Peer Effects and Policy: The Relationship between Classroom Gender Composition and Student Achievement in Early Elementary School

Michael A. Gottfried; Jennifer Graves

doi:10.1515/bejeap-2013-0123

Published by De Gruyter February 1, 2014

Peer Effects and Policy: The Relationship between Classroom Gender Composition and Student Achievement in Early Elementary School

Michael A. Gottfried and Jennifer Graves

From the journal The B.E. Journal of Economic Analysis & Policy

https://doi.org/10.1515/bejeap-2013-0123

Showing a limited preview of this publication:

Abstract

The existence of gender peer effects has been well-documented, yet regarding estimates that are best-suited for policy formation, the literature finds somewhat mixed results. This article builds on the gender peer effects literature in a number of ways. First, we focus on early elementary school students, for which fewer studies exist. We also test whether effects in early elementary grades are subject-specific. Contrary to findings for older grade levels, we find that estimates by gender are subject-specific for the early elementary grades. Second, previous studies using similar estimation have focused on very different geographical areas, while this study makes use of nationally representative elementary school data for the United States. Third, we explore whether effects vary across grades, for which the existing literature finds mixed results. We find that the negative subject-specific effects of having a higher proportion of boys in the classroom increases in magnitude across grades, with insignificant effects in kindergarten, negative and significant by first grade, and larger negative and significant effects by third grade. Our findings suggest that a more balanced gender mix in the classroom is optimal for both reading and math comprehension for both boys and girls. However, regarding math performance, there is also suggestive evidence that a 100% separation of genders could improve girls’ math performance without consequences for boys’ math performance, motivating further research into single-gender subject-specific instruction.

Keywords: educational economics; peer effects; gender

JEL Classification: I20; I21; J16

Appendix

Table 1

Differences in the percentage of boys in the classroom across student, classroom, teacher and school characteristics

	Percent of boys in the classroom when the characteristic in the row heading is “true”			Percent of boys in the classroom when the characteristics in the row heading is “false”
	N	Mean	SD	N	Mean	SD
Binary characteristics (true or false)
Student
Black	3,808	0.51	0.10	25,176	0.51	0.10
Hispanic	3,250	0.51	0.10	25,734	0.51	0.10
Asian	1,285	0.50	0.09	27,699	0.51	0.10
Has a disability	5,182	0.51	0.10	23,802	0.51	0.10
At or below poverty threshold	4,401	0.51	0.10	24,583	0.51	0.10
English is primary language at home	27,111	0.51	0.10	1,873	0.51	0.10
Classroom, Teacher, or School
Class is less than 21 students	10,863	0.51	0.12	18,154	0.50	0.09
Teacher is male	813	0.52	0.10	28,204	0.51	0.10
Teacher experience less than 13 years	16,141	0.51	0.10	12,876	0.51	0.10
Teacher is white	26,094	0.51	0.10	2,923	0.50	0.10
School less than 149 students	1,556	0.49	0.13	27,461	0.51	0.10
School less than 10 percent minority	10,931	0.50	0.10	18,086	0.51	0.10
School is private	6,344	0.49	0.11	22,673	0.51	0.10

Table 2

Table 5, no private schools in sample

	Boys				Girls
	Reading score	Reading percentile	Math score	Math percentile	Reading score	Reading percentile	Math score	Math percentile
30–40%	−2.82**	0.18	−1.91*	−0.16	0.82	0.81	−1.18	−1.02
	(1.4)	(0.72)	(1.08)	(0.7)	(1.73)	(0.83)	(1.33)	(0.8)
40–50%	−3.09**	0.13	−1.9*	−0.03	0.43	0.72	−2.09	−1.44*
	(1.36)	(0.7)	(1.04)	(0.68)	(1.66)	(0.79)	(1.28)	(0.78)
50–60%	−3.88***	−0.26	−2.04**	−0.07	0.35	0.87	−2.16*	1.2
	(1.36)	(0.7)	(1.04)	(0.68)	(1.66)	(0.8)	(1.28)	(0.78)
60–70%	−3.98***	−0.58	−1.64	0.22	0.7	1.06	−2.51**	−1.5*
	(1.43)	(0.75)	(1.1)	(0.72)	(1.69)	(0.81)	(1.3)	(0.8)
70–80%	−4.52**	−1.34	−2.13	−0.55	−1.38	−0.01	−3.87***	−1.76*
	(1.82)	(0.95)	(1.37)	(0.91)	(1.96)	(0.96)	(1.48)	(0.93)
n	11,397	11,397	11,397	11,397	11,149	11,149	11,149	11,149
R²	0.84	0.85	0.85	0.86	0.86	0.86	0.85	0.86

^[1]

Table 3

Table 5, sample excludes all schools with at least one classroom with a percent boys in the class less than 20% or greater than 80%

	Boys				Girls
	Reading score	Reading percentile	Math score	Math percentile	Reading score	Reading percentile	Math score	Math percentile
30–40%	−1.74	0.35	−2.02**	−0.36	−0.48	0.84	−1.16	0.11
	(1.26)	(0.64)	(0.92)	(0.59)	(1.45)	(0.72)	(1.16)	(0.77)
40–50%	−2.2*	0.18	−2.03**	−0.33	−0.33	0.65	−1.73	−0.52
	(1.23)	(0.62)	(0.89)	(0.57)	(1.43)	(0.7)	(1.15)	(0.75)
50–60%	−2.68**	−0.06	−1.87**	−0.19	−0.59	0.7	−1.82	−0.3
	(1.24)	(0.63)	(0.89)	(0.58)	(1.43)	(0.7)	(1.15)	(0.75)
60–70%	−3.42***	−0.43	−1.89**	−0.01	−0.37	0.89	−1.98*	−0.5
	(1.31)	(0.67)	(0.95)	(0.62)	(1.46)	(0.72)	(1.17)	(0.77)
70–80%	−4.5***	−1.18	−2.88**	−0.98	−2.62*	−0.22	−3.4**	−0.81
	(1.74)	(0.88)	(1.28)	(0.85)	(1.71)	(0.85)	(1.34)	(0.88)
n	14,291	14,291	14,291	14,291	14,216	14,216	14,216	14,216
R²	0.85	0.85	0.86	0.86	0.86	0.86	0.85	0.86

^[2]

Table 4

Classroom gender composition, sample broken out by gender, quadratic and cubic terms

Sample restricted to students in classrooms with greater than 20% boys and less than 80% boys
	Reading score		Reading percentile		Math score		Math percentile
Sample: Boys
Percent of class, boys	−10.78	−18.86	4.14	18.51	−10.02	−81.1*	−0.66	−33.85
	(13.19)	(56.19)	(6.94)	(28.26)	(10.28)	(43.88)	(6.5)	(26.61)
Percent of class, boys²	4.99	21.92	−6.48	−36.58	8.73	157.6*	0.67	70.18
	(13.02)	(113.88)	(6.91)	(57.73)	(10.21)	(89.33)	(6.5)	(54.7)
Percent of class, boys³	−11.34	20.17	−99.75*	−46.58
Percent of class, boys³	(75.02)		(38.34)		(58.96)		(36.51)
Calculated Marginal Effect of Boys	−5.79	−5.45	−2.34	−2.94	−1.29	1.69	0.01	1.40
Wald test on joint significance (p-value)	0.01	0.03	0.06	0.13	0.48	0.23	0.99	0.65
n	14,398	14,398	14,398	14,398	14,398	14,398	14,398	14,398
R²	0.85	0.85	0.85	0.85	0.86	0.86	0.86	0.86
Sample: Girls
Percent of class, boys	24.57*	−58.17	9.17	−36.41	2.15	−96.16*	−1.65	−62.41*
	(13.83)	(69.85)	(6.9)	(33.22)	(10.93)	(53.17)	(6.81)	(32.59)
Percent of class, boys²	−25.44*	141.85	−8.95	83.22	−5.8	192.99*	0.38	123.22*
	(13.32)	(138)	(6.67)	(66.15)	(10.48)	(104.38)	(6.57)	(65.1)
Percent of class, boys³	−108.9	−59.99	−129.4*	−79.96*
	(88.71)		(42.86)		(66.73)		(42.31)
Calculated marginal effect of Boys	−0.87	2.00	0.22	1.82	−3.65	−0.22	−1.27	0.84
Wald test on joint significance (p-value)	0.12	0.11	0.41	0.28	0.03	0.01	0.42	0.14
n	14,284	14,284	14,284	14,284	14,284	14,284	14,284	14,284
R²	0.86	0.86	0.86	0.86	0.85	0.85	0.86	0.86

^[3]

Table 5

Table 5, sample broken out by gender, grade level percent boys as an instrument for classroom percent boys

Sample restricted to students in classrooms with greater than 20% boys and less than 80% boys, wave 2 only
	Reading score	Reading percentile	Math score	Math percentile
Sample: Boys
Percent of class, boys	−5.44*	−11.02***	−1.83	−4.00
	(2.90)	(3.35)	(2.72)	(3.17)
First stage for percent boys in the class
Grade-level pct boys	0.31***	0.31***	0.31***	0.31***
	(0.01)	(0.01)	(0.01)	(0.01)
First stage diagnostics
F-stat	830.67	830.67	829.84	829.84
Partial R²	0.14	0.14	0.14	0.14
n	5,140	5,140	5,140	5,140
Sample: Girls
Percent of class, boys	−2.55	−1.80	−1.86	−1.43
	(3.21)	(3.29)	(2.60)	(3.18)
First stage for percent boys in the class
Grade-level pct boys	0.31***	0.31***	0.31***	0.31***
	(0.01)	(0.01)	(0.01)	(0.01)
First stage diagnostics
F-stat	746.06	746.06	745.97	745.97
Partial R²	0.13	0.13	0.13	0.13
n	5,040	5,040	5,040	5,040

^[4]

Table 6

Corresponding estimates from Table 6, using the full sample, omitted category is 20–40% boys in the class

	Boys				Girls
	Reading score	Reading percentile	Math score	Math percentile	Reading score	Reading percentile	Math score	Math percentile
0–20%	−1.83	−3.92	1.56	−2.34	1.92	5.61**	3.55**	3.12***
	(3.45)	(2.63)	(2.35)	(1.72)	(6.90)	(2.70)	(1.47)	(0.95)
40–60%	−0.85*	−0.21	−0.22	0.07	0.02	−0.04	−0.71	−0.48*
	(0.51)	(0.27)	(0.40)	(0.25)	(0.57)	(0.28)	(0.45)	(0.28)
60–80%	−1.80***	−0.78**	−0.24	0.22	−0.02	0.07	−1.06**	−0.64*
	(0.68)	(0.37)	(0.53)	(0.33)	(0.68)	(0.34)	(0.53)	(0.33)
80–100%	−4.35*	−2.27	1.32	1.32	0.20	−2.05	−1.13	−1.95*
	(2.62)	(1.85)	(1.68)	(1.68)	(2.17)	(1.42)	(1.27)	(1.05)
n	14,458	14,458	14,458	14,458	14,374	14,374	14,374	14,374
R²	0.85	0.85	0.86	0.86	0.86	0.86	0.85	0.86

^[5]

Table 7

Classroom gender composition, sub-samples by gender and fall kindergarten test score performance

Sample restricted to students in classrooms with greater than 20% boys and less than 80% boys
	Reading score	Reading percentile	Math score	Math percentile
Sub-sample: Boys in top 50th percentile average Fall K scores
Percent boys in classroom	−6.30**	−1.50	−0.32	0.55
	(3.06)	(1.51)	(2.46)	(1.39)
n	6,850	6,850	6,850	6,850
R²	0.88	0.87	0.89	0.88
Sub-sample: Boys in bottom 50th percentile average Fall K scores
Percent boys in classroom	−4.66*	−2.73**	−2.09	−0.36
	(2.50)	(1.37)	(1.91)	(1.26)
n	7,548	7,548	7,548	7,548
R²	0.86	0.88	0.86	0.88
Sub-sample: Girls in top 50th percentile average Fall K scores
Percent boys in classroom	3.28	2.22*	−2.74	−0.84
	(2.71)	(1.26)	(2.04)	(1.15)
n	7,507	7,507	7,507	7,507
R²	0.88	0.88	0.88	0.88
Sub-sample: Girls in bottom 50th percentile average Fall K scores
Percent boys in classroom	−3.05	−1.54	−3.59*	−0.66
	(2.51)	(1.34)	(1.92)	(1.35)
n	6,777	6,777	6,777	6,777
R²	0.88	0.88	0.86	0.88

^[6]

Table 8

Classroom gender composition interacted with an indicator for top 50th percentile in average Fall K scores

Sample restricted to students in classrooms with greater than 20% boys and less than 80% boys
	Reading score	Reading percentile	Math score	Math percentile
Sub-sample: Boys
Percent boys in the classroom	−3.04	−2.75**	0.65	−0.07
	(2.35)	(1.31)	(1.87)	(1.24)
Student scored in top 50th percentile on Fall K scores	9.98***	4.68***	5.91***	3.31***
	(1.66)	(0.88)	(1.35)	(0.86)
(Percent boys) × (Student top 50th percentile)	−5.76*	1.59	−4.28*	0.53
	(3.16)	(1.71)	(2.56)	(1.67)
Linear combinations of effects:
Total effect of percent of boys for students in top 50th percentile^a	−8.80***	−1.16	−3.63*	0.46
	(2.71)	(1.38)	(2.19)	(1.31)
n	14,398	14,398	14,398	14,398
R²	0.87	0.87	0.87	0.87
Sub-sample: Girls
Percent boys in the classroom	−2.73	−1.54	−3.98**	−2.18*
	(2.39)	(1.26)	(1.90)	(1.29)
Student scored in top 50th percentile on Fall K scores	5.08***	3.09***	3.49***	2.25***
	(1.65)	(0.84)	(1.33)	(0.86)
(Percent boys) × (Student top 50th percentile)	2.88	3.48**	0.53	2.03
	(3.10)	(1.57)	(2.47)	(1.61)
Linear combinations of effects:
Total effect of percent of boys for students in top 50th percentile^a	0.15	1.94	−3.45*	−0.15
	(2.55)	(1.22)	(1.96)	(1.19)
n	14,284	14,284	14,284	14,284
R²	0.88	0.88	0.88	0.88

^[7]

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1
For example, Figlio (2007) studies the effects of having classmates with behavioral issues, Cho (2012) studies effects of having English Language Learner classmates and Gottfried (2011, 2012) studies the effect of having truant or tardy classmates.
2
Separately examined nonlinear effects by gender can also inform a larger literature on gender gaps in academic achievement. For instance, there have been long-standing concerns over female students’ achievement on math and science (Lindberg et al. 2010; Mullis, Martin, and Foy 2008), and more recent concerns over lagging reading performance and lower college attendance rates for males (Sax and Harper 2007).
3
Hoxby (2000) and Lavy and Schlosser (2007) find that more females in the classroom positively impact both genders in both math and reading. Whitmore (2005), also studying younger elementary school students, as we do here, finds different effects by gender. However, she uses the average percentile rank in both math and reading and does not explore the possibility of subject-specific effects.
4
For good reviews of the literature see USDOE (2005) and Morse (1998).
5
In the ECLS-K data, information was first collected from kindergartners (as well as parents, teachers and school administrators) from approximately 1,000 kindergarten programs in both the fall and spring of the 1998–1999 school year. This is a panel study where the initial sample has currently been followed up through grade 8, with data follow-up collection on the full sample in the spring of grades 1, 3, 5 and 8. There is very little turnover between the kindergarten and first-grade waves, with a somewhat higher rate of turnover between the first- and third-grade waves (Fletcher 2010; Cho 2012).
6
The IRT scale scores represent estimates of the number of items students would have answered correctly if they had answered all possible questions on the standardized tests in both reading and math.
7
We also drew multiple iterations of a random sample of students from both boy and girl samples in order to conduct a test of mean differences with a smaller sample. The t-statistics based on this random sampling algorithm are not significant – there are no remaining differences between the gender samples for the descriptive statistics reported in Table 1.
8
This descriptive evidence can be found in Appendix Table 1.
9
These variables include a private school indicator, enrollment size and percent minority at the school level. A total of 32 schools switch between public and private school status (1% of all schools), 593 schools experience a change in enrollment size (20% of all schools) and 523 schools experience a change in minority percentage (17% of all schools) in the sample across waves. The inclusion or exclusion of these measures from regressions using school-fixed effects does not greatly alter estimated effects or any conclusions from results.
10
In addition to the model presented in the tables, we also tested the robustness of our estimation strategy with the following ancillary models: (1) 1-wave lagged measure of testing ability instead of a fall kindergarten baseline measure; (2) Interaction between 1-wave lagged measure and dummy variable for survey wave; and (3) Interaction between kindergarten baseline achievement score and dummy variable for survey wave. The results from these analyses do not differ from those presented in the article. They are available upon request.
11
To account for repeat observations on the same individuals, we have also estimated the same specifications (clustered at the classroom level) presented in this article, when alternatively clustered at the individual level. Significance of results is not changed much by doing so. Additionally, in some specifications, estimation is done separately by wave, with findings supportive of result from the pooled sample.
12
For example, the Wald test rejects that the coefficients for percent boys in the classroom between 30% and 40% and between 60% and 70% are equal with an F-statistic of 5.08 and p-value of 0.0242.
13
The marginal effects of the percent boys in the classroom are reported in Appendix Table 4, along with the p-value from a Wald test for the joint significance of the main effect of the percent boys, the quadratic and cubic terms. The marginal effects are consistent with the main effects of the article in terms of general magnitude, and the p-values from the Wald tests show joint significance for the effect of a higher percent boys in the classroom on boys reading performance and girls math performance.
14
While not reported here, estimates are nearly identical when different ways of controlling for student ability are used. See footnote 10.
15
In addition to estimation with interactions that use a student performing above the 50th percentile in average fall kindergarten test score performance, we also ran estimation with alternative ways of categorizing prior student ability. We ran regressions instead using indicators broken out by quartiles and terciles, finding the same general results as presented here. In each case, results found negative reading effects for boys and not for girls, and negative math effects for girls, but not for boys. The larger negative reading effects for relatively high prior ability boys also remain evident in these additional specifications.

Published Online: 2014-2-1

Published in Print: 2014-7-1

Peer Effects and Policy: The Relationship between Classroom Gender Composition and Student Achievement in Early Elementary School

Abstract

Appendix

References

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