde and Linn, 1990).

Paradoxically, despite evidence of numerous female advantages, many scholars of early childhood focus on the few math-related assessments that show consistent male advantage in early childhood such as visuospatial skills (Lachance and Mazzocco, 2006;

Spelke, 2005). Males outperform females on most tests of spatial ability, including mental rotation and spatial perception in adolescence (Halpern, 2000; Linn and Petersen,

1985). Some argue that boys excel in these skills, compared with girls, as young as age three (Robinson, Abbott, Berninger, and Busse, 1996).

Some scholars of early childhood, and occasionally public figures such as university presidents (e.g., Summers), often speculate that the gender gap in visuospatial skills may be linked to the over-representation of men in science and engineering professions (Ceci and Williams, 2006). On the individual level, some evidence suggests that visuospatial skills are reliable predictors of success in college engineering (Poole and

Stanley, 1972) and in certain academic and industrial occupations (Cooper and Mumaw,

1985), but a clear link between gender differences in these skills with occupational gender gaps in adulthood has not been established (Geary, 1998).9 One reason why this

8 I limit my review to those early-math assessments showing female advantages in early math because this pattern runs counter to trends observed in middle to late childhood. It should be noted that many assessments reveal gender similarities rather than differences (see Spelke, 2005; Maccoby and Jacklin, 1974; Hyde, 2005; Nowell and Hedges, 1998). 9 Most assessments of spatial skill show gender differences in late adolescence (ages 12 and older), not early childhood, suggesting that these differences may be socially rather than biologically based. Some

link may be modest is that gender gaps in these skills may be not be excessively large.

Furthermore, as discussed previously, these skills overlap substantially with math skills, making the distinction between the role of visuospatial skills and math skills on later outcomes difficult.

In sum, given girls’ advantages on many, if not most, early math skills that show a gender difference, what explains girls “reversal of fortunes” after school begins?

Reconciling this puzzle is an important step toward comprehensively addressing the question of when gender gaps emerge.

2. WHY DO FORTUNES REVERSE?

The gender reversal of fortunes, observed only for math, implicates schools as the principal cause of an otherwise positive math trajectory for girls in early childhood. If schools are the culprit, then school-based solutions may be critical to efforts aimed at reducing persistent gender gaps in math.

There are several prevailing explanations that may reconcile the fact that girls, in general, score better than boys on math tests prior to school but fall behind boys after school begins. The maturation argument is drawn from a well-known phenomenon: girls are developmentally ahead of boys in childhood and adolescence (Tanner, 1978; Gullo and Burton, 1992). This is important to consider because comparisons using chronological age may ignore sex differences in maturation, comparing more mature girls to less mature boys (Eaton and Yu, 1989). Lynn (1999) argues that boys would show evidence shows that gender gaps in spatial skills can be narrowed by changing educational practices (Kastens and Liben, 2007).

greater cognitive skill advantages in childhood, but this is offset by the advanced

development of females. Observable male advantages begin to emerge as boys “catch

up” developmentally with girls in young adulthood.

But to date, previous work has shown that the maturation advantage of females

has little to no effect on gender gaps in cognitive skills across any stage of development,

including childhood (Newcombe and Dubas, 1987; see Halpern, 2000 for a review). A

true test of maturation would require the isolation of the effects of biological change between males and females from environmental influences. In practice, this is complex as biological traits are inextricably linked to environmental contexts (Spelke, 2005;

Dehaene, 1997; Spelke and Newport, 1998; Halpern, 2000; Buchmann et al., 2008).

Although the role of biology is often understated within sociological research (Freese,

2008; Huber, 2008), this study is not able to address this issue empirically. It is worth acknowledging that biology may still play a potential role in understanding gender gaps in cognitive skills although its effect cannot be isolated here.

There is some reason to suspect that the role of biology would be small because of one obvious pattern. Maturation differences extend well beyond school entry, even into young adulthood (Geary, 1998). For maturation to explain a reversal of fortune for girls,

boys must make developmental gains largely during the transition to school, years before

boys appear to close the developmental gap.

An informal socialization perspective would argue that parents, caretakers, and peers encourage gender-appropriate behaviors that work to reverse female advantages in math as gender boundaries (e.g., gender roles and sex-typing) become more culturally

rigid during the school years (Worell and Goodheart, 2006). From this perspective,

gender differences emerge as a function of parents’ socializing behavior. There is

considerable evidence for parent-gender socialization (see the following parent

socialization section for a review). Although the informal socialization perspective may

be better able to account for gender differences observed in adolescence, it is harder to

understand why parent socialization efforts would initially encourage female advantages

in early math but then reverse at the onset of schooling.

Are Schools the Culprit?

A formal gender socialization argument posits that schooling, as a formal

institution, is the central factor that encourages females to conform to gendered behavior

(Sadker and Sadker, 1994). Schools disrupt female math trajectories by institutionalizing

gendered expectations that work to discourage girls’ pursuit of math-related skills. This

explanation is especially compelling, given that girls appear to enjoy many math-related advantages prior to school entry but fall behind boys once school-level processes take hold. The induction into formal education is akin to many critical transitions highlighted in the life-course literature yet has been overlooked in the sociological literature. As

transitions to high school and college are marked with significant social and emotional

adjustments (e.g. Ainsworth and Roscigno 2005), so too is the transition to formal schooling. At kindergarten, children navigate new and unexplored social roles.

As Entwisle et al. (1997) succinctly state, children struggle with the continued challenge to just “fit in.” Children are exposed to many unfamiliar individuals from

supervisors to peers. New students are constantly evaluated by rules for behavior and achievement that starkly compare to one’s home life where most of the activities are regulated by familiar parents and caretakers. Although this change need not be considered bad for kids, it is nonetheless a new basis of rewards that may be navigated in gendered ways.

An influential source on the effects of schooling on gender differences in cognitive skill is Sadker and Sadker’s book Failing at Fairness (1994). They argue that there is a war against girls in American schools. They cite evidence of teacher favoritism in the classroom and hidden curricula that specifically guide girls away from cultivating skills in math and science (see also Tiedemann, 2000). Schools may exert an influence, they argue, in multiple ways via teachers’ attitudes and behaviors, curricula, ability groupings, and sex composition of classrooms (Roeser, Eccles, and Sameroff, 2000).

There is some supporting evidence of schools’ effect on gender gaps in math. In math class, teachers are more likely to encourage boys to ask questions and to explain concepts (American Association of University Women, 1992; Jones and Wheatley, 1990;

Kelly, 1988; Halpern et al. 2007). Teachers give 61% of praise and 55% of high level questions to boys (Becker, 1981). Similarly, Dee (2006) finds that the gender of the teacher matters, explaining 8% of the gap. Although Becker (1981) argues that small differences culminate over time, evidence is mixed. Males perform no better when taught by male teachers than by female teachers (Soka, Katz, Chaszewski, Wojick, 2007), and causality is unclear in many of these studies (Sokal et al., 2007). In sum, there was

and continues to be widespread concern that schools shortchange women (see American

Association of University Women, 1991; 1992).10

Although enduring gender differences in standardized math achievement throughout the schooling years seem to be ample evidence that schools are a key source in the reproduction of inequality, seasonal learning research has questioned this view.

Seasonal comparison research leverages tests collected at the beginning and end of school, producing a kind of “natural experiment” to assess the rate of learning in and outside of school. Several scholars have published regarding socio-economic and racial differences with provocative findings; cognitive inequalities grow mostly outside of school, during the summer months (Entwisle and Alexander, 1992; Downey et al., 2004), although black/white gaps are one notable exception (see Downey et al., 2004).

Non-school research also finds that race and class differences in cognitive skills are prevalent before school begins (Lee and Burkam, 2002) with lasting effects (Gibbs, unpublished). Non-school factors, well beyond the reach of school reform, appear to be the biggest source of educational inequalities.

With no discussion of the “schools as culprit” debate, Entwisle and Alexander show (1992) that, remarkably, gender gaps are no different in the summer or schooling months. If schooling truly affects gender differences in cognitive skill, we would expect the gender gap to grow at a faster pace during the nine-month school year than during the summer when children are not in school. Yet they do not. Downey et al. (2004) find

10 To be fair, the AAUW has softened its position in recent years. See their more recent publication, “Beyond the ‘Gender Wars’: A Conversation about Girls, Boys, and Education” (2000). A war against boys argument has also been posited (see Sommers, 2000)

similar patterns with national data. Seasonal data collected in these studies represent comparisons limited to childhood, ultimately data examining adolescent gender differences would be ideal given that gender gaps are late forming in comparison with race and class differences. These findings, nonetheless, cast significant doubt on the school-as-culprit argument.

But finding limited evidence that school environments exacerbate race and class differences does not necessarily indicate that gender gaps are due to non-school factors.

First, gender is uncorrelated with disadvantage; gender ratios are relatively the same across race, class, neighborhoods, and schools (Lieberson, 2001). As a result, many of the confounding factors that obscure the source of achievement gaps for race and class in non-school environments are not present for gender. Second, in terms of math, gender is the only group-level achievement gap that appears to reverse at school entry. While race and class disparities are large and relatively unchanged after school entry (Farkas and

Beron, 2004), gender differences appear to change significantly over time.

3. DOES PARENT SOCIALIZATION EXPLAIN GENDER GAPS?

The review thus far has centered on the origins of gender gaps in math and reading and the puzzle of why a positive female math trajectory abruptly reverses during the transition to school. In this section, I address explanations for gender gaps in math and reading in childhood. A review of the literature in adolescence, as well as the potential influence of schooling, teachers, and peers, will also be touched upon. The

focus on childhood is an ideal period for assessing the role of parent socialization given

that parents exert the greatest influence during the child’s first stages of development.

Biological explanations are a common place to start, but the emphasis on biology as a distinct explanation has been shown to be both difficult to isolate and often tautological (Halpern et al., 2007). Although early childhood is often examined by scholars seeking to unravel the role of biological influence on gender differences, this approach has important limitations. As touched upon previously, biological characteristics interact with the environment. If biological advantages or “abilities” exist

between males and females, these advantages surely interact with or are expressed

through the environment in unknown ways. As humans have innate abilities to learn

speech, for example, the expression of this biological “potentiality” (Bussey and

Bandura, 1999) depends on a concerted effort of others to teach language (Huttenlocher,

Levine, and Vevea, 1998).

Second, even when biological differences vary by sex, such as differences in brain

lateralization, brain size, or hormonal levels, and these differences show links to

cognitive skills (Kimura, 1999; Halpern, Wai, and Saw, 2005; Benbow and Stanley,

1980; 1983), the size of these differences is often very small and diminishes in effect over

time (Spelke, 2005). As Penner shows (2008), finding wide variation in gender gaps

cross-culturally undermines the extreme “biology as destiny” framework. Notable

reviews of gender differences in early childhood acknowledge the limits of purely

biological explanations and call for more integrative orientation in the field of child

development (Halpern, 2000; Bussey and Bandura, 1999; Halpern et al., 2007; Geary,

1998).

Overall, biologically linked factors may play some role in understanding gender

differences in cognitive skill, but data collection at the level of detail needed to show

genetic and hormonal linkages on a national scale has yet to be undertaken. As already

noted, addressing these differences is currently beyond the scope of available data and

therefore can only be considered as a potential, yet untestable, consideration in this study.

PARENT SOCIALIZATION MODEL

It has long been established that what parents do with their children has direct implications for cognitive development (Coleman, 1961; Hollingshed, 1949). Parents, especially in the first years of a child’s life, are gatekeepers to his or her social world.

Because of their strong influence, parents’ perceptions of their children’s abilities and parents’ expectations for the children’s future success have a large impact on children’s developing perceptions of self-competence (e.g., Nicholls, 1978, Eccles-Parsons, Adler,

Futterman, Goff, et al., 1982; Jacobs and Eccles, 1992; Muller; 1998). It follows that any differences in parenting based on the child’s gender would subsequently affect academic outcomes as well.

By slightly modifying the parent socialization model of Jacobs, Davis-Kean,

Bleeker, Eccles, Malanchuk (2005) and Eccles-Parsons, Adler, Futterman, Goff, et al.

(1983), I incorporate child-level specific behaviors and develop a more streamlined version (see Jacobs et al., 2005, p. 251). Although teacher and peer influences are

important considerations for explaining gender gaps in cognitive skills, this study focuses on parental influences. The conceptual model is utilized to principally understand gender gaps in math skill but will also be referred to when exploring processes that may account for gender differences in reading differences as well.

Distal Proximate

A B C

Parent, Family, and Parents' General Beliefs Parents' Specific Beliefs and Behaviors Neighborhood and Behaviors Characteristics e.g., Gender Role Stereotypes, e.g., Expectations in Math, General and Specific Personal Enrollment in Math Tutoring, e.g., Education, Occupation, Values, Child Rearing Beliefs, Involvement with Child in Math Number of Children, Ethnicity, Emotional Warmth, Involvement Enhancing Activities Neighborhood in Activities Child Outcomes Standardized Math Outcomes Item Specific Outcomes Math Grades

Childs' General Beliefs Childs' Specific Beliefs Child and Sibling and Behaviors and Behaviors Characteristics e.g., Perception of Overall Skill, e.g., Use of Computer, Time Self Efficacy, Interests, Spent Studying Math, e.g., Sex, Health Temperament, Approaches to Involvement in Clubs, Activities Learning that Enhance Math Learning, Preferences, Interest in Math

Figure 1: Conceptual Model of Parent Socialization on Gender Differences in Math Outcomes

Distal Factors

Using Figure 1 as a guide, section A represents factors that are more distal, or less directly linked to specific math (and reading) outcomes (see Downey and Gibbs, 2007 for a discussion). These distal factors have direct and indirect relationships to gender differences in academic outcomes as indicated by arrows to section B and directly to child outcomes.

Some research supports this assumption although the role of distal factors is

unclear. Income, for example, can have important effects on how scarce resources are

allocated for children’s educational development. Other restrictions associated with

family structure (e.g., single mother, sibling size) and occupation type can limit parental

involvement. In support of this link, some research shows that gender gaps in test scores

vary across the socio-economic status of the parents. Results are mixed, however, with

some evidence that gender gaps are larger in low-income populations with other work

showing larger gaps in higher income homes (Hinshaw, 1992; Buchmann et al., 2008).

If there is a relationship between socio-economic status and gender gaps, it may be due to

gender differences in the use of neighborhood resources. Gender differences in out-of-

school activities, play, and the time spent outside link to cognitive development (Entwisle

et al., 1994; Downey and Vogt-Yuan, 2005).

There may not be a large effect of socio-economic conditions on gender

differences. Related work on parental investment, a product of socio-economic

resources, supports this finding. Altenburg-Caldwell, Jacobs, and Eccles (1999) show

that parents provide an equal number of extracurricular activities during early to middle

childhood for girls and boys. This suggests that equal investment is being made by

parents for children’s activities, despite some gender differences in the type of activities.

DiPrete and Jennings (2008) use the same data analyzed in this dissertation and find that

gender differences in socio/behavioral skills are unlinked to socio-economic status. Their work did not examine the interaction of gender and socio-economic status on cognitive

skills, however. As a result, this potential relationship merits more empirical investigation.

General Proximate Factors

If distal factors influence gender gaps in cognitive skill, they undoubtedly filter through more proximate causes (see Downey and Gibbs, 2007). As sections B and C represent, proximate factors are mechanisms that more directly shape cognitive learning by gender compared with more distal factors shown in section A. These sections focus on research regarding the role of beliefs and behaviors of both the parent and the child on academic outcomes.

Parent Gender Stereotypes

When parents hold gender stereotypes or preformed expectations of what skills their sons or daughters are capable of achieving, gendered outcomes are more likely.

Parental stereotypes filter how parents interpret their children’s skills (Jacobs and Eccles,

1992). Parents’ interpretations of their sons’ or daughters’ performances tend to influence the children’s self-perceptions and grades in gendered ways even when previous performance is statistically controlled (Jacobs and Eccles, 1992).

More recent research shows that this effect has lasting consequences on children’s later career choices (Bleeker and Jacobs, 2004). To illustrate how parents influence children, Jacobs et al. (2005) found that as fathers’ gender stereotype increases, girls’ math interest declines while boys’ interest in math increased. The role of parent

stereotypes is important because parents’ expectations of their child’s skills provide

evaluative cues that can either promote or dissuade children from participating in

activities deemed as “gendered” (Ginsburg and Bronstein, 1993).

Parental Involvement

Related to gender stereotyping, parents may be differentially involved with their

children’s educational development. Research shows that higher levels of parental

involvement with their children’s educational development is correlated with higher

levels of children’s performance in math (Muller, 1998; Halpern et al., 2007). Stevenson and Baker (1987) find that parents are more involved in school activities with sons than

daughters, especially in the early school years. Likewise, parents are more involved in

“gifted” activities, computer classes, and sports with their sons than daughters (Eccles

and Harold, 1992)

Evidence of gendered parenting and its impact on cognitive skills is scarcer in

early childhood than adolescence. Parents are more likely to encourage their sons than

daughters to be physically aggressive and to adopt other gendered behavior in childhood

(Lytton and Romney, 1991; Power and Parke, 1986); perhaps as a result, fathers have

been found to be more restrictive and spend more time with their boys than girls (Lytton

and Romney, 1991; Harris and Morgan, 1991), and mothers may use more supportive

speech and spend more time with their girls than boys (Leaper, Anderson, Sanders, 1998;

Harris and Morgan, 1991; see McHale, Crouter, and Whiteman, 2003 for a review).

Despite these findings, there are few large-scale studies on differential socialization by

gender and fewer that link these differences to cognitive outcomes (Muller, 1998;

McHale et al., 2003; Ruble and Martin, 1998; Block, 1983).

Feedback Effects

Overall, results regarding whether parental involvement and expectations vary by the gender of child are inconclusive. Raymond and Benbow (1986) find that parents are equally supportive of their mathematically talented sons and daughters, and Muller

(1998) finds that parental involvement in children’s schooling is not gender specific and may even work to offset gender stereotypes regarding math and science. When gendered differences in parental involvement are found, it may be that parents are simply responding to the needs of the child, an often overlooked issue in the literature

(Buchmann et al., 2008). This is plausible, given that when parents are more involved with boys, they may be responding to greater behavior issues and academic troubles that boys have compared with girls (Muller, 1998).

This is an important consideration, but more specific measures of parental involvement are needed as well as more longitudinal data capable of accounting for previous skills before the parent/child feedback effect can properly explored (Buchmann et al., 2008, Halpern et al., 2007; Muller, 1998). Without this consideration, the impact of parenting would be overestimated. Fortunately, the data examined in this study is well-suited to untangle the reciprocal influences of parent-child interactions.

Specific Proximal Factors

Section C represents the more specific parent and child beliefs and behaviors that link to math and reading outcomes. Although parent stereotypes have been reviewed,

there are specific parental expectations parents hold regarding their children’s

development in math and reading that can be gendered.

Parental Expectations

Parental expectations are important for the development of children’s confidence

in math and reading. Parents’ perceptions of their children’s abilities, their expectations

for their child’s success, predicts children’s self-perceptions of competence and their

actual achievement, even after controlling for previous achievement (Eccles-Parsons et

al., 1982; Jacobs and Eccles, 1992; Bleeker and Jacobs, 2004; see Halpern et al., 2007).11

Specifically for girls, parents’ perceptions matter because they affect girls’

efficacy in math and their subsequent math performance (Klebanov and Brooks-Gunn,

1992). Most importantly, parents’ perceptions are linked to their child’s later math

outcomes (Klebanov and Brooks-Gunn, 1992). Although some evidence suggests that

competence is assessed from parents to children and that parents’ views of children’s

abilities are quite stable over time (Yoon, Wigfield, and Eccles, 1993), parents clearly

form opinions based on actual achievement. Expectations, like parental involvement, are

11 Peers can also convey negative influences regarding girls’ confidence and interest in math. Some research shows that girls fall behind in middle school due to peer pressure and societal expectations. Often girls more than boys, minimize their interest and skills in math (Andreescu, Gallian, Kane, and Mertz, 2008).

subject to the needs of the child. Thus, without the inclusion of the child’s skill level,

results will tend to overstate the role of parenting due to feedback effects.

Gendered Activities

Parents have been found to provide more math-supportive environments for their

sons than for their daughters, including buying more math and science toys for their boys

than for their girls (Jacobs et al., 2005). This may partly explain why boys are more

likely to participate in science fairs and other math-related activities and to use a

computer at home (Downey and Vogt-Yuan, 2005).

Girls and boys often cluster into stereotypic activities throughout the schooling years, including sports, social activities, English, and music (Eccles, Wigfield, Flanagan,

Miller, et al., 1989; Eccles, Wigfield, Harold, and Blumenfeld, 1993; Jacobs, Lanza,

Osgood, Eccles, and Wigfield, 2002; Wigfield, Eccles, Mac Iver, Reuman, and Midgley,

1991). Girls participate significantly more than boys in art activities and clubs while

boys participate in team sports significantly more than girls (Altenburg-Caldwell, Jacobs,

and Eccles, 1999). As boys’ participation in sports increases, interest in arts and other

female-dominated activities declines. The same is true for involvement in arts. As

involvement increases in art, interest in sports declines (Altenburg-Caldwell, Jacobs, and

Eccles, 1999). As with parental involvement, however, gender differences in activities

may result from differences in child preferences or skill (Buchmann et al., 2008).

Self-Efficacy and Stereotype Threat

Self-efficacy and stereotype threat cannot be directly accounted for in this

dissertation but are important to review because these factors are accounted for in how

the math and reading assessments are collected. Testing has been designed to minimize

gender differences. Although this study is unable to compare results between testing

formats (as a way to gauge the size of the effect), the data provide results less likely to be

contaminated by gender differences in self-efficacy and stereotype threat. Thus a review

of this literature is needed to illustrate the advantages gained by use of data accounting

for this important literature.

Self-efficacy, defined as the belief that one is capable of obtaining certain

outcomes, is an important concept for understanding academic outcomes. For girls, self-

efficacy is more important for math involvement than girls’ initial interest although girls’

self-perceptions of one’s math “ability” seem to decline over time, reaching parity at 12th grade (Jacobs et al., 2002; Eccles et al., 1989; Wigfield et al., 1991; Wigfield, Eccles,

Yoon, Harold, et al., 1997). But self-efficacy could matter most when girls are tested for math-related skills. When girls hold implicit stereotypes that associate math with male and see themselves as more feminine (compared with other girls), they perform worse on math tests (Kiefer and Sekaquaptewa, 2007).

This phenomenon, referred to as stereotype threat, is the unfounded perception among equally skilled girls that boys outperform them on standardized tests, especially in mathematics. Because of this, girls experience a heightened feeling of anxiety during test taking, which negatively affects their test performance (Steele, 1997; Spencer, Steele, and

Quinn, 1999). Stereotype-threat effect on males’ and females’ performance on math tests has been replicated numerous times (e.g., Ben-Zeev, Fein, and Inzlicht, 2005; Cadinu,

Maass, Rosabianca, and Kiesner, 2005; Ford, Ferguson, Brooks, and Hagadone, 2004;

Inzlicht and Ben-Zeev, 2000; Johns, Schmader, and Martens, 2005; Keller and

Dauenheimer, 2003) although some argue whether covariates should be used to uncover the effect (Sackett et al., 2004a; 2004b). (See Halpern et al. 2007 for an extensive review.)

The Grade/Assessment Puzzle

Given this lengthy review of findings, a puzzle emerges. Although standardized tests provide a clear-cut picture showing girls as better at reading and boys as better at math, these simplified dichotomies are complicated by the examination of grades and classroom citizenship—both correlates of cognitive skills. Girls consistently have higher grades in all classes at all grade levels, including math classes (Kimball, 1989;

Willingham and Cole, 1997; Alexander and Eckland, 1974; Alexander and McDill, 1976;

Mickelson, 1989; Perkins, Kleiner, Roey, Brown, 2004; Duckworth and Seligman, 2006;

Gallagher and Kaufman, 2005). This is puzzling given that math grades are correlated with math and reading skills (Kurdek and Sinclair, 2000). This suggests that gender gaps in math endure despite girls’ successes in the classroom.

And girls’ advantages go beyond grades and classroom citizenship. Girls also possess higher levels of noncognitive skills such as attentiveness and organizational skills

(Farkas, Grobe, Sheehan, and Shuan, 1990; Jacob, 2002) self discipline (Silverman,

2003; Duckworth and Seligman, 2006), leadership qualities, and interest in school, all

linked to academic success (Rosendbaum, 2001). (See DiPrete and Jennings 2008;

Buchmann et al., 2008 for reviews.) Conversely, boys display more developmental

disabilities, more disruptive conduct in class, and fewer positive orientations toward

learning (Zill and West, 2001). High school teachers consistently rate girls as putting

forth more effort and as being less disruptive than boys (Downey and Vogt-Yuan, 2005;

see Buchmann et al., 2008).

In addition, girls outpace boys on the number of college preparatory courses and

Advanced Placement examinations taken (Bae et al., 2000; Freeman, 2004). Girls are

more involved in extracurricular activities (except athletic teams) (Bae et al., 2000) and

participate in more cultural activities within and outside of school (Dumais, 2002). All

these advantages are related to (1) academic success in high school, (2) the likelihood of

enrolling in college, and (3) educational attainment (see Buchmann et al., 2008).

Yet, despite all of these advantages, not to mention advantages in math-related

skills in early childhood, girls still fall behind boys on standardized tests of math skill.

Why? The answer is unclear, but one set of findings provides a clue. Girls appear to

score lower on quantitative tests when content is not closely tied to curriculum (Geary,

1996; Halpern, 2000). Although standardized assessments, especially in this study, are

designed to capture curriculum learning, questions of higher math skill often require

novel solutions not taught formally in the classroom (see Halpern et al., 2007 for a

review). This is relevant given that girls seem to score lower on tests assessing novel solutions (Halpern et al., 2007).

Girls’ advantages form before the start of school when mathematics consists of

computational knowledge and speed. Boys’ advantages emerge when math is centered

on reasoning and creativity to solve problems. These skills are most often applied in

geometry and calculus, classes typically taught in high school (Geary, 1996; Hyde,

Fennema, and Lamon, 1990; see Halpern et al., 2007). Gender gaps, then, may be less about gender gaps in curriculum-based math skills and more about skills in creating new solutions to complex math problems, skills often developed beyond the scope of the school curriculum.

What Gender Gap?

Having considered the gender difference literature above, one question remains: are gender gaps large enough to merit concern? The gender similarities hypothesis argues that males and female are similar on most, but not all, psychological variables including cognitive skills (Hyde, 2005). This hypothesis is supported by extensive reviews of the literature although not always emphasized (see Hedges and Nowell, 1998).

Using effect size as a guide in a review of over 40 meta-analyses of gender differences,

Hyde (2005) concludes that motor skills (across development) and sexuality (in adolescence and adulthood, e.g. sexual satisfaction) are exceptionally large, higher among males than females. All other psychological factors range from small to moderate.

If true, gender differences in early childhood may be overstated. Thus, theories developed to explain the role of early childhood on later life outcomes would merit less

emphasis (for example, see Bussey and Bandura, 1999). More recent work seems to

support this conclusion. Hyde, Linberg, Linn, Ellis, and Williams (2008) find evidence

of gender parity in math and reading skills. Using National Assessment of Education

Progress data, they show that gender gaps in tests of math and reading have nearly

converged from grades 2 to 11. They find that the standardized math score differences,

translated into standard deviations, to be .06 in favor of girls over boys in 2nd grade, with

the same standard deviation difference of .06 in 11th grade. They also find slight variations in these differences by state, suggesting that if there are gender differences in math skill, region of country plays some role in this gender disparity.

There are several reasons to reconsider these findings. First, there is still evidence of gender differences in the NAEP data. Gender differences would be larger if high level math skills were assessed (see Hyde et al., 2008). It may also be that, as Hyde (2005) is careful to relay, effect sizes can be misleading; “small effects can turn out practically important” (quoting Rosenthal et al., 2000, pp. 15-16).

Second, as noted above, girls excel in numerous factors associated with the development of math skills, from grades to classroom behavior. This research will show that as gender gaps in standardized assessments of math reach parity at a bivariate level, math gaps are substantially larger when modeled with the numerous advantages girls utilize to equalize math scores with boys. Despite boys’ disruptive behaviors in the classroom and poorer grades, and despite girls’ advantages in their approaches to learning, gender gaps are relatively small. Given these advantages for girls, why are boys not behind in math?

Unfortunately, the data analyzed here does not extend into adulthood where the impact of gender differences in childhood could be assessed by their labor market returns.

Thus, the gender similarities argument is an important consideration when interpreting results of this study. To facilitate comparisons between this study and the work of Hyde and others, effect sizes will be calculated to allow the reader comparable scales to weigh in on the merit of this hypothesis.

Importance of Subtests

The various claims regarding the origins and explanation of gender gaps in math and reading skills are subject to a central limitation of extant research—the over- utilization of standardized assessment of math and reading skill. Although the use of item-specific tests are common among child developmentalists, there is a significant lack of data measuring disaggregated cognitive skills proscriptively, especially in childhood

(see Leahey and Guo, 2001; Menaghan, 2005).

As a result, understanding the origins and trajectories of gender gaps in math skill has certainly been obscured (e.g. Spelke, 2005). When item-level gender differences are examined, important patterns have been found. Girls often excel in lower level-math skill, whereas boys tend to excel on more complex math assessments (Maccoby and

Jacklin, 1974; Becker, 1990).

Item Difficulty and Gender Bias

Subtests can allow separate analyses across item complexity. This is important

because as assessments become more complex, gender bias is much more likely to affect

results. Although it appears that when content becomes more difficult, boys begin to

excel in math-related assessments, scholars have argued that this pattern might be

tempered by gender bias in the selection of assessment instruments (Penner, 2003;

Doolittle and Cleary, 1987; Reed, Fox, Andrews, et al., 2007). Gender-item-difficulty interaction research has shown that the selection of more computational complex assessments within content areas will show larger gender differences than less complex assessments.12

One way to separate gender neutral assessments of skill from gender bias in item-

level assessments is to conduct differential item performance (DIF). Differential item

performance is an analytic approach indicating whether the probability of answering an

item correctly is associated with group membership, controlling for overall skill in the

content area measured. In the data analyzed in this study, items that favor one group over

another group are submitted to content analysis by reviewers not involved with the test

development. Assessments deemed biased in language or content were discarded

(Mulligan, Flanagan, and Denton, 2006; Rock and Pollack, 2002). Thus, this study is

unique from most national assessments of gender differences in that item difficulty has

12 Some have speculated that female advantages in lower-item difficulty result from the overrepresentation of males in the low end of the distribution of math difficulty (Bielinski and Davison, 1998). Yet, Bielinki and Davison fail to reconcile this speculation with published evidence that larger male variance can be found across content.

been minimized through differential item performance (DIF) analysis (see Doolittle,

1989).13

Indeed, gender bias may also result from response formats, cognitive complexity,

empirical difficulty, differential guessing, and serial position (see Bielinski and Davison,

1998). Due to the limitations of the testing format of the data in this study, these

considerations could not be explored but should be kept in mind when interpreting the

results of this study.

ADVANCING THE LITERATURE

What should we make of the literature on gender differences in cognitive skill?

First, the origins and explanations of gender differences in math and reading have been

examined in two different literatures with little cross-fertilization. As a result,

educational sociologists often overlooked early childhood, whereas child

developmentalists often under-explored adolescent and adult outcomes. Because these

literatures are focused on different developmental periods, without empirical links

between the two, distortions emerge (see Entwisle et al., 1994). Child developmentalists

often overstate the relevance of early childhood for adolescent and adult outcomes, and

educational sociologists often understate (or altogether ignore) the impact of group-level

differences formed in early childhood. As a result, competing trends in gender

differences are difficult to theoretically and empirically reconcile.

13 It is important to note that although the contribution of DIF analysis is important for accounting for possible gender bias in testing, as long as curriculum is closely tied with assessments, they should not simply be removed because of group differences (Doolittle, 1989; Mulligan, Flanagan, Denton, 2006; Rock and Pollack, 2002).

Second, pinpointing the origins of gender differences in cognitive skills depends

greatly on which measures are used. It is not enough to have data linking two

developmental periods. Gender differences in math skills, in aggregated form, will show

very different points of divergence when measured in disaggregated form. As a result,

the selection of which measures best represent a given skill moves to the forefront of the

gender differences debate, especially when puzzles, such as the reversal of fortunes

hypothesis, are difficult to resolve when skills are examined at the aggregate level.

What is the way forward? Both points reveal a glaring problem: the origins and

explanations of gender gaps in cognitive skills throughout childhood are unclear without

better data.14 Despite extensive investigation in early childhood regarding gender

differences, few studies have explored the formation of math- and reading-related skill from an early age to late childhood. By looking at gender differences in math skill with better data, we may be able to examine: the origins of gender differences in math and reading, the puzzling reversal of girls’ fortunes that appears to occur around school entry, and whether parental influences play a role.

The data analyzed in this study are well-suited to move the literature forward.

The two data assessed in this dissertation are rich in assessments of cognitive skills and socio-structural measures, are longitudinal and nationally representative in design, and are relatively large. In addition, the data includes multiple assessments of cognitive skills and parent-child interactions, sampling an unprecedented number of children from early

14 In a review of 46 meta-analyses complied by Hyde (2005), only 5% are national representative and fewer longitudinal assessed. As a result, more is known about adults on a national-scale than children (Ruble and Martin., 1998).

to middle childhood and late childhood to early adolescence. As a result, the data can

allow a thorough examination of the mechanisms and explanations for gender gap in

math over time. With two longitudinal data sets connecting early childhood with middle

and late childhood, this study will provide an up-to-date national portrait of gender differences in the United States.

Chapter Three: Methods

The two data sets analyzed in this dissertation were collected by the National

Center for Educational Statistics in response to increased interest in school readiness and

the relative lack of data connecting children’s early health, home, and out-of-homes

experiences with later academic outcomes (Magnuson and Waldfogel 2005; Mulligan,

Flanagan, and Denton, 2006; Rock and Pollack, 2002). Data collected at the scale of

these two data sets is unprecedented. The goal of the data collection is to provide comprehensive data to further understand children’s early development; to understand

key transitions during the early childhood years; and to understand how their early

experiences relate to their later development, learning, and experiences in school

(Mulligan, Flanagan, and Denton, 2006). As a result, measurement of cognitive

development is the central feature of the data. The data contain the best available

assessments of skill across numerous cognitive domains.

Although there are several aspects of these data that is similar with other studies

on early childhood development and growth, the collection of information directly from

children’s fathers, mothers, caretakers, and teachers as well as videotaped parent-child

interactions make the study design truly unique. In all, the data is a collection of nine

data sets following two cohorts, one from 9 months to 4 years of age and the other, from

kindergarten to 5th grade. Given all these features, these data provide an authoritative

source for exploring questions on gender differences in cognitive skill.

FIRST SAMPLE

The Early Childhood Longitudinal Survey-Birth Cohort 2001 (ECLS-B) follows a nationally representative sample of over 10,000 children representative of the roughly four million American children born in 2001 (Flanagan and West, 2004; Mulligan,

Flanagan, and Denton, 2006).15 The sample of children and their parents were first

assessed at 9 months of age during in-home interviews and then reassessed at 2 and 4

years of age.

This dataset is particularly well-suited for exploring gender gaps in cognition

because the ECLS-B offers the opportunity to explore a broad range of parent-child

interactions that may link to the earliest cognitive disparities across early childhood,

including items from the Home Observation Measurement of Environment (HOME)

inventory (Bradley and Caldwell, 1981). An exhaustive list of all parent interaction

measures in the data can be found in the psychometric reports (Flanagan and West, 2003;

Mulligan, Flanagan, and Denton, 2006). Those measures associated with the HOME

inventory are detailed below. The response rate for ECLS-B was 77% for the

parent interview and 96% for the child assessment at 9 months of age; 93% for the parent

interview and 94% for the child assessment at 2 years of age; and 91% for parent

15 For ECLS-B data, no reported cases were missing for gender; therefore the sample was not restricted.

interview and 98% for the child assessment at 4 years of age (Mulligan, Flanagan, and

Denton, 2006).

MEASURES

Dependent Variables

I use several measures to assess cognitive skills over time. The Bayley Short

Form-Research Edition (BSF-R), administered at 9 and 2 years of age, like the full

version (Bayley Scale of Infant Development; see Bayley, 2006), is designed to measure

children’s mental and motor development at a very early ages. The BSF-R assesses child

development in terms of exploring objects (e.g., reaching for and holding objects),

exploring objects with a purpose (e.g., attempting to determine what makes the ringing

sound in a bell), babbling, early problem solving (e.g., using an object to retrieve an out-

of-reach toy), and communicating with words (see Mulligan and Flanagan, 2006 for tests

of reliability and validity). I use these measures to establish and account for early

forming cognitive disparities at 9 months and 2 years of age.

At 4 years of age, I use two sets of Item Response Theory (IRT) measures which reflect more specific assessments of math and reading skill: (1) the Test of Early

Mathematics Ability-2 (TEMA-2), which assesses number sense, basic geometry, counting, operations and patterns; and (2) literacy, which measures letter recognition, letter sounds, early reading, phonological awareness (Pre-CTOPP), knowledge of print

conventions, and matching words. Item Response Theory assumes that the respondent’s

probability of answering an item correctly matches his or her skill level for the construct

being measured. Both data sets use a three-parameter IRT logistic model using the pattern of right, wrong, and omitted responses to the items administered and the difficulty, discrimination power, and probability of guessing correctly (see Mulligan,

Flanagan, and Denton, 2006).

Control Variables

Race is measured as white, black, Hispanic, or other. The “other” category contains groups such as Asian-American, Native American and other racial/ethnic identifications not sampled in sufficient size for extended analysis. Although no gender differences in age of assessment was anticipated, it is modeled to provide a metric to indicate how much a given outcome measures increases in a given month of development.

Distal Factors

Child Health Characteristics

Child health characteristics include birth weight, gestation age, APGAR score,

Body Mass Index, and early health factors that were controlled for. Girls and boys have been shown to vary in early health factors (Geary 1998) and are therefore considered in this analysis. Birth weight is coded as normal (greater than 5.5 pounds), moderate (5.5 to

3.5 pounds), and low (less than 3.5 pounds). Gestation is measured in weeks, ranging from 17 to 47 weeks. The APGAR score, devised to assess the initial newborn health

(Caseym NcIntire, and Leveno, 2001), is included to account for any gender differences

in health shortly after delivery. The child’s Body Mass Index follows the standard

calculation (weight divided by the square of height). Child health includes parent reports of asthma, ear infections and breathing difficulty. These measures are based on parent reports of whether the child has seen the doctor for any of these conditions.

Socio-economic Status, Family Structure, Neighborhood.

Socio-economic status is a composite scale comprising of income, occupational prestige and educational level of the child’s parents. I use a zero-centered score to aid in interpretation of gender interaction effects. This allows one to assess the size of the interaction of gender and socio-economic status, centered at the average socio-economic status of the population. As a way to consider inter-generational effects of education on the child’s cognitive development, child’s grandmother’s education is included. It is measured on a 22 level scale from “no formal schooling,” to “professional degree after bachelor’s degree.” Sibling size ranges from 0-9 biological siblings in the household.

Biological Mother and Father in Home is a dichotomous measure: 1= “both biological parents in the home” and 0= “other parental arrangements.” Finally, a measure for living in an unsafe neighborhood is coded as 1= “very safe” to 4= “very unsafe.” This measure is included to indirectly capture the gender differences in how neighborhood conditions might influence cognitive outcomes (Entwisle et al., 1994; Downey and Vogt-Yuan

2005).

Mediating Variables

Mediating factors are expected to account for, at least partially, gender gaps in

cognitive skills. Assessments of parent-child interactions were developed directly from

the Home Observation for Measurement of the Environment (HOME). Adapted from the

National Household Education Survey (NHES), the HOME scale is designed to measure

the quality and extent of stimulation in the home environment available to a child

(Manual, Caldwell and Bradley, 2001; Caldwell and Bradley, 1979). Items from the

NHES were selected that could be applied to young children and measured given the

scale of the sample. Many items from the HOME measure require extensive observation

of the child’s environment beyond the limits of the home visit (see Mulligan, Flanagan, and Denton, 2006).

HOME measures were collected from four sources, mother surveys, father questionnaires, interviewer observations, and video-taped interactions. Interviews were collected by computer-assisted personal interviewing (CAPI). The interview was conducted in the child’s home at 9 months of age and again at 2 and 4 years of age. The primary provider was interviewed who had the most knowledge about the care and education of the child. This was either the child’s mother of female guardian in nearly all cases (100 % at 9 months, 98 % at 2 years, and 95 % at 4 years, see Mulligan, Flanagan, and Denton, 2006). Questionnaires were mailed to fathers to complete and return, whether they lived in the home or elsewhere. 16

16 To limit the complexity of adding only a small number of other parental arrangements, the sample is restricted to only biological mothers responding to in-home surveys and assessments.

The parent’s frequency of reading, singing songs and telling stories was collected from the parent survey at 9 months and at 2 years of age. Response categories ranged from: 1= “not at all” to 4= “everyday.” Paternal provision of child needs is a factor of several measures collected from the father questionnaire at 2 years of age (alpha score= .875). Measures asked about how often fathers change child’s diaper, feed child, feed child, and dress child. Response categories ranged from: 1= “more than once a day” to 4= “rarely.”

Interviewers observed parent-child interaction throughout the assessment of the child’s cognitive development. Shortly after the parent completed the computer survey with the interviewer, the interviewer rated parent-child interactions observed during the home visit. Responses categories were adaptations from the HOME inventory. Several questions conceptually captured Maternal Warmth, as measured by whether the mother spoke spontaneously to her child, verbally responded to her child, and caressed, hugged, or kissed her child during the in-home interview. Alpha score were moderate at .582 for the factor at 9 months and .629 at 2 years of age.

Videotaping parent-child interactions in childhood at a national scale is a unique feature of the sample and therefore requires some detail to demonstrate the utility of this important assessment. Partly collected due to the limitations of extensive interviewing and testing, videotaping of parent-child interaction also allows for inter-rater reliability to be assessed and further coding to be developed. A total of 8,138 DVDs were completed with 503, or 6.2 %, not coded due to poor quality and other technical problems

(Mulligan, Flanagan, and Denton, 2006).

Two Bags Task

At age two, the Two Bags Task—a modification of the Three Bags Task used in the Early Head Start Research and Evaluation Project) was used to assess aspects of the parent-child relationship. The Two Bags Task is a unique semi-structured assessment that documents parent-child interactions in a context of directed child play. Items collected in this assessment are simplified versions of the Three Bags Assessment administered in other large-scale studies such as the Study of Early Child Care (Mulligan,

Flanagan, and Denton, 2006).

In this task, the parent and child are directed to two separate bags. The first bag contains a children’s book, Courduroy (Freeman 1968), and the second bag contains two containers of Play-Doh©, two cookie cutters, and a rolling pin. The parent and child are given ten minutes to play with the contents in the first, then the second bag. Interactions are recorded on DVD and later coded based on (1) five global scales for the parent and

(2) three global scales for the child (more details in Mulligan, Flanagan, and Denton,

2006). Scales are on a 7-point Likert-type assessment ranging from 1= “very low” to 7=

“very high.” Scales were based on the Two Bag assessments in the Early Head Start

Research and Evaluation Project (Brady-Smith, Fauth, and Brooks-Gunn, 2003).

The parent and child were both rated for parent-child interactions during the task.

Eight parent-child interaction measures were produced, defined as parental emotional supportiveness, parental stimulation of cognitive development, parental intrusiveness, parent negative regard, parental detachment, child engagement of parent, child quality of play, and child negativity towards parent. Of these constructs, five were found to relate

to a larger construct capturing parent-child behavior which I have labeled “parent-child cognitive stimulation” (alpha= .856). A review of what these five constructs capture is

detailed below.

Three of the five measures assess parents’ behavior. (1) Parental Emotional

Supportiveness captures the emotional availability of the parent, whether the parent

provides a “secure base” from which a child can explore in addition to providing

emotional support and enthusiasm towards the child’s autonomous work. (2) Parental

Stimulation of Cognitive Development is designed to capture a parents’ concerted effort

to teach perceptual, cognitive and language skills. If the approach of the parent is not at

or slightly above the child’s’ skill level, the parent is not rated as providing cognitive

stimulation. (3) Parental Detachment measures the parent’s awareness of his/her

engagement with the child. This includes the quantity and quality of parent and child

interactions.

The children’s behavior includes two measures. Child Engagement of Parent is

meant to capture the extent that the child seeks interaction with the parent and does so in

a positive way. This is measured by smiling, laughter, etc. The child frequently looks at

the parent and attempts to interact. At the lower end of the scale, the child ignores or

rejects the parent’s interaction. The other child scale is Child Quality of Play. This

captures the child’s sustained involvement with the objects at hand and the attention to

the object, self-direction and the complexity of play.

Because parent cognitive stimulation is measured by both parent and child

behaviors, it is important to consider the role of feedback effects as discussed in Chapter

Two. Although children’s responsiveness is a product of parents’ stimulation, parent

stimulation could equally be responding to a child’s behavior. Although this factor is

designed to capture parent-child cognitive stimulation, it cannot isolate the result of

parent stimulation and child behavior. This task will be undertaken with the second data

set.

Linking Cognitive Assessments

One important consideration with measuring cognitive skill in the ECLS-B is the

relationship between measures of skill in infancy and later math and reading skill.

Because infants are at such an early stage of development, the cognitive skills tested are

necessarily different from the more advanced cognitive skills tested among older children

measured at 4 years of age. Previous research suggests that the Bayley Scale of Infant

Development (BSID) demonstrates some predictive validity as it correlates positively

with children’s later performance on the Stanford-Binet and Wechsler tests, although

these correlations are modest—ranging from approximately .15 to .35 (for a review, see

Fryer and Levitt, 2006).

While there is some evidence that the BSID measures cognitive dimensions that

overlap with those indicated by later tests, the BSID may represent a more general

approach to cognition that assumes that skills measured among infants are necessarily

different from specific skill in early math and reading measured just a few years later.

Bayley cognitive measures at 2 years of age and the math and reading assessments at 4

years of age are modestly correlated at around .4, suggesting a relationship.

Analysis

With the ECLS-B, I use Structural Equation Modeling (SEM) to model covariates and mediating factors on gender gaps in early math and reading at 4 years of age.

Covariates and mediating factors are selected that best represent aspects of the parent socialization model. SEM has several advantages over Ordinary Least Squares (OLS) regression; it can (1) account for causal ordering of exogenous (distal factors) and endogenous variables (proximate factors) on gender gaps in cognitive skills, (2) model latent constructs derived from multiple variables using factor analysis, and (3) account for missing data omitted by listwise deletion in OLS regression (see Kline, 2005).

To address missing values, Full Information Maximum Likelihood is used in all analyses (see Kline, 2005).17 Although the ECLS-B uses two psychometrically distinct cognitive outcomes, (Bayley at 9 months and 2 years of age and early math and reading skill at 4 years of age), assessments are highly correlated. Therefore, for ease of interpretation, analysis is conducted at each wave without the inclusion of previous cognitive skill and results should be interpreted with this analytic omission in mind.18

SECOND SAMPLE

The Early Childhood Longitudinal Study—Kindergarten Cohort 1998-99 (ECLS-

K) is a nationally representative survey of over 20,000 children in approximately 1,000

17 Results were also conducted using OLS using listwise deletion with no discernable differences in the general findings reported below. Missing data are modest for most variables in the data. Missing values for socio-economic status were computed by NCES using the hot-decking technique (see Flanagan and West, 2004). 18 If previous assessments are included and share a high correlation, estimates would better reflect a change model (see Allison 1990). This would needlessly complicate the interpretation of results.

schools beginning at the start of kindergarten in 1998.19 Math and reading skills are

assessed across six waves: the beginning and end of kindergarten, the beginning and end

of 1st grade, the spring of 3rd grade, and the spring of 5th grade. In all, nearly 12,000

children are followed to 5th grade.20

Unlike the ECLS-B, the ECLS-K data are designed to study individual cognitive growth throughout the entire study. By using a developmentally vertical scale of cognitive skills, achievement levels from year to year can be compared (Rock and

Pollack, 2002). The response rate for ECLS-K data is 88% for the parent interview and

84% for the child assessment at 5th grade.

Limitations of Comparing Samples

Unfortunately, the ECLS-B collects data of children who are younger than those

in the ECLS-K; the ECLS-B cohort reaches kindergarten age around the year 2006, eight

years after the ECLS-K kindergarten cohort was sampled. An imperfect yet reasonable

way to consider the magnitude of period effects for gender gaps in cognitive skills is to

consider how much the gap changed during the same time period for the nine-year olds in

NAEP data. This comparison suggests no period effects for math and a slight decline in

the female advantage in reading between 1998 and 2006, the time period difference at

stake between the ECLS-B and ECLS-K data (see Appendix for more discussion).

As the results will show, patterns from ECLS-B and ECLS-K show logical

connections that suggest that any period effects may be minimal. Fortunately, were

19 The ECLS-K reports nine cases missing for gender that are excluded from analyses as a result. 20 Following NCES guidelines, samples sizes have been rounded.

appropriate, cognitive assessments in the ECLS-B are specifically designed to be comparable measure to the ECLS-K. Although the period of assessments may not coincide chronologically, where possible the cognitive assessments used are identical.

MEASURES

Dependent Variables

In the ECLS-K, the math test evaluates understanding of numbers, geometry, and spatial relationships. Standardized reading tests are designed to assess knowledge of letters and word recognition, beginning and ending sounds, vocabulary, and passage comprehension. The subtests that compromise the aggregate measures are grouped by level of proficiency. For math and reading, groups are ordered from baseline proficiency to highest proficiency (see Table 11 for details of tests and ordering by proficiency).

Baseline assessments for math assessed knowledge of numbers and shapes. This assessment tests the child’s skill in identifying some one-digit numerals, recognizing geometric shapes, and one-to-one counting of up to ten objects. The highest level of proficiency is in area and volume. This highest level of proficiency captures the child’s skill in solving word problems involving area and volume, including change of units of measurement (see Table 11 for all assessments).

For reading, the baseline assessment is letter recognition. This tests the child’s skill in identifying upper- and lower-case letters by name. The highest level of proficiency is in evaluating nonfiction. The child is tested on his/her skill in critically

evaluating, comparing and contrasting, and understanding the effect of features of

expository and biographical texts (see Table 11 for all assessments).

These cognitive assessments are designed to be calibrated vertically. Participants

are first tested for core knowledge and routed to appropriate questions designed to match

the individuals demonstrated skill level. This adaptive testing approach allows for the

minimization of ceiling and floor effects common is most national assessments of

cognitive skill (e.g., NAEP; Penner, 2003). To remove the possibility of ceiling and floor

effects, test items responses are pooled and recalibrating using Bayesian procedures that reflect the ability distributions associated with average developmental progress. This provides for reasonable item parameters and ability scores (Rock and Pollack, 2002;

Mulligan, Flanagan, and Denton, 2006). The removal of these ceiling and floor effects is also important for gender differences, given that gender differences are greatest for extreme scores, which would otherwise be minimalized if assessments contained clustering at the bottom or top of the distribution of scores (see Penner, 2003).

The selection of item questions are developed from two sources, judgment by experts in the filed of testing and results of psychometric testing. Experts in curriculum as well as teachers gave input regarding cognitive skills that are typically taught and developmentally important. Test items that comprise the final standardized assessments were selected to fit these specifications. After field test item were pooled, test items were finalized and reviewed by experts to assure that final assessments appropriately reflected curriculum based testing. Statistical tests of the cognitive assessment indicate good reliability (Rock and Pollack, 2002).

The use of raw scores carries the assumption that the metric capturing “cognitive growth” are similar across development. Although this is difficult to estimate, analyses have also been conducted using standardized, cohort-referenced test scores, resulting in similar patterns (see also DiPrete and Jennings, 2008).

Linking Cognitive Assessments

As discussed earlier, ECLS-B and ECLS-K data are developed for comparison purposes. The role of disaggregating these dependent variables by their component measures is essential in this study to link pattern over time. Two subtests of math and reading skill in the ECLS-K are identical measures with two subtests of math and reading skills in the ECLS-B.

In the ECLS-K, math subtests include number and shape, relative size, ordinality and sequence, addition and subtraction, multiplication and division, place value, rate and measurement, fractions, and area and volume. For reading, the subtests include letter recognition, beginning sounds, ending sounds, sight words, comprehension of words in context, literal inference, extrapolation, evaluation, and evaluating nonfiction (see Table

11). The levels of proficiency for math and reading subtests are shown in the Appendix,

Table 17. Of these measures, number and shape and letter recognition complement the equivalent subtests measures in the ECLS-B data. Considerable documentation exists elsewhere, describing the psychometric properties of these subtests and their relationship to an overall standardized measure of skill (Andreassen and Fletcher, 2007; Pollack,

Najarian, Rock, and Atkins-Burnett, 2005; Mulligan, Flanagan, and Denton, 2006). The

inclusion of subtests is an important feature of this project because it allows the

examination of the more specific gender gaps across development that would otherwise be masked by aggregated assessments.

Testing Format and Gender Bias

Before moving on to sample measures, it is worth noting the steps taken in both studies to remove gender bias. Gender bias may occur from the testing format. Gender differences are often larger when tests are timed and formally administered (Reed, Fox,

Andrews, et al., 2007). In the ECLS-K, assessments were untimed and individually administered—respondents met face-to-face with interviewers. This approach minimized testing bias and resulted in only slight interviewer effects, explaining 1% to 3% of the variance (see Rock and Pollack, 2002). Although untimed testing sometimes differentially affects participates motivation to do well (see Schiefele and

Csikszentmihalyi, 1995), analyses conducted by NCES found that participants in the

ECLS-K data were highly motivated to do well (Rock and Pollack, 2002).

Control Variables

Like the ECLS-B, race is measured as white, black, Hispanic or other. The

“other” category includes children identified by parents as Asian-American, Native

American and other groups not sampled in sufficient sizes for extended analysis. Again, although no gender differences in age of assessment is anticipated, it is modeled to provide a metric to indicate how much a given outcome increases in a month of

development. Age is measured continuously by months from kindergarten to 1st grade.

In third grade, response categories were converted from a continuous scale (number of months) to a 5 or 6 item response representing age groups rather than months. Age of assessment should be interpreted with this difference in mind.

Distal Factors

Child Health Characteristics, Socio-economic Status, and Family Structure

Child health characteristics were limited to birth weight. Like the ECLS-B, birth weight is coded as normal (more than 5.5 pounds), moderate (5.5 to 3.5 pounds), and low

(less than 3.5 pounds). Comparable to the ECLS-B, socio-economic status is a composite scale comprising of income, occupational prestige and educational level of the child’s parents. I also use a zero-centered score to aid in interpretation of gender interaction effects. Sibling size ranges from 0 to 9 biological siblings in the household. Biological

Mother and Father in Home is a dichotomous measure, 1= “both biological parents in the home” and 0= “other parental arrangements.”

Mediating Variables

As Tables 11 to 16 shows, many potential parent socialization factors that have been shown to link to gender gaps in math and reading are explored. For the final analysis, three factors emerge as the most important mediators: parents’ expectations of child’s math and reading skill, parents’ investment in math and reading tutoring for their child, and the child’s teacher-rated classroom citizenship or approaches to learning.

Parent expectations were measured by parents’ evaluation of their child’s proficiency in math and reading compared with other children in their class. Responses range from 1= “much worse” to 5= “much better.” These measures are relevant for the parent socialization because the measure of expectations in this study is similar to measures assessed in previous work. Parents’ investment in tutoring is measured by the question asking if their child was tutored in math or reading. Tutoring in math and reading shows direct effort on behalf of parents to cultivate their child’s specific skills, although this assumption is tempered by the impact of teachers’ encouragement for tutoring, which cannot be isolated in this data. If differences are found by gender this may suggest the parent and teacher influences shape resources that can help develop math and reading skill.

These measures of expectations and investment are especially interesting given that on the bivariate level, boys do better on standardized math tests than girls and girls do better than boys on standardized reading tests. If parents are responding to the child’s deficiencies, it follows that they would invest more in girls’ tutoring of math and boys’ tutoring of reading. At one level, results will show that this is the case. But accounting for previous skills changes this relationship, as subsequent analyses in the next chapter will reveal.

Citizenship in the classroom, or approaches to learning, is a teacher-rated assessment of how one learns in the classroom. Teachers rate the child based on his or her openness and curiosity for tasks and challenges, task persistence, imagination, attentiveness, and cognitive learning style (Hair, Halle, Terry-Humen, Lavelle, and

Calkins, 2006; Rock and Pollack, 2002). One’s approach to learning is considered

because it shows a strong link to cognitive skill outcomes and has large gender

differences at the bivariate level. As Diprete and Jennings show (2008), much of the

gender differences in social/behavior skills are explained by the child’s approach to

learning in the classroom, which link to reading and math skill outcomes. Likewise,

approach to learning is considered in this research to determine the role of citizenship in

understanding gender gaps in math and reading.

Analysis

I perform two analyses with the ECLS-K. In the first, I use growth curve analysis

in AMOS to model change over time and account for unmeasured error using fixed

effects modeling (Schneider, Carnoy, Kilpatrick, Schmidt and Shavelson, 2007; Singer

and Willett, 2003). Specifically, I employ autoregressive latent trajectory modeling

(ALT). This is important to account for the autoregressive effect of measuring highly

correlated skill assessments over time (see Bollen and Curran, 2004). This is illustrated

by the causal arrows from the initial cognitive skill as kindergarten (Fall) to proceeding

assessments.21 This approach, of course, assumes that the change in math and reading

skills content over time is capturing some common overall ability or proficiency (Singer

and Willett, 2003). In this dissertation, I have articulated cognitive growth as an accumulation of skill; therefore this approach may not be best suited for this assumption.

21 Growth models were also created using HLM6 and Stata’s xtreg function to demonstrate comparability of the SEM approach.

The benefit of this analysis here is to compare this approach with other findings in this dissertation as well as findings in the literature using similar methods and assumptions.

In the second analyses, I use Structural Equation Modeling (SEM) to model covariates and mediating factors on gender gaps in math and reading at 5th grade.

Covariates and mediating factors are selected that best represent aspects of the parent socialization model. Like the analysis of the ECLS-B data, Full Information Maximum

Likelihood is used in all analyses (see Kline, 2005) to address missing values.22

Rule of Thumb

To calculate effect sizes of the results from both samples, I use the Cohen’s d statistic (Cohen, 1988). This simple procedure calculates the standard deviation for any result in terms of male or female advantage. Below in figure 3, MM is the mean score for males, MF is the mean score for females, and SW is the average within-sex standard deviation (p. 582, Hyde, 2005).

Thus, positive values represent female advantage and negative values represent male advantage. As a rule of thumb, the effect size is considered “close to zero” if d is less than or equals .10; “small” if d is great than .11 but less than .35; “moderate” if d is greater than .36 but less than .65; and “large” if d is .66 or greater (Cohen, 1988; Hyde,

2005).

22 Results were also conducted using OLS using listwise deletion with no discernable differences in the general findings reported below. Missing data are modest for most variables in the data. Missing values for socio-economic status were computed by NCES using the hot-decking technique (see Flanagan and West, 2004).

Figure 2. Autoregressive Latent Trajectory Model of Gender Differences in Cognitive Skill

M m - M F d =

S W

Figure 3. Cohen’s d calculation

Some of the analyses presented next use Structural Equation Modeling. Two fit indices are reported in the appropriate tables to indicate whether the mediating variables appropriately fit with the data. The first measure, Root Mean Square of Error of

Approximation (RMSEA) is a parsimony-adjusted index. A low value (.05 ≤ ) represents a close approximate fit, values between .05 and .08 represent reasonable error of approximation and RMSEA ≥ .10 suggests poor fit (see Kline, 2005). To assess the improve in fit, or the amount explained, with the researcher’s model compared with a baseline model, the Comparative Fit Index is used. CFI ≥ .90 represent a good fit compared with a baseline model. (see Kline, 2005).

Chapter Four: Results

Descriptive Results

Controls

In total, the following descriptive results are drawn from 9 data sets, 3 from early

childhood (ECLS-B) and 6 from middle to late childhood (ECLS-K). Although the ratio of the male and females is consistently 49% female across data sets, the proportion of white, black, Hispanic, and other racial/ethnic groups is slightly higher in the ECLS-B

(42% white, 16% black, 21% Hispanic, 22% other) data than in the ECLS-K data (56%

white, 14% black, 17% Hispanic, 9% other). This is due to oversampling in the ECLS-B

data (see Tables 1 and 2). Oversampling was also conducted among low birth weight

children and twins in the ECLS-B data (Mulligan, Flanagan, and Denton, 2006). Because

gender is equally distributed across the population (Lieberson, 1994) or, more specifically, uncorrelated with the factors in question, regression with and without sample weights resulted in nearly identical outcomes.

The administration of the survey and assessments were within a 2 to 3 month window as a some children were slightly older or younger than the collection period average suggests (e.g., 9 months, 4 years of age). (See Tables 1 and Table 2 for results.)

These differences varied across social-economic and racial groups, most likely due to the

increased difficulty of coordinating or finding lower income respondents over time.

Although this is not a factor for gender, accounting for age of assessment is a necessary control when creating an interaction term of gender with socio-economic status or race.

In the ECLS-K data, only a few students repeated kindergarten (4.5%). As the literature suggests, boys are more likely to be held back in school with 5.5% of boys repeating kindergarten compared with 3.5% of girls (see Table 2).

Child Health

As the ECLS-B data show, girls are born with slightly lower birth weight than boys. Twenty-eight percent of girls were born with either moderate or low birth weight compared with normal birth weight versus 25% of boys (see Table 1). A similar pattern is found in the ECLS-K. Seven percent of girls born with either moderate or low birth weight compared with normal birth weight versus 6% of boys (see Table 2). Again, the lower percentage of boys and girls born below normal birth weight in the ECLS-B data compared with the ECLS-K data reflects oversampling by birth weight in the ECLS-B data. For other early health factors, results show that boys are more likely than girls to have been treated for asthma and ear infections (.12 and .09 standard deviation difference, respectively). Other factors of early child health, gestation age, and APGAR show no gender differences.

Early Childhood Proximate Factors

Central to this study are the effects of proximate factors on gender gaps in cognitive skills. Proximate factors represent the more direct influences experienced in the child’s social environment. Of the factors explored, measures of parental investments and involvement are isolated for this study although many other factors were explored.

(See Appendix for descriptives and T-tests of these other factors.)

Maternal warmth, a factor of maternal emotional and verbal support of the child during the in-home visit, revealed slightly more verbal interaction with their daughters than sons, especially at 2 years of age (.05 and .10 standard deviation difference for speaking spontaneously to child and verbally responding to child). Two of the 4 indicators of paternal provision show a gendered pattern. Fathers are slightly more likely to change their child’s diaper (.08 standard deviation differences) and dress their child

(.09 standard deviation difference) if the child is a boy rather than a girl. There is no effect of gender, however, in whether the father prepares meals or bottles or feeds their child. Although these small differences were examined and show no impact for cognitive development, they at least reveal active gendered parenting early in childhood.

One parent-child interaction that has known effects on children’s cognitive skill development is the frequency that parents read, sing songs and tell stories to their children. These measures were developed from the HOME inventory. Across childhood, parents read, tell stories, and sing songs more often to their daughters compared with sons, especially at 2 years of age (.06, .06, .12 standard deviation difference in reading, telling stories, and singing songs, respectively). Once children enter school, parents

continue to read, tell stories, and sing more with daughters than sons as measured in 1st

grade, and sing songs more often with daughters than sons when measured in 3rd grade

(see Table 14 and 15). Although these are important differences in early childhood, the role of these activities with children diminish over time as more specific activities are developed by parents and teachers to develop skills in math and reading. As a result, these differences in the ECLS-K are not considered in the final regressions.23

Unique to the ECLS-K data, parent cognitive stimulation was developed from videotaped interaction while parents and their child interacted during the Two Bags Task.

No known study has compiled national level data in early childhood with videotaped interaction, providing a window into early parenting practices that may have gender-

based differences. Descriptive results for parent-child cognitive stimulation show that

the parent (the mother) is more engaged with the child in cognitive learning across all the

indicators for girls than boys, including stimulation of cognitive development,

engagement, and positive regard (.10, .22, and .03 standard deviation difference,

respectively). Mean comparisons show, however, that positive regard is not statistically

significant. For the child measures of cognitive stimulation, girls scored higher on

average than boys on measures of the child’s sensitivity and sustained attention with an

object during the two bags task (.08 and .26 standard deviation difference, respectively).

Due to the cross-sectional nature of this assessment, assessing parent-child feedback

effects cannot be explored (see Chapter 2 for discussion).

23 In results not shown, these factors had only small effect on math and reading skills when modeled.

One indirect way to capture gender-based parenting is to examine what behaviors

parents allow in the home. The number of hours children watch television was selected

as a possible gauge for gender differences in parenting, yet descriptive results show no statistical difference between boys and girls.

Middle to Late Childhood Proximate Factors

Moving to the ECLS-K data, many parenting factors are explored but two show

important differences. Parental expectations have been shown to be gendered with

parents evaluating their boys as better in math-related skills than their girls and girls as

better in reading-related skills than their sons. At the descriptive level, results confirm this pattern. Table 2b shows that these differences increase from 1st to 5th grade, from a

.08 standard deviation difference and to a .15 standard deviation difference.

One argument is that these gender differences would be larger had fathers been asked to evaluate their child’s math and reading skills. Mothers are more likely than fathers to espouse views of gender equality, thus less likely to make gender stereotypic evaluations of children’s math and reading skill (Jacobs et al., 2005). Had fathers been interviewed, results may have shown larger gender differences.

Tutoring in math is more common than reading with 7% of child having had some tutoring in math in 1st grade and 5% in 3rd grade, compared with 2% in 1st grade and 3%

in 3rd grade for reading. Boys are tutored in math more often than girls in 1st and 3rd

grade (.06 and .08 standard deviations, respectively). Girls are tutored in reading more

often than boys in 3rd grade, although the differences in slight (.01). Without further

empirical investigation, it appears that boys and girls are relegated to the cognitive skills

parents and teachers expect these children to process—given that boys do better in

standardized math skills than girls and girls do better than boys on standardized tests of

reading skill. Another view is that parents and teachers simply respond to the skills their

child/student needs.

Other proximate factors including child’s involvement in activities, parents’

contact with school, parents educational expectations of their child, and library use, to

name a few, are reported in the appendix (see Tables 11 to 16). Although some patterns

show gender differences, most factors did not correlate with gender gaps in math skills or

did not align to a clear theoretical explanation for inclusion in this study. Many factors,

however, were considered in preliminary analyses but ultimately are excluded in the final

models.

Distal Factors and Approaches to Learning

As expected, no gender differences are found across socio-economic levels, the

child’s grandmother’s level of education, the number of biological siblings in the house,

whether both parents lived in the home, or what type of neighborhood the child lives in.

Again, these factors are included to account for any moderating influences, especially

socio-economic status, as some results have suggested a potential relationship.

As DiPrete and Jennings (2008) have shown with the same data, there is a significant gender difference for the approach to learning measure. Of all the differences examined thus far, this factor shows the greatest standard deviation difference of .49.

This assessment measures the child’s level of classroom citizenship based on the

teacher’s report. As with the feedback effect with parent-child interactions, this measure may also contain an evaluation of child behavior that conforms to gendered expectations and actual socio/behavioral skills demonstrated in the classroom.

Conclusion

In sum, descriptive statistics and t-tests show important gender differences across child health, aspects of parenting, and approaches to learning. The most striking result is the gender differences in evaluation of the child’s performance in math and reading skill and investment in math and reading tutoring. At the bivariate level, these differences

lend support for parent gender socialization. These patterns, however, are subject to

actual assessments of the child’s skill level and therefore require further exploration to

determine how influential feedback effects are for parents beliefs and behaviors

associated with their child’s cognitive skill development.

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In the next three sections, results will be organized by each of the three research

questions stated earlier. Evidence is garnered from both data sets, based on descriptive

results, structural equation modeling, and growth curve modeling analysis.

1. When do gender gaps in math and reading emerge?

To answer this question, results are drawn from three different analyses. The first

is from descriptive results comparing male and female mean scores for cognitive skills

from 9 months of age to 5th grade; the second is from latent growth curve modeling

(ALT); and the third is from descriptive results of item-level math and reading tests

(subtests).

Examining the ECLS-B descriptive data (see Table 3), girls have small advantage in Bayley Mental Scores at 9 months of age (.05), which grows larger by 2 years of age

(.32). Of course, at this age children have yet to develop skills that link directly to early math or reading, but these more global assessments of general skill show that girls, especially by age 2, are not disadvantaged in comparison with boys. By 4 years of age, children are beginning to develop early math and reading skills. For both global assessments of early math and reading, girls are .14 and .12 standard deviations higher than their male counterparts.

This finding coincides with Sadker and Sadker’s observation that girls begin childhood looking like the favored sex (1994). Indeed, at the start of kindergarten, there appears to be a reversal in gender differences in math from early childhood. Boys’ advantages in math skill appear to emerge by the end of 1st grade (.08) and continue to

grow to 5th grade (.20). Gender gaps in reading, on the other hand, appear to favor girls throughout the preschool and schooling years with little change (.12 at the lowest and .17 at its highest). This is interesting because unlike gender differences in math, reading skills do not grow over time. If schools “shortchanged boys” (Sommers, 2000), surely this advantage would continue to grow as boys and girls are continually exposed to an environment that favors one group over the other.

Figures 4 and 5 show cognitive growth curves for math and reading skills by gender. These figures provide a visual inspection of gender gaps accounting for cognitive growth over time. Boys’ advantages slightly grow ahead of girls from 1st to 5th grade as the descriptive results also show. Girls’ advantages in reading appear to be only slightly ahead of boys throughout early schooling.

These results provide a familiar story in literature. They show a gender difference in math originating at around 1st grade, becoming more visible in size only until 5th grade.

The origin of girls’ reading skill advantage over boys appears to develop early and stay

consistently above boys through childhood. Despite these somewhat conventional

findings, one pattern is unclear. Why do advantages girls enjoy in math-related skill in

early childhood abruptly change upon school entry? As the results in the following

section will show, when the subtests of these standardized scores are examined, assessing

the origins and explanations of gender gaps becomes more complex.

Table 3. Descriptive Statistics Comparing Female and Male Mean Differences. ECLS-B.

Variable Name Female S.D. Male S.D. P d Bayley Mental Score (9 months) 75.1 10.1 74.6 10.1 ** .05 Bayley Mental Score (24 months) 127.3 10.6 123.8 11.1 *** .32 Early Math Skill (48 months) 22.9 7.4 21.9 7.7 *** .14 Early Reading Skill (48 months) 13.7 7.1 12.8 7.1 *** .12 *P<.05 **P<.01 ***P<.001 Note: positive d values=female advantage.

Table 4. Descriptive Statistics Comparing Female and Male Mean Differences. ECLS-K. Variable Name Female S.D. Male S.D. P d Math K-Fall 22.8 8.3 23.1 9.4 -.03 Math K-Spring 33.0 10.8 33.5 12.3 ** -.04 Math 1st-Fall 39.7 12.7 40.3 14.7 -.04 Math 1st-Spring 56.8 15.7 58.2 18.0 *** -.08 Math 3rd-Spring 90.3 20.7 93.8 22.2 *** -.16 Math 5th-Spring 111.8 21.2 116.0 21.3 *** -.20

Reading K-Fall 30.3 10.0 29.0 10.2 *** .13 Reading K-Spring 42.2 13.8 39.9 13.6 *** .17 Reading 1st-Fall 49.4 17.9 46.5 17.4 *** .17 Reading 1st-Spring 73.7 22.0 69.8 22.7 *** .17 Reading 3rd-Spring 120.2 24.3 116.0 25.8 *** .17 Reading 5th-Spring 141.0 22.1 137.9 24.1 *** .13 *P<.05 **P<.01 ***P<.001

Note: positive d values=female advantage.

150 140 130 120 110 100 90 Female 80 Scores Male 70 60 50

Math 40 30 20 10 0 K‐Fall K‐Spring 1st‐Fall 1st‐Spring 3rd‐Spring 5th‐Spring

Figure 4: Growth Curve (ALT) of Standardized Math Scores by Gender, ECLS-K .

150 140 130 120 110 100 Scores 90 Female 80 Male 70 60 50

Reading 40 30 20 10 0 K‐Fall K‐Spring 1st‐Fall 1st‐Spring 3rd‐Spring 5th‐Spring

Figure 5: Growth Curve (ALT) of Standardized Reading Scores by Gender, ECLS-K .

2. Why do girls math fortunes reverse?

Figure 6 shows the comparison of gender differences of the Bayley assessments at

9 months and 2 years of age compared with early math gender differences at 4 years of

age and 5th grade. A visual inspection confirms Sadker and Sadker’s claim. A reversal in

the female math gap moves from a .12 standard deviation female advantage in math at

age 4 to a .16 disadvantage 6 years later (Figure 6, light gray bars). This pattern holds

when other covariates are modeled (see Figure 6, dark gray bars).

But this conclusion would be misleading. With the subtests of these aggregated

measures, I map the standard deviation gaps from preschool to 5th grade to reveal a

different pattern (compare Figure 6 with Figure 8). For the one identical measure used in

ECLS-B data (see results in Figure 8, “Count, Number, and Shape”), girls maintain an

advantage across kindergarten to the end of 1st grade. Other subtests have different

trends. Using scores at school entry as a baseline (Kindergarten-Fall), the gender gap

among some measures grows and then fades (relative size) while multiplication and

division gender differences remain relatively unchanged over time. The sharpest

increases are for subtests measuring place value, rate and measurement, fractions, and

area and volume. For a point of comparison, Figures 7 and 8 show results for reading.

Unlike gender differences in math subtests, girls’ advantages in reading persist across childhood and subtests.

Thus, what appears to be support for the reversal thesis shown in Table 3 is actually the result of aggregated assessments of math skill. Skills in place value, rate and measurement, fractions, and area and volume show the largest growing gender gaps,

skills learned well after early childhood. With results dependent on the type of math assessment examined, it follows that the use of global assessments requires unique justification over the more simple and specific subset measures, especially when puzzling patterns emerge.

Overall, there is no clear indication that school-entry disrupts cognitive trajectories for either gender, for math- or reading-related skill. There is, however, evidence that gender differences are the result of increased item complexity over time.

As reviewed in Chapter Two, the largest gender gaps are not necessarily due to when the gender gaps are assessed but what types of gender gaps are being assessed. As the subtests reveal, girls excel in skills assessing count, number, and shape across childhood.

As assessment items become more difficult, boys’ advantages grow.

This could be interpreted as evidence that girls do have innate differences in math that surface as math tasks become harder. A couple analyses (not shown) challenge this conclusion. First, an examination of class differences across item complexity reveals the same pattern. Differences between children from high socio-economic backgrounds and children from low socio-economic status become larger across as item complexity increases. Second, gender differences in math vary based on the parent’s (mother’s) country of origin (not shown). Although this is not a direct country-level comparison, it is secondary evidence that gender differences may be culturally bound. Penner’s findings

(2008) support this conclusion—gender gaps in cognitive skills are found more often in countries that hold more gender stereotypic views than countries with more gender egalitarian beliefs.

Assuming that the relationship between gender gaps and item complexity is

culturally bound, one explanation might be that higher-level math skills are more difficult

to acquire and require concerted cultivation of parents and others to obtain them (Lareau,

2003). This may explain why parental investments in tutoring or other related activities are gendered, as reported in the descriptive results, although the next section of findings will show this may not be the case. Another explanation is that more complex math requires novel approaches to solving math problems. As math skill assessments become more complex in this way, they are increasingly uncoupled from classroom curriculum

(Halpern et al., 2007). The acquisition of these skills may not be school-bound, as

Entwisle et al. (1997) and Downey and Vogt-Yuan (2005) show. To square these findings with seasonal data showing that schools do not appear to change gender gaps in math when compared with non-school environments, gender differences may stem from non-school environments year-round.

Upon closer inspection, the evidence garnered here is inconsistent with the schools as culprit position. What at first appears to be a major juncture in the math skills of girls is readily explained when subtests, rather than global math skills, are the focus.

A pattern showing a clear change in the gender gap trajectory at the time formal schooling begins would have been formidable evidence that schools are the problem, supporting the view of some educational sociologists. But the patterns found here show no such disruption. These results support a growing movement away from the Sadker and Sadker (2004) indictment of schools and the early AAUW reports (Kimmel, 2006).

Returning to the first question, “when go gender differences in math and reading

emerge?” subtests show that this depends on (1) the type of assessment and (2) the developmental period of childhood examined. The most significant gender gaps are found in multiplication and division, whereas gender gaps in place value and rate and measurement grow increasing large over time. Conversely, count, number, and shape and relative size assessments show female advantages across schooling.

1.00

.80

.60

.40 .31 .32

.12 .14 .20 .07 .05 Bivariate .00 Multivariate* -.20 -.16 -.20 -.40 Standard Deviations

-.60

-.80

-1.00 Bayley Bayley Early Math Math (9 months) (24 months) (48 months) (5th Grade)

Note: Bivariate and multivariate results significantly different than zero at P<.001 *Includes: controls, child characteristics, socioeconomic factors, child care arrangements, parenting measures.

Figure 6: Gender Differences in Cognitive Skill from 9 months to 5th grade. (Converted into standard deviations. Positive values equate to female advantage)

1.00

.80

.60

.40

.17 .13 .20 .12 .12 Bivariate .00 Multivariate* -.20

-.40 Standard Deviations Standard

-.60

-.80

-1.00 Early Reading Reading (48 months) (5th Grade)

Figure 7: Gender Differences in Reading Skill from 48 months to 5th grade. (Converted into standard deviations. Positive equate to female advantage)

Preschool* Kindergarten (Fall) (Spring) Kindergarten (Fall) First Grade (Spring) First Grade Third Grade (Spring) Fifth Grade (Spring) Volume Fractions and Area Measurement Place Value Rateand and Division Multiplication Math Score Subtests Score Math Subtracting Adding and Adding Sequence Relative SizeRelative Ordinality and and Shape Count, Number,

(Positive values equate to female advantage) female to equate values (Positive *Collected at age four, ECLS-B 2001. All other data points from ECLS-K 1998-1999. ECLS-K from points data other All 2001. ECLS-B four, age at *Collected

0.25 0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 0.25 ‐ ‐ ‐ ‐ ‐

Standard Deviations Deviations Standard Standard Figure 8: Subtests of Math-Related Measures from Preschool to 5th Grade.

Preschool* (Fall) Kindergarten (Spring) Kindergarten First (Fall) Grade First (Spring) Grade Third (Spring) Grade Fifth (Spring) Grade Fiction Grade. th Reading Score Subtests Score Reading Ending SoundsEnding Words Sight in Contexts Word Inference Literal Extrapolation Evaluation Non- Evaluation Sounds Beginning Letter Recognition

(Positive values equate to female advantage)

*Collected at age four, ECLS-B 2001. All other data points from ECLS-K 1998-1999. ECLS-K from points data other All 2001. ECLS-B age four, at *Collected 0.05 0.10 0.15 0.20 0.25 0.25 0.20 0.15 0.10 0.05 0.00

‐ ‐ ‐ ‐ ‐ Standard Deviations Deviations Standard Standard Figure 9:Figure of Reading-Related Subtests Measures from to 5 Preschool 85

3. Does parent socialization explain gender gaps in childhood?

As figures 6 and 7 show, comparing the bivariate results with the multivariate results, the gender gap is remarkably resilient across early childhood. For Bayley outcomes at 9 months and 2 years of age, few factors reduce the female advantage in these assessments. In fact, early health factors appear to increase the size of the gender gap in math and reading (see Table 5, Model 6 and Table 6, Model 6). This is most likely due to boys’ susceptibility to poor initial health than girls (Geary, 1998).

By 4 years of age, children begin to develop early math and reading skills. Much of the gender difference in these early skills is unexplained (see Table 7, compare Model

1 with Model 8). One exception is the combined influence of parents’ reading, singing songs, telling stories, of parents’ cognitive stimulation of their child; and of maternal warmth. Yet, the reduction of 1.119 to .880 differences is modest, representing roughly a month of developmental difference.24 It may be that modest differences represent the earliest influence of gendered parenting, but without a link to math outcomes into later life, this conclusion is merely speculative. The interaction of gender and socio-economic status is explored with no evidence of a relationship—the interaction term was not statistically significant (see Table 7, Model 13). For early reading differences at 4 years of age, findings are nearly identical (see Table 8, Model 13).

In sum, girls’ advantages in early math and reading are only modestly explained by parenting factors at 4 years of age (see Tables 7 and 8, Model 10). Although some research in the gender differences literature documents a relationship between socio-

24 This is calculated by considering that math skills increase at .609 a month. (See the coefficient for Age in Months (wave 3), Model 2).

economic status and gender differences in cognitive skill, no empirical evidence is found

here.

Moving to the schooling years, results from analyses conducted with the ECLS-K

data are compiled in Tables 9 and 10. Although many factors across the six waves of

data are available for analysis (see Appendix), proximate factors in 1st and 3rd grade are

modeled to allow a more time dependent analysis of causal relationships between parenting and cognitive skills.

Parents’ evaluation of their child’s math skill (based on whether they faired better or worse than other students in school) appears to be a significant predictor of math skill.

Parent’s evaluation of their child’s math skill reduces the gender gap in math by 30 %

(see Table 9a, Model 8). When tutoring in math is considered, however, the gender gap slightly increases, suggesting that the small difference in the number of boys being tutored than girls may represent the math skill needs of the child (see Table 9, Model 9).

Although tutoring clearly does not help explain gender differences in math skills, the influence of parents’ evaluation may present a feedback effect—parents may be accurately assessing their child’s math and reading skills. When the child’s previous math skills from 1st and 3rd grade are considered in the model, the effect of parents’

evaluation is a mere 6% (see Table 9b, Models 3 and 4). Interestingly, the effect of

tutoring, when controlling for the child’s skill level, is not associated with increased math

skills. This suggests that tutoring reflects the skill level of the child and not parent or teacher gender stereotypes as the bivariate results (Table 2b) seemed to suggest.

Results are similar for reading skill gaps. Parents’ evaluation of reading skills

reduces the gender gap in reading by 40% (Table 10, Model 8). Parents’ investment in

tutoring for reading is not significant (Table 10, Model 9). Accounting for previous skills

in reading in a change model produces no gender gap (analysis not shown).

It should be noted that accounting for previous skills produces different outcomes

than gender gaps in math skills. Rather, the outcome is the change in gender gaps in

math from 3rd grade to 5th grade. Thus, parents’ evaluation of their child’s math or

reading skill explains part of the change in gender gaps in math or reading from 3rd to 5th

grade (see Allison (1990) for more discussion).

Finally, the role of children’s citizenship or approaches to learning is modeled.

Because girls are more likely to score higher on this measure than boys at the bivariate level, it is no surprise that when this advantage is considered, the gender gap in math

grows as the gender gap in reading shrinks. For math, the size of the gender gap more than doubles (Table 9b, compare Models 1 and 2), and for reading, the gender gaps can be completely explained.

What is significant about this finding is that even if a model with all covariates— like in Table 9a, Model 10—could successfully explain gender gaps in math, gender parity would be reached despite all the academic strengths girls display in school, as

Table 9a, Model 11 shows. In other words, if research shows gender parity in math, as have been recently found (Hyde, Linberg, Linn, Ellis, and Williams, 2008), these bivariate assessments mask what boys and girls do differently to reach the same outcome.

True gender parity, it seems, would be reached when equal effort produces equal results.

Given all the good things girls do in school that enhance their academic standing, one

would expect girls to excel in both reading and math assessments. Yet, boys—on

average—manage to obtain higher math skills than girls. The anomaly of why boys excel

in one of the more critical skills linked to later success—despite “how schools fail

boys”—is an interesting puzzle for further investigation.

Summary

Results show that female-favorable gender gaps in math exist at 4 years of age

when skills in math can be reliably assessed (Flanagan and West, 2004; Mulligan,

Flanagan, and Denton, 2006). Girls’ advantages continue despite the transition to school, suggesting that this “critical period” does not disrupt gender differences in cognitive skill.

Instead, the introduction of complex math, or “item-complexity,” accounts for boys’

eventual advantage over girls in math-related skill, emerging towards the end of 1st grade.

At first, it seems that boys’ advantage in math can be partly understood by parent socialization, specifically parents’ evaluation of their child’s skill and investment in math and reading tutoring. Further analyses accounting for parent-child feedback effects show that these gendered differences reflect the learning needs of the child more so than parental stereotypes and differential investments in tutoring. Finally, knowing the child’s citizenship skills in the classroom reveals that gender gaps in math would be much larger in fifth grade if boys were equally matched with girls in terms of classroom citizenship or their approach to learning.

*** *** * *** *** 10

.064 .270 .532 .411 ‐ ‐ ‐ 2.965 7.055 1.298 (.077) ‐ ‐ ‐ *** *** * *** *** 9

.126 .126 .273 .527 .411 ‐ ‐ ‐ 2.968 7.055 1.293 (.207) (.207) ‐ ‐ ‐ Model 8Model *** *** * *** ***

.556 *** .556 *** .556 *** .100 .097 .096 .274 .520 .412 ‐ ‐ ‐ 4.097 *** 4.099 *** 4.108 *** 2.967 7.058 1.294 (.084) (.084) (.084) (.948) (.948) (.948) (.097) (.097) (.097) ‐ ‐ ‐ *** ** * *** *** *** 7Model

.673 *** .655 *** .645 *** .646 *** .478 .500 .437 ‐ ‐ ‐ 7.114 1.250 2.943 (.249) (.248) (.249) (.249) (.121) (.120) (.121) (.121) (.324) (.323) (.323) (.323) ‐ ‐ ‐ Model *** *** *** *** 6

.508 ***.504 *** .501 *** .499 *** .498 *** .499 *** .498 *** .498 *** .498 *** .498 *** .570 .436 ‐ ‐ 7.257 2.977 (.182) (.181) (.182) (.182) (.182) (.312) (.312) (.312) (.312) (.312) (.025)(.082) (.025) (.082) (.025) (.082) (.025) (.082) (.025) (.082) ‐ ‐ Model ** .401 * .462 * .662 *** .655 *** .657 *** *** 5

.411 * .426 ** .421 ** .432 ** .439 ** .438 ** .705 .588 ‐ ‐ (.197) (.160) (.160) (.160) (.161) (.161) (.062) (.051) (.051) (.051) (.051) (.051) Model t 2001.

B ‐ *** 4

ECLS

.407 *** .334 *** .254 ** .259 ** .141 .136 .087 .028 .021 .025 .022 .007 .007 .007 .908 ‐ (.096) (.101) (.082) (.083) (.085) (.085) (.104) (.018) (.018) (.015) (.015) (.015) (.015) (.015) Model Model,

the

*** 3

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Various

for 2Model

(.038) (.038) (.038) (.038) (.031) (.031) (.031) (.031) (.031) Model Controlling

Gender,

(.199) (.143) (.143) (.142) (.142) (.115) (.115) (.115) (.115) (.194) (.140) (.413) (.418) (.482) (.530) (1.193) (1.192) (1.188) (1.188) (1.188) Model 74.576 *** 35.091 *** 35.060 *** 34.499 *** 34.864 *** 9.242 *** 9.515 *** 9.874 *** 9.877 *** 9.878 *** months

age.

text).

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Enrolled Asthma Ear Stopped

<.01 ‐ <

Parent

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P p

* Outcomes **

Low Maternal Table Female .546 ** .558 *** .574 *** .577 *** .617 *** .703 *** .721 *** .698 *** .697 *** .568 ** Age Paternal Black Gestation Child Note: Hispanic Other Female*Socio APGAR Child R2RMSEACFI N/A .001 N/A N/A .488 N/A .493 N/A N/A .494 N/A N/A .499 N/A N/A .671 N/A N/A .672 N/A N/A .675 .030 .973 .675 .029 .973 .675 .028 .978 Constant Note: Socio Grandmother

Two *** Child Sibling Child Moderate Parent t

* *** *** *** *** *** *** 10

.445 *** .795 .053 .223 Model ‐ ‐ ‐ 2.600 1.400 2.988 1.925 2.346 5.446 (.134) ‐ ‐ ‐ ‐ ‐ ‐ * *** *** *** *** *** *** 9

.793 .053 .217 ‐ ‐ ‐ 1.640 *** 1.644 *** 2.618 3.010 1.950 1.366 2.356 5.451 (.360) (.360) ‐ ‐ ‐ ‐ ‐ ‐ * *** *** *** *** *** *** 8Model

.185 .808 .043 ‐ ‐ ‐ 6.801 *** 6.887 *** 6.949 *** 1.600 *** 1.602 *** 1.598 *** 2.597 3.027 1.961 5.478 2.264 1.375 (.148) (.147) (.147) (.167) (.167) (.167) ‐ ‐ ‐ ‐ ‐ ‐ (1.659) (1.658) (1.657) 7 *** *** *** *** *** *** *

.379 .311 .210 .184 .870 ‐ 1.034 *** .998 *** .868 *** .878 *** 2.562 3.420 2.446 5.616 2.812 1.239 (.568) (.563) (.562) (.562) (.437)(.212) (.433) (.210) (.433) (.212) (.433) (.211) ‐ ‐ ‐ ‐ ‐ ‐ 6Model *** *** *** *** *** ***

.324 *** .315 *** .304 *** .303 *** .303 *** .476 *** .474 ** .484 *** .477 *** .472 *** .850 ‐ 2.557 3.510 2.565 5.699 2.886 (.318) (.318) (.317) (.317) (.316) (.547) (.548) (.545) (.544) (.544) (.043) (.043) (.043) (.043) (.043) (.144) (.144) (.143) (.143) (.143) ‐ ‐ ‐ ‐ ‐ 5Model ** .064 .031 *** *** *** ***

.160 .105 .164 .162 .260 .248 .163 .962 ‐ ‐ 3.193 1.476 3.756 (.093) (.089) (.090) (.089) (.089) (.089) (.295) (.281) (.281) (.280) (.280) (.280) Model ‐ ‐ ‐ t 4Model *** ** *** ***

2001.

.150 *** .131 *** .132 *** .126 *** .091 *** .088 *** .088 *** .162 B ‐ 2.563 *** 2.524 *** 2.468 *** 2.516 *** 2.144 *** 2.087 *** 1.739 *** 1.249 3.070 3.877 (.143) (.151) (.144) (.145) (.148) (.149) (.181) (.027) (.027) (.026) (.026) (.026) (.025) (.025) ‐ Model ‐ ‐ ‐ ECLS

Model,

*** *** *** *** 3

the

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1.370 5.447 5.864 (.295) (.315) (.314) (.299) (.299) (.302) (.302) (.302) (.290) (.287) (.286) (.276) (.277) (.280) (.280) (.279) (.323) (.328) (.343) (.328) (.330) (.333) (.333) (.333) ‐ ‐ ‐ Factors

2Model ***

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‐ (.061)(.087) (.059) (.085) (.058) (.083) (.058) (.082) (.055) (.078) (.056) (.078) (.056) (.078) (.056) (.078) (.056) (.078) Model Controlling

Gender,

(.161) (2.117) (2.056) (2.044) (2.060) (2.728) (2.727) (2.706) (2.703) (2.701) (.230) (.225) (.219) (.213) (.212) (.202) (.202) (.201) (.201) (.338) Model by

years

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Paternal Moderate Low Maternal Parent Other Note: Grandmother Socio Two Sibling Female*Socio Constant 123.837 *** 80.177 *** 80.528 *** 75.433 *** 76.360 *** 59.984 *** 60.510 *** 61.589 *** 61.762 *** 61.731 *** ME N/AN/AN/AN/AN/AN/AN/A.028.028.027 R2RMSEA CFI N/AN/AN/AN/AN/AN/AN/A.969.969.976 .025 .073 .125 .168 .179 .257 .259 .274 .276 .277 *** Age Black Age Table Female 3.447 *** 3.461 *** 3.485 *** 3.479 *** 3.542 *** 3.632 *** 3.682 *** 3.604 *** 3.593 *** 2.668 *** Hispanic Note: Child Gestation APGAR Child Child Child t

* ** ** *** *** *** *** *** 13

.406 .621 .477 .330 .162 .742 *** .098 .041 .071 .367 * .923 .224 .002 .069 .172 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 11.576 1.213 2.065 (.088) ‐ ‐ ‐ ** *** *** *** *** 12 Model

.380 .379 .408 .621 *** .476 .335 .164 .741 *** .097 ** .042 .072 .367 * .922 .224 * .002 .171 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 11.598 1.211 2.063 (.236) (.236) ‐ ‐ ‐ * ** ** ** *** *** *** *** 11

.011 .013 .013 .624 .386 .446 .338 .155 .742 *** .096 .048 .076 .367 * .951 .215 .173 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 11.639 1.208 2.076 (.018) (.018) (.018) ‐ ‐ ‐ ** ** ** *** *** *** *** 10 Model

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.624 *** .402 .676 .404 .091 .429 .402 .083 .102 .483 ** .180 .029 .089 Model ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 11.999 1.182 *** 1.278 2.337 (.095) (.160) (.160) (.160) (.160) (.110) (.108) (.108) (.108) (.108) ‐ ‐ ‐ ‐ (1.097) (1.143) (1.143) (1.143) (1.143) 8Model ** *** *** ** *** ***

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.286 .402 .370 .471 .541 *** .005 .695 .082 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 1.318 *** 1.231 2.282 (.287) (.318) (.317) (.314) (.314) (.314) (.314) (.139) (.145) (.144) (.143) (.143) (.144) (.144) (.372) (.372) (.371) (.367) (.367) (.367) (.367) ‐ ‐ ‐ 14.229 ‐ 6 *** *** *** ***

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.903 *** .911 *** .867 *** .865 *** .860 *** .809 *** .811 *** .833 *** .836 *** .531 ** .083 .738 .070 .572 ‐ ‐ ‐ ‐ ‐ 1.218 *** (.059) (.059) (.059) (.059) (.059) (.058) (.058) (.058) (.058) (.187) (.184) (.185) (.184) (.184) (.183) (.183) (.183) (.183) ‐ 10.425

‐ t 2001.

B ‐ 4Model * *** ***

ECLS

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the

** * *** *** 3

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Various

2Model ** ** ** for

.124 .195 ‐ ‐ 4.326 (.044) (.042) (.038) (.037) (.037) (.038) (.038) (.038) (.038) (.038) (.038) (.038) (.065) (.062) (.056) (.055) (.055) (.055) (.055) (.054) (.054) (.054) (.054) (.054) (.020) (.020) (.018) (.017) (.017) (.017) (.017) (.017) (.017) (.017) (.017) (.017) Model ‐ Controlling

Age,

(.116) (1.547) (1.491) (1.368) (1.371) (1.837) (1.838) (1.921) (1.916) (1.901) (1.901) (1.901) (1.901) (.165) (.156) (.151) (.135) (.134) (.133) (.133) (.134) (.134) (.135) (.135) (.135) (.222) Years Model 21.884 ***

Gender

age.

text).

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reported

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(wave (wave (wave

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(wave (wave

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for Home

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Infections Infections

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Unsafe Months Months Months ‐

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Ear Stopped Asthma Asthma Ear Body Enrolled

<.01 ‐ <

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P p

* Outcomes Modeled

R2RMSEACFI N/A .005 N/A N/A .110 N/A N/A .178 N/A .049 .341 .976 .044 .353 .979 .038 .372 .987 .035 .373 .988 .031 .374 .978 .027 .379 .960 .032 .400 .920 .032 .400 .919 .031 .400 .919 .031 .400 .929 *** Child Hispanic Moderate Child Low Child Child Socio Gestation APGAR Other Grandmother Live Child Parent Child Table FemaleAge 1.039 *** 1.088 *** 1.114 *** 1.190 *** 1.232 *** 1.297 *** 1.266 *** 1.218 *** 1.199 *** .880 *** .877 *** .877 *** 1.024 *** Parent Maternal Maternal Two Note: Paternal Hours Sibling Note: Parent Child Age Female*Socio Constant Age Black 1 t

** *** *** *** *** ** 13

8.287 .153 .160 .127 .053 .087 .573 .019 .010 .692 *** .340 * .859 *** .765 .459 .101 .148 .835 Model ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 1.196 (.086) ‐ ** *** *** *** *** ** 12

8.324 .152 .166 .128 .052 .571 .019 .010 .691 *** .339 * .860 *** .761 .462 .100 .147 .839 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 1.193 (.232) (.232) ‐ ** ** *** *** *** *** 11 Model

8.320 .100 .153 .167 .127 .571 .020 .011 .690 *** .338 * .860 *** .762 .462 .147 .840 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 1.194 (.018) (.018) (.018) ‐ *** ** *** ** *** *** 10 Model

8.264 .956 *** .953 *** .954 *** .959 *** .101 .154 .166 .124 .011 .568 .694 *** .340 * .858 *** .462 .761 .150 .823 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 1.158 *** 1.153 *** 1.152 *** 1.151 *** 1.189 (.207) (.207) (.207) (.207) (.122)(.879) (.122) (.879) (.122) (.879) (.123) (.879) ‐ 9Model *** *** *** *** ***

8.369 .710 *** .102 .104 .104 .106 .106 .103 .199 .109 .036 .562 .433 ** .892 *** .482 .789 .129 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 1.443 .678 .679 .679 .668 1.321 1.014 *** (.093) (.157) (.157) (.157) (.157) (.107) (.106) (.106) (.106) (.106) ‐ ‐ (1.072) (1.123) (1.123) (1.123) (1.123) 8 *** *** *** ***

8.654 *** .496 * .464 .402 .401 .401 .405 .002 .003 .009 .012 .012 .014 .104 .101 .164 .120 .005 .547 .482 ** .920 *** .488 .782 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 1.364 1.156 *** (.249) (.248) (.246) (.246) (.246) (.246) (.136) (.136) (.135) (.135) (.135) (.135) (.031) (.031) (.031) (.031) (.031) (.031) ‐ ‐ 7Model *** *** ***

Model .096 .151 .005 .002 .575 .481 ** .915 *** .274 .734 10.747 *** ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 1.263 1.166 *** (.364) (.364) (.363) (.360) (.360) (.360) (.360) (.136) (.142) (.141) (.140) (.140) (.141) (.141) (.280) (.311) (.310) (.308) (.308) (.308) (.308) ‐ ‐ ‐ 6Model *** ***

Model .014 .015 .013 .008 .006 .006 .006 .006 .000 .099 .023 .467 ** .929 *** .748 10.699 *** ‐ ‐ ‐ ‐ ‐ 1.276 1.111 *** (.351) (.352) (.352) (.351) (.350) (.350) (.350) (.350) (.028) (.028) (.028) (.028) (.027) (.027) (.027) (.027) (.204) (.204) (.204) (.204) (.203) (.203) (.203) (.203) (.092) (.092) (.092) (.092) (.091) (.091) (.091) (.091) ‐ ‐ ‐ t 5

2001.

Model .622 *** .618 *** .575 ** .569 ** .570 ** .544 ** .540 ** .538 ** .541 ** .093 .052 .463 ** .945 *** B 10.260 *** ‐ ‐ ‐ ‐ ‐ (1.328) (1.797) (1.797) (1.879) (1.872) (1.864) (1.864) (1.864) (1.864) 1.075 *** (.057) (.057) (.058) (.057) (.057) (.057) (.057) (.057) (.057) (.181) (.180) (.181) (.180) (.180) (.179) (.179) (.180) (.180) ‐ ‐ ECLS

Model,

the

Model .045 ** .031 .032 * .035 * .035 * .021 .006 .005 .005 .005 .959 *** .100 .051 .522 ** in ‐ ‐ ‐ ‐ 10.912 ***

(1.333) 3.492 *** 3.386 *** 3.373 *** 3.332 *** 3.328 *** 3.180 *** 2.838 *** 2.830 *** 2.832 *** 2.900 *** (.096) (.100) (.099) (.100) (.100) (.102) (.110) (.110) (.110) (.128) (.017) (.017) (.017) (.016) (.016) (.016) (.016) (.016) (.016) (.016) (.164) (.161) (.161) (.160) (.160) (.160) (.158) (.158) (.158) (.158) ‐ Factors

3 *** .492 * .750 *** .882 *** .831 *** .791 *** 1.016 *** 1.437 *** 1.455 *** 1.460 *** 1.460 *** **

Various

5.529 *** .192 .104 * ‐ for ‐ ‐ 1.520 *** 1.487 *** 1.263 *** 1.098 *** 1.037 *** 1.021 *** 1.217 *** 1.525 *** 1.533 *** 1.532 *** 1.529 ***

2.151 3.386 *** (.216) (.203) (.210) (.211) (.212) (.212) (.214) (.221) (.222) (.222) (.222) (.199)(.195) (.195) (.178) (.193) (.176) (.192) (.177) (.192) (.178) (.192) (.178) (.195) (.180) (.200) (.184) (.200) (.185) (.200) (.185) (.200) (.185) ‐ ‐ Controlling ***

2Model

3),

4.856 ** .969 *** .983 *** 1.069 *** 1.122 *** 1.159 *** 1.123 *** 1.085 *** 1.062 *** .841 *** .844 *** .844 *** 1.028 *** .207 .088 * ‐ Model ‐ ‐ (.019) (.019) (.017) (.017) (.017) (.017) (.017) (.017) (.017) (.017) (.017) (.017) (.062) (.061) (.055) (.054) (.054) (.053) (.053) (.053) (.053) (.053) (.053) (.053) (.042) (.041) (.037) (.036) (.037) (.037) (.037) (.037) (.037) (.037) (.037) (.037) (wave

Age

1 ***

Years

(.109) (1.496) (1.450) Model 12.828 *** (.156) (.151) (.147) (.132) (.130) (.130) (.130) (.131) (.131) (.132) (.132) (.132) (.218) Gender

Skills

text).

1) 2) (see

Reading

(wave (wave

Early (wave

reported

of (wave

parentheses. (wave1)

Child 1) not in Stories Stories

Model

Needs 2) 1)

paths

(wave

1) 2) Status

(wave Telling

Telling

(ref=normal)

(BMI) Stimulation Education

reported

3) .447 *** .467 *** .487 *** .485 *** .485 *** .485 *** .485 *** .488 *** .486 *** .488 *** .488 *** .487 *** 2) 1) Child

2) 1) of

(wave (wave Watched

Equation of (wave (wave

weeks)

Index Daycare Status Singing, Singing,

Weight

errors

mediating

(wave (wave (wave

(in economic

Breathing Neighborhood in Level

‐

(wave (wave

Cognitive

Home for

Mass

Birth Age Weight

Warmth Warmth

Infections Infections

Television Provision

Structural

Score Child Reading, Reading, .05 Size

Unsafe Months Months Months

‐

Standard <.001 economic 8.

(ref=white)

Asthma Ear Body Stopped Enrolled Ear Asthma

<.01 ‐ <

Parent

Birth in in in in P

P p

* Outcomes **

Black Age Hispanic Child Child Child Constant Child Child Female*Socio R2RMSEACFI N/A .004 N/A N/A .067 N/A N/A .128 N/A .048 .300 .975 .044 .322 .979 .038 .327 .987 .035 .328 .987 .031 .330 .977 .027 .337 .960 .032 .349 .919 .032 .349 .918 .031 .349 .919 .031 .350 .929 Age Gestation ***

Grandmother Moderate Other Socio Table FemaleAge .932 APGAR Child Live Two Low Child Note: Sibling Parent Maternal Paternal Parent Parent Maternal Hours t

* * * * *** *** *** *** *** *** *** *** *** 11

) 7 5 9 38 .4 .824 .092 .327 ‐ ‐ 82.088 1. 8.495 *** 3.673 *** 3.358 5.855 1.486 1.110 3.192 5.605 3.607 3.214 ( (.263) ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 12.272 ‐ * * ** ** *** *** *** *** *** *** *** *** Continued *** 10

) 28 623 . .4 .852 .182 .327 ‐ ‐ 97.878 2 4.905 4.448 *** 2.923 1.820 1.068 4.834 5.870 4.769 2.146 ( Model ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 13.743 ‐ * ** ** *** *** *** *** *** *** *** *** *** 9Model

) 1 28 .511 . .187 .751 .348 ‐ ‐ 3 1.147 6.376 4.086 5.129 *** 2.392 1.355 8.020 4.136 6.444 ( (.817) (.766) (.737) (.663) (.621) (.597) ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 127.419 11.786 ‐ ** *** *** *** ** *** *** * ** *** *** 8Model )

602 . .474 .871 .214 .241.999 .012 1.000 .024 .998 .042 .991 .329 ‐ ‐ 2 3.994 *** 3.851 *** 3.323 *** 4.732 *** 4.657 *** 3.521 *** 2.734 4.682 *** 1.889 1.085 4.867 5.899 2.186 ( (.190) (.189) (.182) (.181) (.180) (.174) ‐ ‐ ‐ ‐ ‐ ‐ ‐ 13.677 95.548 Model ‐ *** *** *** ** *** *** ** *** *** 7 )

80 366 . .229 .750 .351 ‐ ‐ 3 1.182 3.871 5.454 *** 2.502 1.392 8.175 4.108 ( (.772) (.721) (.766) (.717) (.690) ‐ ‐ ‐ ‐ ‐ ‐ ‐ 11.623 (1.763) (1.646) (1.748) (1.637) (1.575) Model ‐ 125.279 *** *** *** *** *** ** *** 6 )

57 3 . .218 .756 .351 ‐ ‐ 3 1.178 3.914 5.586 *** 1.408 4.169 ( (.387)(.162) (.386) (.161) (.361) (.151) (.383) (.160) (.359) (.150) (.348) (.145) ‐ ‐ ‐ ‐ ‐ 11.799 Model ‐ 125.459 *** *** *** ** *** * Spring. 5 ‐ )

.457 .474 .4 .173 .353 ‐ 9.861 *** 9.241 *** 9.220 *** 8.060 *** 9.181 *** 8.056 *** 6.909 *** 3.927 5.692 *** 1.497 4.265 1.383 ( (.239) (.247) (.247) (.232) (.245) (.231) (.227) ‐ ‐ ‐ Grade ‐ ‐ 12.978

‐ 129.582 5th

Wave * *** *** *** ** *** ***

4Model )

6 7 6 . .542 .378 ‐ 4.170 6.380 *** 1.481 4.464 ( (.558) (.543) (.553) (.554) (.518) (.549) (.516) (.498) (.524) (.514) (.512) (.512) (.478) (.507) (.476) (.458) (.683) (.641) (.640) (.640) (.598) (.634) (.594) (.574) ‐ ‐ ‐ ‐ Spring, 19.876 11.237 ‐ ‐ ‐ 122.713 t 98. Grade ‐

3rd

1999

*** *** *** 5= K

3Model ‐ )

000 .428 .399 ‐ ECLS 1. 4.159 9.347 *** 1.103 ** (

Wave ‐ ‐ ‐

(1.119) (1.066) (.995) (.990) (.988) (.922) (.980) (.917) (.883) 110.126 Model. Spring,

the

*** *** *** Grade

2Model )

1st

022 .826 .400 ‐ 1. 4.045 1.170 ** ( (.282) (.281) (.266) (.249) (.247) (.247) (.231) (.245) (.229) (.221) (.417) (.412) (.391) (.364) (.362) (.362) (.338) (.359) (.336) (.324) (.573) (.578) (.551) (.513) (.511) (.510) (.477) (.506) (.474) (.457) (.314) (.319) (.304) (.283) (.282) (.282) (.263) (.279) (.261) (.252) (.512) (.511) (.484) (.452) (.450) (.449) (.419) (.446) (.417) (.401) (.630) (.627) (.595) (.557) (.554) (.554) (.517) (.549) (.514) (.494) 4= Factors ‐ ‐

Model 120.274 Wave

Various

Fall, ‐ for

*** ***

1 )

Grade

.400 4.150 ( (.279) (13.466) (13.498) (12.823) (11.978) (11.923) (11.907) (11.146) (11.807) (11.085) (10.686) ‐ 1st

Model Controlling

Wave

Gender,

Spring, ‐ Skills

text).

Math

Grade)t Grade)t (see

Kindergarten

Grade

(1st (3rd

5th

model. reported

parentheses. in Wave

not in

Fall, ‐ Model Performance Performance

paths

variable

(ref=normal)

) reported Math Math

1 2) 3) 4) .846 ** .572 1.219 *** .945 *** .936 *** .931 *** .505 .824 ** .436 .478 5) .612 .402 .483 .522 .560 .575 .324 .484 .262 .250 6) 1.204 1.108 1.155 2.095 *** 1.857 *** 1.828 *** 1.672 ** 1.904 *** 1.733 *** 1.614 **

of of Grade)t Equation Grade)t

Status Weight wave

errors mediating Kindergarten

( (wave (wave (wave (wave (wave

mediating

(3rd (1st

s a Learningt Kindergarten

for Home

Birth in as to Weight

ze Structural Math Math Evaluation Evaluation

.05 Si Months Mont Months Months Months Months

Standard Wave economic <.001 in in 9. (ref=white)

<.01 ‐ <

n Time

Parent

Birth i in in in in in

P p

* Outcomes Modeled

Note: Table Female Age Socio Sibli Two Age Moderate Note: Approach Black Constant 115.994 Age Low

CFI R2RMSEA .009 .017 .024 .137 .250 .258 .260 .365 .271 .367 .403 *** Hispanic Age Parents Age Age Parents First Tutor Other Tutor 1 t 94

‐ Grade

5th

* ** ** *** *** *** Wave ***

) .653 *** .228 * .292 .561 .937 .523 .079 .315 .194 .260 .255 .830 .967 Spring, .190 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 49.710 ‐ 3.125 1.003 (.109) (.361) (.444) (.113) ( ‐ ‐ Model Grade

* 3rd

** ** *** *** *** *** 5= Change

) .170 *** .162 *** .343 .075 .067 .043 .612 .274 .740 *** .728 *** Wave .928 .327 .193 .285 .269

.190 ‐ ‐ ‐ ‐ ‐ 51.480 1.402 *** 1.400 *** 1.494 *** 1.322 *** 1.232 *** 1.264 *** 2.744 1.002 1.042 Model 1.033 (.534) (.533) (.009) (.010) (.298) (.297) (.302)(.277) (.305) (.277) (.345) (.344) (.153) (.152) (.241) (.240) (.276) (.276) (.195) (.195) (.416) (.415) ( (.133) (.133) (.144)(.209)(.087) (.144) (.208) (.087) (.950) (.947) (.007) (.007) ‐ ‐ ‐ ‐ Spring,

*** *** Grade

2Model )

1st

.165 .028 .375 1.000 .997 8.817 ( (.285) 4= ‐

14.712 *** 73.213 Model Wave

Fall, ‐ *** ***

1 )

Grade

.400 4.150 (.279) (.862) (6.421) (6.416) ( ‐ 1st

Model 3=

Wave

Spring, ‐ text).

Grade)t Grade)t (see

Kindergarten

(3rd (1st

model. reported

parentheses. in Wave

not in

Fall, ‐ Performance Performance

paths

variable

(ref=normal)

) reported Math Math

5) 6) 4) 3) 2) 1

t of of Grade)t Grade)t

Grade) Status

Grade) Weight

wave errors mediating

Kindergarten

(wave (wave (wave (wave (wave (

mediating

(1st (3rd

s a Learningt Kindergarten

h for Home

Birth (First (Third in as to Weight

Math Math Continued. Evaluation Evaluation

.05 Size Months Months Months Months Months Mont

Standard Wave economic <.001 in in 9. Skill Skill (ref=white)

<.01

‐ <

Time

Parent

Birth in in in in in in

P ing p

* bl Outcomes Modeled

Black Math Tutor Tutor Approach Math First Hispanic Other Socio Age Age Age Parents Age Low *** Age Two Si Moderate Parents

CFI R2RMSEA .009 .218 .788 .789 Constant 115.994 Spring. Table Female Age Note: Note: 1 t

*** *** *** *** *** *** *** 11

.200 .317 .285 .354 .530 .185 .252 ‐ ‐ ‐ ‐ ‐ ‐ 93.140 8.212 *** 7.690 7.031 4.546 1.911 5.039 (.282) Model ‐ ‐ ‐ ‐ ‐ 10.768 ‐ *** *** *** *** *** *** *** 10

.229 .130 .108 .482 .559 .294 ‐ ‐ ‐ ‐ 8.007 5.992 5.353 1.915 1.208 5.689 1.538 ‐ ‐ ‐ ‐ ‐ ‐ ‐ 107.604 12.312 ‐ * * *** *** *** *** *** *** *** 9Model

.167 .371 .389 .311 ‐ ‐ ‐ 5.934 4.467 4.976 2.398 2.591 7.163 1.003 4.143 9.547 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 140.363 (1.348) (1.241) (1.202) (1.169) (1.076) (1.042) *** *** *** *** *** *** 8Model

.200 .093 .474 .634 .023.999 .006 1.000 .017 .999 .041 .992 .284 ‐ ‐ ‐ ‐ 5.690 *** 5.686 *** 4.521 *** 3.726 *** 3.727 *** 3.137 *** 8.089 6.331 1.896 5.702 1.656 (.188) (.188) (.183) (.186) (.186) (.181) ‐ ‐ ‐ ‐ ‐ 12.414 ‐ 107.767 *** *** *** *** *** * *** 7Model

.353 .384 .332 ‐ ‐ ‐ 6.028 4.801 2.374 7.187 1.064 4.331 9.649 (.825) (.760) (.824) (.759) (.735) ‐ ‐ ‐ ‐ ‐ ‐ ‐ (1.884) (1.735) (1.882) (1.733) (1.678) Model 140.471 *** *** *** *** *** *** 6

.338 .376 .345 ‐ ‐ ‐ 3.319 *** 3.323 *** 2.371 *** 3.306 *** 2.355 *** 1.325 *** 6.058 4.801 2.372 7.263 9.730 (.413) (.413) (.381) (.413) (.380) (.371) (.172) (.172) (.159) (.172) (.159) (.154) ‐ ‐ ‐ ‐ ‐ Model 140.580 *** *** *** *** *** 5

.037 .350 .461 ‐ ‐ 6.292 5.750 7.270 (.256) (.263) (.263) (.243) (.263) (.243) (.241) ‐ ‐ ‐ 11.641 *** 10.912 *** 10.902 *** 9.746 *** 10.963 *** 9.799 *** 8.678 *** 11.000 Model ‐ 144.801 *** *** *** *** *** 4

.565 .225 .177 .173 .747 .497 ‐ ‐

9.468 1.045 8.082 (.570)(.742) (.552) (.688) (.547) (.683) (.546) (.683) (.504) (.630) (.546) (.685) (.503) (.631) (.488) (.613) (.607) (.583) (.590) (.591) (.547) (.591) (.546) (.531) t ‐ ‐ ‐ 19.141 14.541 Model ‐ ‐ 136.212 99. ‐ 1998

K ‐ *** *** ***

ECLS

.159 ‐ 1.192 1.501 ‐ ‐ 11.595 (1.218) (1.159) (1.067) (1.055) (1.055) (.971) (1.054) (.970) (.940) ‐ 117.076 Model.

the

*** *** 2Model

Factors

3.293 *** 3.158 *** 3.166 *** 3.445 *** 3.470 *** 3.492 *** 2.081 *** 3.489 *** 2.074 *** 1.091 1.624 (.307) (.306) (.290) (.267) (.264) (.264) (.243) (.264) (.243) (.235) (.685) (.683) (.647) (.597) (.591) (.591) (.544) (.590) (.543) (.526) (.454) (.449) (.426) (.392) (.388) (.388) (.357) (.387) (.356) (.346) (.625) (.629) (.602) (.552) (.547) (.547) (.503) (.546) (.503) (.488) (.342) (.347) (.331) (.304) (.301) (.301) (.277) (.301) (.277) (.268) (.557) (.556) (.527) (.485) (.480) (.480) (.442) (.480) (.441) (.427) ‐ ‐ Model 129.228 Various

for

*** ***

Controlling

(.436) (.436) (.434) (.411) (.379) (.375) (.375) (.347) (.375) (.347) (.348) (.305) (14.658) (14.691) (13.940) (12.844) (12.720) (12.717) (11.730) (12.704) (11.718) (11.376) Model Gender,

Skills

text).

Reading

Grade)t Grade)t

(see

(1st (3rd

Grade

5th

of model. reported

parentheses. in

not in

Performance Performance

Model

paths

variable

(ref=normal)

reported Reading Reading

Grade)t 6) 1) 1.168 *** 1.161 *** .774 ** .509 .554 * .556 * .581 * .549 * .573 * .471 * 2) 3) .429 .844 4) .162 5) 1.361 * 1.100 * 1.243 * 1.320 ** 1.374 ** 1.381 ** .922 * 1.384 ** .921 * .930 * Grade)t

Equation

of of

(1st (3rd

Status Weight

errors mediating

(wave (wave (wave (wave (wave (wave

mediating

a Learningt Kindergarten

for Home

Birth as in to Weight

Structural

Reading Reading Evaluation Evaluation

.05 Size Months Months Months Months Months Months

Standard economic <.001 in in 10. (ref=white)

<.01 ‐ <

Time

Parent

Birth in in in in in in

P p

h * t Outcomes Modeled

Socio Two Sibling Age Table FemaleO 3.095 Tutor Age Note: First Tutor Moderate Age Approach Constant 137.871

CFI R2RMSEA .004 .013 .022 .129 .265 .282 .282 .406 .284 .407 .428 Low Age *** Age Black Age Parents Parents Hispanic 1 t 96

Chapter Five: Conclusion and Discussion

Summary

Surveying the literature, the origins of gender differences in cognitive skills is unclear. This is partly due to the limited view of sociological investigations, which often

overlooks processes in early childhood (Menaghan, 2005). This study merges the findings of child developmentalists and educational sociologists to provide a coherent

portrait of gender differences throughout childhood. The results show the utility of using

the subtests’ measures to reconcile competing findings. One might reasonably ask, under

what conditions is it more useful for social scientists to employ global measures of

“math” versus the more specific subtests? Of course in stratification research, the more

global the measure, the more clarity is achieved in assessing larger group-level patterns, but as this study reveals, this “parsimony” approach has utility as long as it does not distort narrower patterns. In future work, exploring (and reporting) both the global and

item-level assessments serves as a needed check against distortions that may result from the limits of a singular approach.

This study shows that gender gaps in math-related skills fluctuate based on the

type of skill assessed and the period observed. Why girls have advantages in early math

skill is unknown, but a clear pattern emerges as girls and boys move into middle and late

childhood. Girls fall behind boys as math complexity increases although simultaneously maintaining advantages in more basic math skills. Part of these emerging differences appears, at first, to be a product of how parents treat boys and girls differently. At the bivariate level, they are more likely to evaluate boys’ math skills favorably and to invest in tutoring for boys. But when examined further, parental differences in math and reading evaluation seem to be accurately based on the child’s current and past skill level.

The effect of tutoring is not significant when the previous skill level is considered, suggesting that—not surprisingly—that children who are tutored need the help. These conclusions support the critical role of including children’s previous skills in models when assessing the impact of parent or school effects on gender differences in math and reading skill. What appears to be support for the parent socialization model is the result of model misspecification, highlighting a critical limitation of past research on parent socialization effects on gender differences and cognitive skill development (Buchmann et al., 2008).

Despite speculation that schools disrupt girls’ early advantages in math, it appears that school entry does little to affect math or reading patterns observed before school entry. Drawing from Entwisle et al.’s (1992) and Downey et al.’s (2004) findings, there appears to be little evidence of schooling’s negative effects on girls compared with boys as these researchers found that the gender gap in math was constant across school and non-school periods. How students approach learning in the classroom (classroom citizenship) illustrates this point. Girls are nearly a half standard deviation ahead of boys on teacher-rated approaches to learning in 3rd grade. This measure, capturing student

citizenship in the classroom, learning style, interest in learning, etc., is strongly linked to

reading and math skill outcomes. Thus, the picture that emerges is one in which girls

behave well in school, directly resulting in increased cognitive skill, especially in math.

Are schools hurting boys? This has been a popularized counterargument

(Sommers, 2000), but a logical next step is to consider why boys continue to excel on higher order math skills despite all the challenges boys have behaviorally and academically in school? If girls are more likely to take advantage of the school experience to learn than boys, how is it that boys still perform better, on average, than girls on standardized math tests? One might reasonably wonder how boys manage to achieve general math parity with girls despite their poor classroom behavior. While my study focused on standardized test scores, when the focus is on older children’s grades, boys’ greater propensity for behavioral problems will manifest itself more distinctly, reducing their grade point average.

Although no direct evidence can be drawn upon in the analyses, it appears that gender differences in cognitive skills, at least for math, are developed beyond the school setting, as some research has found (Downey and Vogt-Yuan, 2005). Drawing from this study, it is the higher order math skills that boys manage to excel in despite their behavior problems at school. One explanation is that standardized testing of higher order math skills is not as tightly linked to school curriculum and thus boys’ out of school activities compensate for their in-school challenges (Halpern et al., 2007).

To understand more specifically how out-of-school factors influence gender gaps in math skills, scholars should conceptualize parenting behaviors that contribute directly

to higher order math. Therefore, rather than testing how often parents work on science projects with their sons versus daughters, we need more specific information about how often they work on decimals, fractions, and algebra. Available measures in large surveys like ECLS-K often capture parental investment generically without the level of specificity needed to uncover why boys and girls perform differently in more complex math. As the parental investment measures show, parents (and perhaps teachers) appear more willing to provide math tutoring to the sons than daughters despite evidence that boys perform as well if not slightly better than girls. But we need to know more

concretely what parents are doing with their sons versus daughters.

Are gender gaps in cognitive skills important?

Although not an unusual problem in the social sciences, gender differences

literature often equates statistical significance with practical significance (Hyde, 2005;

Daniel, 1977). Statistical significance is important and observed differences solicit

explanation. However, the relevance of a theory of gender difference depends not only

on the statistical significance of gender difference but its practical significance too.

The gender literature has, at times, emphasized statistical significance without

acknowledging how small gender differences often are. The gender difference literature

is large. Thousands of studies have explored gender differences in cognitive skills. The

work of Maccoby and Jacklin (1974) was the first comprehensive evaluation of the

gender differences literature. They reviewed over 2,000 studies of gender differences,

spanning several cognitive domains. Although finding many gender similarities in

100

domains such as sociability, self-esteem, and achievement motivation, subsequent studies

often emphasize their findings that boys outperform girls on mathematical skill and girls

excel over boys in verbal skill (Hyde, 2005).

Soon after this pivotal study, meta-analyses emerged as a way to consolidate an overwhelming number of findings. This approach employs a statistical method for aggregating research findings across many studies addressing the same research subject

(Hedges and Becker, 1986). In Hedges and Nowell’s notable meta-analysis (1995), they critiqued the narrow focus on statistical significance over practical significance.

Evidence of consistent statistical significance by gender was selectively referenced in the gender difference literature and, as a result, reinvigorated the field (Hyde and Linn,

2006).

But a handful of studies have begun to shed doubt on the gender difference conclusion, arguing instead that statistically significant findings should be interpreted regarding their practical relevance (Hyde, 2005, Leahy and Guo, 2001). In this work, gender differences in various cognitive skills have been found to be occasionally statistical significant but not substantively important in practice. In fact, when using effect size as a guide, boys and girls are surprisingly more alike than different on standardized tests of math and reading (Hyde, Linberg, Linn, Ellis, and Williams, 2008).

From this perspective, some argue that early childhood is notable for gender parity in a

number of cognitive measures (Spelke, 2005).

But three considerations should give pause to this conclusion regarding the

practical significance of gender differences. First, “small effects can turn out to be

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practically important” (Rosenthal, Rosnow and Rubin, 2000, pp. 15–16). Although the

results of this dissertation show that there are consistent gendered differences in math and

reading early in the life course, the relevance of this claim relies on linking childhood

gender differences in cognitive skill to adulthood. Second, gender gaps in math are much

larger when girls’ citizenship in the classroom is considered. In other words, if not for

girls’ considerably better citizenship in the classroom, math gaps would be much larger

than those observed. And if school policies were successful in improving the overall

behavior of boys to match girls, it is probable that gender gaps in math would widen.

Third, gender gaps are much larger for more complex math assessments. Although

average gender differences in math may appear slight, of the more complex math skills,

gender gaps are more substantial.

A more thorough assessment of the significance of gender differences in cognitive

skills needs to employ prospective longitudinal data linking both averages and extreme score differences observed in childhood and adolescence to labor market outcomes.

Limited evidence of this link currently exists despite considerable speculation (see Ceci

and Williams, 2008).

Theoretical Implications

This research has implications for several broader questions:

1. How do the findings of this study relate to Summers’s suggestion that boys’ possess

more innate math abilities than girls?

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Recall that Summers (as well as numerous scholars in the child development

field, e.g., Baron-Cohan, 2004; see Geary, 1998), assumed that what is observed in early

childhood is developmentally linked to later life outcomes. This study shows that the

gender patterns in early childhood contradict the populist claim that boys dominate in

math-related skills in early childhood—at least before school begins. If girls excel in

many assessments in early childhood—as this study shows—how can this be reconciled

with the few skills boys may excel in during this period? And more importantly, why do

girls appear to begin life ahead of boys in cognitive skills, yet later fall behind in some

areas (e.g., math)?

The reversing of girls’ fortunes—or more accurately the effect of shifting item

complexity—suggests that basic skill differences found in early childhood are not the critical gender differences linked to stratification outcomes. If they were, gender differences in math during early childhood would be strong predictors of gender differences in math throughout childhood and adolescence. Without clear evidence

explaining this reversal, the results of this analysis suggest that early childhood is not a

critical part of the gender stratification story. For gender stratification scholars, item-

complexity is the clear skill difference of interest.

Educational sociologists have yet to articulate this point theoretically. Gender

gaps in item-complexity undermine the empirical assumption of “cognitive growth.”

Surely, skills accumulate, but causality and correlation do not, in themselves, imply that a

general domain of ability underlies these correlates as growth models assume. Yet, this is

clearly evident in the assumption of growth curve modeling and the concomitant use of

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vertically scaled assessments of mathematical skill (Singer and Willett, 2003; as modeled in Figures 3 and 4 in this study). Although educational sociologists need not abandon the

“cognitive growth” assumptions entirely, given the benefits of assessing general patterns over time, it would seem imprudent to ignore revising the assumptions of many child developmentalists to fit a more sociological frame.

Regardless of how one interprets gender differences in math skills at the global or item-specific level, the results of this dissertation push the sociological literature to incorporate and explain what child developmentalists have already identified: the relationship between gender and item complexity. This relationship reorients the field to examine the specific math skills that show the greatest gender disparities.

2. What is the role of childhood in understanding gender differences in cognitive skill?

An examination of childhood reveals that gender differences in cognitive skills are well underway. As gender stratification scholars have largely been engaged in the analysis of adult processes and outcomes, this study reveals that childhood is an active time for gender differences in cognitive skills. How might a refocusing on the gender differences that precede high school, college, and the labor force—a predominant focus in the field—lead to the uncovering of the origins and early explanations of some of the field’s most puzzling findings?25

25 One puzzle is examining processes in childhood that work to direct girls to pursue gendered majors and occupations despite girls’ advantages in the classroom, gender parity in college attendance, and girls’ higher rates of college completion. As one study put it, girls may come to feel equally skilled in math, but conclude, “I can, but I don’t want to” (Jacobs et al., 2005).

104

There is one hesitation for optimism based on the results of this study. Although

evidence suggests that early childhood surely plays an important role for understanding

stratification across racial/ethnic and socioeconomic groups (Farkas and Beron, 2004;

Downey and Gibbs, 2007), especially as cognitive skills are coming to the forefront of

modern-day stratification, this study shows that the kinds of gender differences that would link to gendered outcomes in adulthood are late forming when compared with large race and class differences evident at and before school entry (Lee and Burkam,

2002). While gaps in cognitive skills across social class and race/ethnicity are large as early as 24 months, gender differences are smaller and more nuanced, showing varied patterns over time across subtests in math and reading. This cannot be overstated in this

study. Gender differences show patterns that are fundamentally unique from race and class differences. Gender is randomly assigned across many of society’s cleavages: class,

race, neighborhoods, regions, etc. Therefore, the disparities that emerge will come from

more subtle sources and, at times, contradict other group-level trajectories, as the gender

reversal in math skills shows.

3. How important are schools for understanding gender differences in math skills?

Schools are not an obvious culprit for gender differences in math skill for two

reasons. First there is no apparent disruption in math or reading trajectories in the

transition to school. The speculation that schools disrupt female advantages in early

childhood receives no empirical support in this study. A more consistent explanation is

that the content of math assessments shifts to include increasingly more difficult concepts

105

and skills. Second, and this is more speculative as the data did not allow direct

comparison between curriculum and math specific items, research shows that item-

complexity, at the highest levels, becomes more and more removed from curriculum

(Halpern et al., 2007; Geary, 1996; Halpern, 2000). Thus, at least part of the gender gap

in the higher order math skills is likely a result from influences beyond the curriculum.

Schools may still matter but perhaps in less direct ways. Schools convey culture.

As stereotype threat and the link between self-efficacy and testing reveal, there are significant gender differences in expectations in regard to cognitive skills. In a culture where peers are rewarded for engaging in gendered activities and skills, schools are the stage where this cultural transmission is displayed. Nevertheless, the results from this study, along with those of seasonal comparison researchers, direct our attention outside of school as the source of gender gaps in cognitive skills.

4. How does parent socialization shape gender differences in cognitive skills?

Only a modest relationship between parent gender socialization and math and reading skills is supported in this study. At the bivariate level, parents evaluate their sons’ math skills more favorably than their daughters even when test scores are statistically controlled. And parents seem more willing to provide math tutoring for their sons than their daughters. But when previous math and reading skills of the child are considered, there is minimal evidence of a direct relationship. This adds more empirical evidence to the speculation that any gendered relationship between parents’ evaluation of

106

their child’s skills is partly contaminated by the omission of past skills (see Buchmann et al., 2008 for discussion).

Where now?

The new story for gender stratification scholars is not when do gender gaps in global assessments of math emerge, but rather when do gender gaps in more complex math skills emerge. This specific line of inquiry may bear more fruit. By focusing on specific skill sets showing the largest gender disparities, more specific processes found in non-school and school settings can be identified and explored. In this study, even videotaped interactions of parents’ cognitive stimulation cannot isolate the more specific parenting behavior aimed at teaching children more complex math skills. Future parent- child data would need to extend beyond broad questions, such as “how often do you help your child with homework” to the more specific “how often do you help your child learn fractions”; “how do you help your child learn rates and measurements?” or “if your child struggled to understand place values, what would you do?” As gender gaps in math are specific to certain complex skills, future work should capitalize on the more subtle patterns that item-specific data reveal. And while nationally representative survey data are useful for identifying the magnitude of gender differences, more focused ethnographic data may be needed to understand the more detailed parenting approaches that may produce gendered outcomes.

Two conceptual frameworks need reconsideration. There is no evidence here of any direct role of schooling’s effect on gender gaps in math and reading skill. This need

107

not imply that social processes are altogether unimportant, but that children’s more subtle

experiences beyond the scope of the school-as-culprit explanation are more relevant.

Although the parent socialization approach is an obvious step in this direction, the

literature lacks specificity in the measurement of parent-child interactions and seldom

addresses the obvious effect of girls’ and boys’ interests and needs on parents’ attitudes and behaviors. To move forward, specific gender differences need to be matched with specific interactions of parents (and others) with their children. As long as there is a commitment to explaining gender gaps in math and reading, conventional approaches will undoubtedly result in conventional conclusions.

108

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Appendix

Period Effects

Unfortunately, the ECLS-B collects data of children who are younger than those in the ECLS-K, the ECLS-B cohort reaches kindergarten age around the year 2006, eight years after the ECLS-K kindergarten cohort was sampled. As a result, this introduces the possibility that changes in the gender gap between ECLS-B and ECLS-K might not represent a developmental effect but rather broader societal changes that occurred during the eight-year period separating the two cohorts of children.

There are several reasons for considering the role of period effects in this article.

Gender gaps in cognitive skills have fluctuated historically, sometimes in important ways in just eight years. For example, significant changes in the gender wage gap have occurred within a decade’s time. In the eight years from 1983 to 1991, the wage gap saw significant decline, a result of marked changes in college participation of women. Yet, in the following eight years, wage gap trends flattened (Bobbitt-Zeher, 2008). Similarly, from 1998 to 2006, important changes in factors affecting child rearing practices by gender may have occurred.

If parents are investing more time with their children in developmental activities, as has been the trend in the 80s and 90s (Sayer, Bianchi, and Robinson, 2004), and parents interact with their children in gendered ways (i.e. parents read more to girls than boys, see Freeman, 2004), it is possible that gender differences in cognitive skills have

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changed too. Thus, when examining the results of the ECLS-B data showing cognitive

advantages among female infants and toddlers, one might speculate that a new trend of female advantage is emerging; girls are beginning to outpace boys on tests of cognitive skill. Consistent with this position, NAEP data suggests that gender gaps in math skill among middle and high school students are beginning to converge (Hyde and Linn, 2006;

Hyde, et al., 2008).

Significance tests for gender gaps in math skill were conducted comparing 1994,

1996, and 1999 with 2004 data. For reading scores, only the comparison of 1996 reading

scores with 2004 shows significant change, indicating a reduction in the gender reading

gap (results created using NAEP data explorer, see National Associated on Educational

Progress, http://nces.edu.gov/nationsreportcard/Ittnde). No NAEP gender gap data were

collected for years 1998 and 2006 so direct comparison to the ECLS data is not possible.

But while it is important to acknowledge potential period effects, other patterns

suggest that, at least for the time period studied here, this influence may be modest. An

imperfect yet reasonable way to consider the magnitude of period effects for gender gaps

in cognitive skills is to consider how much the gap changed during the same time period

for the nine-year olds in NAEP data. This comparison suggests no period effects for

math and a slight decline in the female advantage in reading between 1998 and 2006, the time period difference at stake between the ECLS-B and ECLS-K data. Of course, while these comparisons suggest a minimal period effect, they focus on nine-year olds and may not apply to the juncture point between the ECLS-B and ECLS-K data, which occurs

between the ages of four and five.

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Math (Fifth Grade-Spring) Reading (Fifth Grade-Spring) Figure 18. Gender Distribution in Math Figure 19. Gender Distribution in Reading 127

Table 11. Descriptives including gender comparisons, Kindergarten‐Fall. ECLS‐K 1998‐99. Female Male Variable Description Metric Mean S.D. Mean S.D. Mean S.D. P d Controls Age in Months (wave 1) (54‐79) 68.448 4.3063 68.158 4.1419 68.727 4.4405 *** ‐.13 First time kindergartener (0‐1) .045 .207 .035 .183 .055 .227 *** ‐.10

Cognitive Measures Math IRT Score (7‐107) 22.972 8.907 22.848 8.311 23.092 9.444 ‐.03 Subtests Count, Number, Shape (0‐1) .923 .173 .930 .163 .918 .182 *** .07 Relative Size (0‐1) .556 .345 .559 .340 .553 .350 .02 Ordinality, Sequence (0‐1) .203 .307 .198 .300 .208 .313 * ‐.03 Add/Subtract (0‐1) .037 .121 .032 .105 .042 .135 *** ‐.08 Multiply/Divide (0‐1) .002 .030 .001 .014 .004 .039 *** ‐.09 Place Value (0‐1) .000 .007 .000 .001 .000 .010 ‐.04 Rate and Measurement ‐‐‐‐‐‐‐ Fractions ‐‐‐‐‐‐‐ Area and Volume ‐‐‐‐‐‐‐ Reading IRT Score (15‐124) 29.633 10.100 30.325 10.001 28.968 10.151 *** .13 Subtests Letter Recognition (0‐1) .682 .327 .714 .317 .652 .333 *** .19 Beginning Sounds (0‐1) .309 .331 .340 .338 .279 .321 *** .18 Ending Sounds (0‐1) .173 .261 .192 .268 .155 .253 *** .14 Sight Words (0‐1) .033 .135 .035 .134 .032 .136 .02 Word in Context (0‐1) .015 .084 .015 .083 .015 .085 .01 Literal Inference (0‐1) .004 .038 .003 .036 .004 .039 ‐.01 Extrapolation (0‐1) .000 .009 .000 .010 .000 .009 .00 Evaluation ‐‐‐‐‐‐‐ Evaluation of Non‐fiction ‐‐‐‐‐‐‐ Other Measures Highest Reading Profeciency (0‐8) 1.189 1.145 1.286 1.149 1.097 1.133 *** .17 Highest Math Profeciency (0‐8) 1.767 .962 1.792 .922 1.741 1.000 ** .05 Appraches to Learning (1‐4) 3.115 .481 3.166 .469 3.065 .487 *** .21 Appraches to Learning (1‐4) 2.983 .673 3.121 .642 2.851 .677 *** .41

Child Characteristics Birthweight (1‐14) 7.3806 1.326 7.2416 1.288 7.5158 1.3483 *** ‐.21

Proximate Factors Frequency of child reading outside of school? (1‐4) 2.978 .913 3.186 .832 2.776 .941 *** .46 Educational expectations for child? (1‐6) 4.100 1.108 4.144 1.092 4.058 1.121 *** .08 How often does family member: Read Books (1‐4) 3.250 .785 3.287 .768 3.215 .800 *** .09 Tell Stories (1‐4) 2.742 .923 2.753 .911 2.732 .934 .02 Sing Songs (1‐4) 3.090 .939 3.217 .897 2.968 .963 *** .27 Do Arts and Crafts (1‐4) 2.665 .876 2.717 .884 2.615 .866 *** .12 Involve Child in Household Chores (1‐4) 3.255 .890 3.287 .863 3.225 .915 *** .07 Play Games/Puzzles (1‐4) 2.792 .831 2.769 .818 2.814 .843 ** ‐.05 Talk About Nature or Science Projects (1‐4) 2.209 .877 2.181 .861 2.236 .891 ** ‐.06 Build or Play Construction with Child (1‐4) 2.350 .921 2.151 .881 2.543 .918 *** ‐.43 Play a Sport or Excersice Together (1‐4) 2.659 .917 2.577 .918 2.737 .908 *** ‐.18 How many children's books in home? (0‐200) 74.345 59.870 75.834 60.034 72.907 59.680 ** .05 How Important is it that your child: Counts (1‐5) 3.672 .892 3.699 .884 3.646 .898 *** .06 Shares (1‐5) 4.260 .574 4.266 .579 4.255 .569 .02 Draws (1‐5) 3.918 .762 3.956 .751 3.882 .772 *** .10 Is Calm (1‐5) 4.050 .679 4.060 .679 4.041 .679 .03 Knows Letters (1‐5) 3.805 .826 3.841 .817 3.770 .833 .09 Communicates Well (1‐5) 4.276 .591 4.285 .587 4.268 .595 *** .03 How often does child look at a picture book outside of school? (1‐4) 3.298 .819 3.396 .782 3.203 .843 *** .24 How many records, tapes in home? (0‐200) 15.373 17.856 16.009 18.087 14.759 17.611 *** .07

Distal Factors Socio‐economic Status (1‐5) 3.0961 1.4128 3.1068 1.4105 3.0857 1.415 .01 Two Parent Home (0‐1) 0.5826 0.4931 0.5852 0.4927 0.5809 0.4934 .01 Sibling Size (0‐11) 1.4662 1.1853 1.4717 1.1948 1.4609 1.1761 .01 *P<.05 **P<.01 ***P<.001

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Table 12. Descriptives including gender comparisons, Kindergarten‐Spring. ECLS‐K 1998‐99. Female Male Variable Description Metric Mean S.D. Mean S.D. Mean S.D. P d Controls Age in Months (wave 2) (52‐102) 74.713 4.464 74.379 4.275 75.031 4.614 *** ‐.15

Cognitive Measures Math IRT Score (9‐105) 33.277 11.587 33.027 10.765 33.516 12.318 ** ‐.04 Subtests (0‐1) .989 .057 .991 .051 .988 .062 ** .04 Count, Number, Shape (0‐1) .851 .229 .856 .223 .847 .235 * .04 Relative Size (0‐1) .554 .385 .557 .383 .551 .388 .01 Ordinality, Sequence (0‐1) .169 .256 .161 .242 .177 .268 *** ‐.06 Add/Subtract (0‐1) .015 .077 .011 .054 .020 .093 *** ‐.13 Multiply/Divide (0‐1) .001 .016 .000 .006 .001 .022 *** ‐.09 Place Value ‐‐ ‐‐‐‐‐ Rate and Measurement ‐‐ ‐‐‐‐‐ Fractions ‐‐ ‐‐‐‐‐ Area and Volume ‐‐ ‐‐‐‐‐ Reading IRT Score (16‐138) 41.052 13.753 42.218 13.840 39.942 13.576 *** .17 Subtests Letter Recognition (0‐1) .932 .162 .946 .145 .918 .176 *** .17 Beginning Sounds (0‐1) .703 .319 .741 .299 .668 .334 *** .23 Ending Sounds (0‐1) .512 .341 .548 .332 .477 .345 *** .21 Sight Words (0‐1) .158 .266 .176 .277 .142 .254 *** .13 Word in Context (0‐1) .066 .161 .073 .168 .059 .153 *** .09 Literal Inference (0‐1) .014 .074 .015 .076 .013 .071 * .03 Extrapolation (0‐1) .002 .027 .002 .028 .002 .026 .01 Evaluation ‐‐ ‐‐‐‐‐ Evaluation of Non‐fiction ‐‐ ‐‐‐‐‐ Other Measures Highest Reading Profeciency (0‐8) 2.391 1.234 2.514 1.191 2.273 1.262 *** .20 Highest Math Profeciency (0‐7) 2.605 1.018 2.611 .968 2.600 1.065 .01 Appraches to Learning (1‐4) 3.126 .480 3.190 .469 3.065 .481 *** .26 Appraches to Learning (1‐4) 3.121 .683 3.264 .642 2.984 .694 *** .42

Proximate Factors Frequency of child reading outside of school? (1‐4) 2.998 1.003 3.209 .919 2.797 1.039 *** .42 Do you have a home computer that the child uses? (0‐1) .443 .497 .443 .497 .443 .497 .00 How often does child use the computer? (1‐4) 2.647 .777 2.594 .754 2.698 .795 *** ‐.13 Outside of School Participation Dance Lessons (0‐1) .825 .380 .676 .468 .968 .176 *** ‐.91 Athletic Activities (0‐1) .541 .498 .612 .487 .474 .499 *** .28 Clubs/Recreational Programs (0‐1) .866 .341 .811 .392 .918 .274 *** ‐.32 Music lessons (0‐1) .920 .271 .909 .288 .931 .253 *** ‐.08 Art Classes/Lessons (0‐1) .926 .261 .917 .276 .935 .246 *** ‐.07 Performing Arts Programs (0‐1) .857 .350 .800 .400 .911 .285 *** ‐.32 Contacted school regarding assignment/homework? (0‐1) .978 .145 .981 .138 .977 .151 .03 Gone with child to the zoo, aquarium, or petting farm? (0‐1) .601 .490 .592 .491 .609 .488 * ‐.04 Child visited a art gallery, museum, or historical site? (0‐1) .692 .462 .697 .459 .687 .464 .02 Child been to a play, concert, or other live shows? (0‐1) .620 .486 .597 .490 .641 .480 *** ‐.09 Distal Factors Two Parent Home (0‐1) .624 .484 .627 .484 .623 .485 .01 Sibling Size (0‐14) 1.485 1.185 1.489 1.194 1.481 1.177 .01 *P<.05 **P<.01 ***P<.001

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Table 13. Descriptives including gender comparisons, 1st Female Male Variable Description Metric Mean S.D. Mean S.D. Mean S.D. P d Controls Age in Months (wave 3) (64‐107) 79.996 4.497 79.682 4.217 80.302 4.736 *** ‐.14

Cognitive Measures Math IRT Score (9‐105) 39.994 13.761 39.726 12.740 40.256 14.687 ‐.04 Subtests Count, Number, Shape (0‐1) .995 .037 .996 .033 .994 .041 * .07 Relative Size (0‐1) .922 .172 .931 .154 .914 .188 *** .10 Ordinality, Sequence (0‐1) .735 .344 .743 .335 .726 .353 .05 Add/Subtract (0‐1) .318 .328 .309 .318 .326 .338 ‐.05 Multiply/Divide (0‐1) .046 .140 .038 .120 .053 .157 *** ‐.11 Place Value (0‐1) .003 .032 .002 .017 .005 .042 *** ‐.11 Rate and Measurement ‐ ‐‐‐‐‐‐ Fractions ‐ ‐‐‐‐‐‐ Area and Volume ‐ ‐‐‐‐‐‐ Reading IRT Score (17‐146) 47.911 17.733 49.405 17.937 46.452 17.411 *** .17 Subtests Letter Recognition (0‐1) .964 .123 .974 .107 .955 .136 *** .15 Beginning Sounds (0‐1) .824 .262 .853 .234 .797 .285 *** .22 Ending Sounds (0‐1) .667 .318 .700 .301 .634 .331 *** .21 Sight Words (0‐1) .285 .339 .315 .351 .255 .325 *** .18 Word in Context (0‐1) .134 .237 .149 .246 .119 .227 *** .13 Literal Inference (0‐1) .037 .125 .041 .130 .033 .120 * .06 Extrapolation (0‐1) .007 .054 .007 .055 .006 .053 .02 Evaluation (0‐1) .008 .029 .008 .031 .007 .028 .05 Evaluation of Non‐fiction ‐ ‐‐‐‐‐‐ Other Measures Highest Reading Profeciency (0‐9) 2.904 1.323 3.044 1.285 2.767 1.345 *** .21 Highest Math Profeciency (0‐6) 3.032 1.043 3.033 .989 3.031 1.093 .00

Proximate Factors Educational expectations for child? (1‐6) 3.661 1.084 3.706 1.090 3.617 1.077 ** .08 Tutoring Reading (0‐1) .229 .421 .268 .446 .200 .402 .16 Math (0‐1) .470 .501 .437 .499 .495 .503 ‐.12 Science (0‐1) .898 .304 .887 .318 .905 .294 ‐.06 Foriegn Language (0‐1) .880 .327 .901 .300 .863 .346 .12 Other (0‐1) .819 .386 .746 .438 .874 .334 * ‐.33 How long did family read to child in past week? (1‐4) 1.800 .823 1.802 .824 1.797 .822 .01 *P<.05 **P<.01 ***P<.001

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Table 14. Descriptives including gender comparisons, First Grade‐Spring. ECLS‐K 1998‐99. Female Male Variable Description Metric Mean S.D. Mean S.D. Mean S.D. P d Controls Age in Months (wave 4) (72‐96) 86.869 4.280 86.563 4.136 87.162 4.393 *** ‐.14

Cognitive Measures Math IRT Score (10‐121) 57.546 16.882 56.825 15.653 58.236 17.954 *** ‐.08 Subtests Count, Number, Shape (0‐1) .999 .015 .999 .014 .999 .015 .02 Relative Size (0‐1) .987 .068 .989 .061 .986 .073 ** .04 Ordinality, Sequence (0‐1) .947 .168 .952 .160 .943 .176 ** .05 Add/Subtract (0‐1) .714 .317 .716 .309 .712 .325 .01 Multiply/Divide (0‐1) .231 .295 .211 .275 .250 .311 *** ‐.13 Place Value (0‐1) .031 .113 .022 .089 .040 .131 *** ‐.16 Rate and Measurement (0‐1) .003 .019 .002 .014 .004 .023 *** ‐.11 Fractions ‐‐‐‐‐‐‐ Area and Volume ‐‐‐‐‐‐‐ Reading IRT Score (19‐163) 71.665 22.436 73.656 22.021 69.761 22.663 *** .17 Subtests Letter Recognition (0‐1) .996 .042 .997 .038 .995 .045 ** .05 Beginning Sounds (0‐1) .970 .112 .978 .096 .963 .126 *** .13 Ending Sounds (0‐1) .928 .170 .942 .148 .914 .188 *** .17 Sight Words (0‐1) .758 .320 .792 .297 .726 .338 *** .21 Word in Context (0‐1) .474 .326 .505 .321 .444 .329 *** .19 Literal Inference (0‐1) .168 .235 .183 .240 .155 .229 *** .12 Extrapolation (0‐1) .035 .121 .038 .122 .033 .120 ** .04 Evaluation (0‐1) .034 .062 .037 .061 .032 .063 *** .08 Evaluation of Non‐fiction ‐‐‐‐‐‐‐ Other Measures Highest Reading Profeciency (0‐9) 4.336 1.251 4.455 1.191 4.222 1.296 *** .19 Highest Math Profeciency (0‐7) 3.909 .968 3.879 .921 3.938 1.012 *** ‐.06

Proximate Appraches to learning (1‐4) 3.095 .492 3.155 .486 3.037 .490 *** .24 Appraches to learning (1‐4) 3.037 .707 3.187 .674 2.893 .708 *** .43 How often does child read to themselves outside of school? (1‐4) 3.132 .853 3.268 .804 3.002 .877 *** .32 How far in school do you expect your child to go? (1‐6) 3.997 1.100 4.051 1.072 3.945 1.124 *** .10 How often does family member: Read Books (1‐4) 3.152 .879 3.174 .879 3.130 .877 ** .05 Tell Stories (1‐4) 2.745 .883 2.762 .880 2.729 .885 * .04 Sing Songs (1‐4) 2.812 .982 2.944 .954 2.687 .992 *** .26 Do Arts and Crafts (1‐4) 2.297 .796 2.374 .800 2.224 .785 *** .19 Involve Child in Household Chores (1‐4) 3.250 .863 3.280 .840 3.221 .883 *** .07 Play Games/Puzzles (1‐4) 2.633 .799 2.597 .794 2.667 .803 *** ‐.09 Talk About Nature or Science Projects (1‐4) 2.187 .849 2.155 .832 2.218 .863 *** ‐.07 Build or Play Construction with Child (1‐4) 2.091 .878 1.907 .823 2.267 .894 *** ‐.42 Play a Sport or Excersice Together (1‐4) 2.668 .911 2.576 .913 2.756 .900 *** ‐.20 How many children's books in home, including library? (0‐5000) 102.558 147.062 105.659 142.641 99.598 151.110 * .04 Do you have a home computer that the child uses? (0‐1) .333 .471 .329 .470 .336 .472 ‐.01 In a typical week, how often does child use the computer? (1‐4) 2.606 .747 2.576 .740 2.635 .752 *** ‐.08 Outside of School Participation Dance Lessons (0‐1) .800 .400 .634 .482 .959 .197 *** ‐.96 Athletic Activities (0‐1) .431 .495 .509 .500 .358 .479 *** .31 Clubs/Recreational Programs (0‐1) .703 .457 .674 .469 .731 .444 *** ‐.12 Music lessons (0‐1) .885 .319 .860 .347 .909 .288 *** ‐.15 Art Classes/Lessons (0‐1) .889 .314 .870 .336 .907 .290 *** ‐.12 Organized performing Arts Programs (0‐1) .808 .394 .738 .440 .875 .330 *** ‐.36 Contacted school regarding assignment/homework (0‐1) .961 .192 .958 .200 .964 .185 ‐.03 Tutoring Reading (0‐1) .193 .395 .199 .400 .188 .391 .03 Math (0‐1) .732 .443 .702 .458 .756 .430 * ‐.12 Science (0‐1) .967 .178 .970 .169 .964 .185 .03 Foriegn Language (0‐1) .942 .234 .927 .260 .954 .209 * ‐.11 Other (0‐1) .912 .284 .935 .247 .892 .310 ** .15 How long did family member read to child average for past week (1‐60) 22.500 11.193 22.805 11.359 22.209 11.026 ** .05 Compared to other kids in child's class, how is he/she in reading/language arts? (1‐5) 3.971 1.048 4.071 1.019 3.876 1.068 *** .19 Compared to other kids in child's class, how is he/she in math? (1‐5) 3.964 .955 3.927 .959 4.000 .950 *** ‐.08 How often does a family member help child with reading, writing or working with numbers? (1‐4) 3.381 .723 3.418 .709 3.346 .735 *** .10 Respondent has library card. (0‐1) .248 .432 .242 .428 .254 .435 ‐.03 Child has own library card. (0‐1) .479 .500 .462 .499 .495 .500 *** ‐.07 In the past month, has anyone in family visited the library with child? (0‐1) .533 .499 .523 .500 .543 .498 * ‐.04 In the past year, has anyone in family visited the library with child? (0‐1) .360 .480 .357 .479 .362 .481 ‐.01 How often does child use the computer for educational purposes? (1‐4) 2.339 .775 2.353 .772 2.325 .777 .04 In child tutored on a regular basis other than by someone in family on subject such as reading, math, science, or foreign language? (0‐1) .884 .321 .892 .310 .876 .330 ** .05 How often does child do homework at home? (1‐5) 4.009 1.007 4.028 1.004 3.991 1.010 * .04 During the school year how often do you help child with homework? (1‐5) 3.817 1.029 3.807 1.044 3.826 1.014 ‐.02

Distal Socio‐economic Status (1‐5) 3.159 1.413 3.156 1.405 3.162 1.422 .00 Two Parent Home (0‐1) .592 .491 .592 .491 .593 .491 .00 Sibling Size (0‐11) 1.522 1.165 1.523 1.178 1.521 1.152 .00 *P<.05 **P<.01 ***P<.001 131

Table 15. Descriptives including gender comparisons, Third Grade‐Spring. ECLS‐K 1998‐99. Female Male Variable Description Metric Mean S.D. Mean S.D. Mean S.D. P d Controls Age in Months (wave 5) (1‐6) 3.494 1.410 3.397 1.380 3.588 1.433 *** ‐.14

Cognitive Measures Math IRT Score (32‐147) 92.107 21.550 90.321 20.738 93.848 22.177 *** ‐.16 Subtests Count, Number, Shape ‐‐‐‐‐‐‐ Relative Size ‐‐‐‐‐‐‐ Ordinality, Sequence ‐‐‐‐‐‐‐ Add/Subtract (0‐1) .972 .085 .972 .083 .972 .088 .00 Multiply/Divide (0‐1) .775 .307 .762 .307 .788 .306 *** ‐.09 Place Value (0‐1) .432 .395 .395 .385 .467 .402 *** ‐.18 Rate and Measurement (0‐1) .136 .235 .112 .209 .159 .257 *** ‐.20 Fractions (0‐1) .008 .063 .005 .045 .012 .077 *** ‐.11 Area and Volume Reading IRT Score (46‐179) 118.078 25.152 120.218 24.340 115.984 25.752 *** .17 Subtests Letter Recognition ‐‐‐‐‐‐‐ Beginning Sounds ‐‐‐‐‐‐‐ Ending Sounds ‐‐‐‐‐‐‐ Sight Words (0‐1) .988 .060 .992 .049 .985 .070 *** .11 Word in Context (0‐1) .913 .155 .926 .135 .901 .171 *** .17 Literal Inference (0‐1) .700 .288 .725 .274 .677 .299 *** .17 Extrapolation (0‐1) .441 .378 .469 .378 .414 .375 *** .15 Evaluation (0‐1) .251 .207 .265 .209 .236 .205 *** .14 Evaluation of Non‐fiction (0‐1) .009 .048 .009 .045 .009 .051 .00 Other Measures Highest Reading Profeciency (1‐9) 6.397 1.271 6.510 1.239 6.287 1.292 *** .18 Highest Math Profeciency (1‐9) 5.355 1.126 5.232 1.057 5.475 1.177 *** ‐.22 *P<.05 **P<.01 ***P<.001 Continued

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Table 15. Continued. Female Male Variable Description Metric Mean S.D. Mean S.D. Mean S.D. P d

Proximate Appraches to learning (1‐4) 3.058 .681 3.220 .639 2.897 .684 *** .49 How often does child read to themselves outside of school? (1‐4) 3.226 .829 3.344 .768 3.113 .868 *** .28 How far in school do you expect your child to go? (1‐6) 4.045 1.056 4.107 1.024 3.986 1.083 *** .12 How often does family member: Read Books (1‐4) 2.498 1.082 2.511 1.096 2.486 1.068 .02 Tell Stories (1‐4) 2.582 .895 2.600 .888 2.564 .902 * .04 Sing Songs (1‐4) 2.729 1.036 2.880 1.006 2.586 1.044 *** .29 Do Arts and Crafts (1‐4) 2.225 .805 2.306 .792 2.148 .809 *** .20 Involve Child in Household Chores (1‐4) 3.393 .811 3.413 .791 3.374 .829 ** .05 Play Games/Puzzles (1‐4) 2.559 .802 2.527 .789 2.588 .813 *** ‐.08 Talk About Nature or Science Projects (1‐4) 2.193 .822 2.155 .803 2.229 .839 *** ‐.09 Build or Play Construction with Child (1‐4) 1.943 .870 1.754 .796 2.123 .900 *** ‐.44 Play a Sport or Excersice Together (1‐4) 2.670 .921 2.576 .920 2.759 .912 *** ‐.20 How many children's books in home, including library? (0‐5000) 123.160 183.634 129.248 196.113 117.367 170.730 *** .06 Do you have a home computer that the child uses? (0‐1) .200 .400 .199 .399 .202 .402 ‐.01 In a typical week, how often does child use the computer? (1‐4) 2.691 .756 2.675 .749 2.706 .763 * ‐.04 Outside of School Participation Dance Lessons (0‐1) .864 .342 .761 .426 .962 .190 *** ‐.65 Athletic Activities (0‐1) .394 .489 .470 .499 .322 .467 *** .31 Clubs/Recreational Programs (0‐1) .666 .472 .632 .482 .699 .459 *** ‐.14 Music lessons (0‐1) .799 .401 .758 .429 .838 .369 *** ‐.20 Art Classes/Lessons (0‐1) .881 .324 .857 .350 .903 .296 *** ‐.14 Organized performing Arts Programs (0‐1) .762 .426 .686 .464 .834 .372 *** ‐.35 Has anyone in the past month gone with child to the zoo, aquarium, or petting farm? (0‐1) .691 .462 .682 .466 .699 .459 * ‐.04 In the past month, has the child visited a art gallery, museum, or historical site? (0‐1) .669 .471 .668 .471 .670 .470 .00 In the past month, has the child gone to a play, concert, or other live shows? (0‐1) .608 .488 .577 .494 .638 .481 *** ‐.13 Contacted school regarding assignment/homework (0‐1) .840 .367 .844 .363 .837 .370 .02 Tutoring Reading (0‐1) .258 .438 .288 .453 .233 .423 ** .13 Math (0‐1) .470 .499 .408 .492 .523 .500 *** ‐.23 Science (0‐1) .914 .280 .919 .272 .909 .287 .04 Foriegn Language (0‐1) .964 .186 .956 .205 .971 .167 ‐.08 Other (0‐1) .965 .184 .963 .188 .966 .181 ‐.01 How long did family member read to child average for past week (1‐60) 25.064 11.685 25.255 11.978 24.885 11.402 .03 Compared to other kids in child's class, how is he/she in reading/language arts? (1‐5) 3.913 1.044 3.986 1.021 3.842 1.060 *** .14 Compared to other kids in child's class, how is he/she in math? (1‐5) 3.877 1.013 3.800 1.016 3.950 1.004 *** ‐.15 How often does a family member help child with reading, writing or working with numbers? (1‐4) 3.292 .806 3.318 .801 3.267 .810 *** .06 Respondent has library card. (0‐1) .178 .383 .174 .379 .183 .386 ‐.02 Child has own library card. (0‐1) .264 .441 .248 .432 .280 .449 *** ‐.07 In the past month, has anyone in family visited the library with child? (0‐1) .441 .497 .422 .494 .459 .498 *** ‐.08 In the past year, has anyone in family visited the library with child? (0‐1) .249 .433 .235 .424 .262 .440 * ‐.06 How often does child use the computer for educational purposes? (1‐4) 2.187 .763 2.228 .749 2.148 .774 *** .10 In child tutored on a regular basis other than by someone in family on subject such as reading, math, science, or foreign language? (0‐1) .865 .342 .873 .333 .857 .350 ** .05 Do you have internet access at home? (0‐1) .134 .341 .140 .347 .129 .335 .03 Does child use computer to get access to the internet? (0‐1) .318 .466 .318 .466 .317 .465 .00 How often does child do homework at home? (1‐5) 4.309 .819 4.339 .795 4.281 .840 *** .07 How often do you read newspapers/magizines? (1‐4) 3.163 .854 3.146 .859 3.179 .849 * ‐.04 How often do you read books? (1‐4) 2.830 1.005 2.824 1.009 2.835 1.002 ‐.01 How often do you read letters/notes/e‐mails? (1‐4) 3.120 1.043 3.122 1.040 3.118 1.045 .00 How often do you read the internet or web pages? (1‐4) 2.447 1.208 2.426 1.203 2.466 1.211 ‐.03 Is there a place set aside for your child to do homework? (0‐1) .083 .276 .091 .287 .075 .264 ** .06 How long is set aside for child to do homework (1‐180) 49.731 34.434 50.059 34.512 49.418 34.358 .02 In the past month, has the child attended a sporting event in which he/she was not a player? (0‐1) .506 .500 .532 .499 .481 .500 *** .10 Family recieves newspaper(s) on a regular basis (0‐1) .383 .486 .384 .486 .382 .486 .00 Family recieves magazine on a regular basis (0‐1) .246 .431 .250 .433 .242 .428 .02 Family has dictionary or an encyclopedia (0‐1) .043 .203 .043 .202 .043 .204 .00 Family has pocket calculator (0‐1) .038 .191 .036 .185 .040 .197 ‐.03

Distal Socio‐economic Status (0‐5) 3.217 1.411 3.219 1.405 3.214 1.417 .00 Two Parent Home (0‐1) .503 .500 .504 .500 .504 .500 .00 Sibling Size (0‐11) 1.564 1.152 1.564 1.157 1.565 1.147 .00 *P<.05 **P<.01 ***P<.001

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Table 16. Descriptives including gender comparisons, Fifth Grade‐Spring. ECLS‐K 1998‐99. Female Male Variable Description Metric Mean S.D. Mean S.D. Mean S.D. P d Controls Age in Months (wave 5) (1‐5) 2.943 .805 2.886 .786 3.000 .818 *** ‐.14

Cognitive Measures Math IRT Score (47‐151) 113.934 21.330 111.844 21.156 115.994 21.302 *** ‐.20 Subtests Count, Number, Shape ‐‐‐‐‐‐‐ Relative Size ‐‐‐‐‐‐‐ Ordinality, Sequence ‐‐‐‐‐‐‐ Add/Subtract ‐‐‐‐‐‐‐ Multiply/Divide (0‐1) .935 .174 .929 .178 .941 .169 *** ‐.07 Place Value (0‐1) .768 .347 .742 .358 .794 .334 *** ‐.15 Rate and Measurement (0‐1) .467 .389 .426 .383 .507 .391 *** ‐.21 Fractions (0‐1) .140 .293 .109 .258 .171 .321 *** ‐.21 Area and Volume (0‐1) .019 .073 .014 .060 .025 .083 *** ‐.15 Reading IRT Score (58‐181) 139.408 23.182 140.966 22.089 137.871 24.117 *** .13 Subtests Letter Recognition ‐‐‐‐‐‐‐ Beginning Sounds ‐‐‐‐‐‐‐ Ending Sounds ‐‐‐‐‐‐‐ Sight Words ‐‐‐‐‐‐‐ Word in Context (0‐1) .974 .068 .979 .055 .969 .078 *** .14 Literal Inference (0‐1) .880 .188 .894 .169 .866 .204 *** .15 Extrapolation (0‐1) .733 .333 .756 .318 .711 .345 *** .13 Evaluation (0‐1) .464 .266 .479 .261 .449 .270 *** .11 Evaluation of Non‐fiction (0‐1) .077 .186 .079 .188 .074 .184 .03 Other Measures Highest Reading Profeciency (1‐9) 7.131 1.091 7.224 1.059 7.038 1.114 *** .17 Highest Math Profeciency (2‐9) 6.305 1.147 6.150 1.121 6.458 1.152 *** ‐.27

Proximate Appraches to learning (1‐4) 3.067 .677 3.251 .624 2.887 .679 *** .56 How far in school do you expect your child to go? (1‐6) 4.029 1.052 4.112 1.034 3.949 1.064 *** .15 How often does child read to themselves outside of school? (0‐5000) 106.497 172.419 109.188 171.956 103.885 172.843 .03 How far in school do you expect your child to go? (0‐1) .153 .360 .150 .357 .155 .362 ‐.01 How often does family member: (1‐4) 2.852 .822 2.882 .811 2.823 .831 *** .07 Athletic Activities (0‐1) .353 .478 .417 .493 .291 .454 *** .27 Clubs/Recreational Programs (0‐1) .710 .454 .681 .466 .738 .440 *** ‐.13 Music lessons (0‐1) .697 .460 .649 .477 .743 .437 *** ‐.20 Art Classes/Lessons (0‐1) .889 .314 .869 .337 .909 .288 *** ‐.13 Organized performing Arts Programs (0‐1) .760 .427 .672 .469 .845 .362 *** ‐.41 Contacted school regarding assignment/homework (0‐1) .823 .382 .839 .368 .808 .394 *** .08 Child has own library card. (0‐1) .190 .392 .171 .376 .208 .406 *** ‐.10 In the past month, has anyone in family visited the library with child? (0‐1) .497 .500 .474 .499 .519 .500 *** ‐.09 In the past year, has anyone in family visited the library with child? (0‐1) .256 .436 .232 .422 .277 .448 *** ‐.11 How often does child use the computer for educational purposes? (0‐4) 2.204 .739 2.265 .725 2.145 .747 *** .16 How often does child do homework at home? (1‐5) 4.383 .799 4.428 .764 4.339 .830 *** .11 Do you have internet access at home? (0‐1) .107 .310 .111 .314 .104 .305 .02 Does child use computer to get access to the internet? (0‐1) .130 .336 .131 .337 .129 .335 .01 Is there a place set aside for your child to do homework? (0‐1) .088 .283 .093 .290 .083 .276 .03 How long is set aside for child to do homework (0‐240) 37.255 41.514 37.461 42.141 37.055 40.895 .01

Distal Socio‐economic Status (0‐5) 3.192 1.409 3.181 1.404 3.203 1.414 ‐.02 Two Parent Home (0‐1) .410 .492 .412 .492 .408 .491 .01 Sibling Size (0‐12) 1.570 1.166 1.573 1.196 1.567 1.137 .00 *P<.05 **P<.01 ***P<.001

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Table 17. Proficiency levels.

Reading proficiency levels

Level 1 Letter recognition: identifying upper- and lower-case letters by name Level 2 Beginning sounds: associating letters with sounds at the beginning of words Level 3 Ending sounds: associating letters with sounds at the end of words Level 4 Sight words: recognizing common words by sight Level 5 Comprehension of words in context: reading words in context Level 6 Literal inference: making inferences using cues that are directly stated with key words in text (for example, recognizing the comparison being made in a simile) Level 7 Extrapolation: identifying clues used to make inferences, and using background knowledge combined with cues in a sentence to understand use of homonyms Level 8 Evaluation: demonstrating understanding of author’s craft (how does the author let you know…), and making connections between a problem in the narrative and similar life problems Level 9 Evaluating nonfiction: critically evaluating, comparing and contrasting, and understanding the effect of features of expository and biographical texts.

Mathematics proficiency levels

Level 1 Number and shape: identifying some one-digit numerals, recognizing geometric shapes, and one-to- one counting of up to 10 objects. Level 2 Relative size: reading all single-digit numerals, counting beyond 10, recognizing a sequence of patterns, and using nonstandard units of length to compare objects. Level 3 Ordinality, sequence: reading two-digit numerals, recognizing the next number in a sequence, identifying the ordinal position of an object, and solving a simple word problem. Level 4 Addition/subtraction: solving simple addition and subtraction problems. Level 5 Multiplication/division: solving simple multiplication and division problems and recognizing more complex number patterns. Level 6 Place value: demonstrating understanding of place value in integers to the hundreds place. Level 7 Rate and measurement: using knowledge of measurement and rate to solve word problems. Level 8 Fractions: demonstrating understanding of the concept of fractional parts. Level 9 Area and volume: solving word problems involving area and volume, including change of units of measurement.

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