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New Trends in Gender and Mathematics Performance: A Meta-
Analysis
Sara M. Lindberg, Janet Shibley Hyde, and Jennifer L. Petersen
University of Wisconsin – Madison
Marcia C. Linn
University of California – Berkeley
Abstract
In this paper, we use meta-analysis to analyze gender differences in recent studies of mathematics
performance. First, we meta-analyzed data from 242 studies published between 1990 and 2007,
representing the testing of 1,286,350 people. Overall, d = .05, indicating no gender difference, and
VR = 1.08, indicating nearly equal male and female variances. Second, we analyzed data from
large data sets based on probability sampling of U.S. adolescents over the past 20 years: the
NLSY, NELS88, LSAY, and NAEP. Effect sizes for the gender difference ranged between −0.15
and +0.22. Variance ratios ranged from 0.88 to 1.34. Taken together these findings support the
view that males and females perform similarly in mathematics.
Keywords
mathematics performance; gender; meta analysis
Policy decisions, such as funding for same-sex education, as well as the continuing
stereotype that girls and women lack mathematical ability, call for up-to-date information
about gender differences in mathematical performance. Such stereotypes can discourage
women from entering or persisting in careers in science, technology, engineering, and
mathematics (STEM). Today women earn 45% of the undergraduate degrees in mathematics
(NSF, 2008a), but women make up only 17% of university faculty in mathematics (NSF,
2008b). We report on a meta-analysis of recent studies of gender and mathematics. We
estimate the magnitude of the gender difference and test whether it varies as a function of
factors such as age and the difficulty level of the test.
Stereotypes about Gender and Mathematics
Mathematics and science are stereotyped as male domains (Fennema & Sherman, 1977;
Hyde, Fennema, Ryan, Frost, & Hopp, 1990b, Nosek, et al, 2009). Stereotypes about female
Correspondence concerning this article should be addressed to Janet Hyde, University of Wisconsin, Department of Psychology, 1202
W. Johnson Street, Madison, WI 53706. jshyde@wisc.edu.
Sara M. Lindberg, School of Medicine & Public Health, University of Wisconsin – Madison; Janet Shibley Hyde and Jennifer L.
Petersen, Department of Psychology, University of Wisconsin – Madison; Marcia C. Linn, Graduate School of Education, University
of California, Berkeley.
Publisher's Disclaimer: The following manuscript is the final accepted manuscript. It has not been subjected to the final copyediting,
fact-checking, and proofreading required for formal publication. It is not the definitive, publisher-authenticated version. The American
Psychological Association and its Council of Editors disclaim any responsibility or liabilities for errors or omissions of this manuscript
version, any version derived from this manuscript by NIH, or other third parties. The published version is available at
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Published in final edited form as:
Psychol Bull
. 2010 November ; 136(6): 1123–1135. doi:10.1037/a0021276.
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inferiority in mathematics are prominent among children and adolescents, parents, and
teachers. Although children may view boys and girls as being equal in mathematical ability,
they nonetheless view adult men as being better at mathematics than adult women (Steele,
2003). Implicit attitudes that link males and mathematics have been demonstrated repeatedly
in studies of college students (e.g., Kiefer & Sekaquaptewa, 2007; Nosek, Banaji, &
Greenwald, 2002).
Parents believe that their sons' mathematical ability is higher than their daughters'. In one
study, fathers estimated their sons' mathematical “IQ” at 110 on average, and their
daughters' at 98; mothers estimated 110 for sons and 104 for daughters (Furnham et al.,
2002; see also Frome & Eccles, 1998). Teachers, too, tend to stereotype mathematics as a
male domain. In particular, they overrate boys' ability relative to girls' (Li, 1999; but see
Helwig, Anderson, & Tindal, 2001).
These stereotypes are of concern for several reasons. First, in the language of cognitive
social learning theory, stereotypes can influence competency beliefs or self-efficacy;
correlational research does indeed show that parents' and teachers' stereotypes about gender
and mathematics predict children's perceptions of their own abilities, even with actual
mathematics performance controlled (Bouchey & Harter, 2005; Frome & Eccles, 1998;
Keller, 2001; Tiedemann, 2000). Competency beliefs are important because of their
profound effect on individuals' selection of activities and environments (Bandura, 1997;
Bussey & Bandura, 1999). According to an earlier meta-analysis, girls report lower
mathematics competence than boys do, although the difference is not large (d = +.16, Hyde
et al., 1990b). In recent studies, elementary-school boys still report significantly higher
mathematics competency beliefs than girls do (Else-Quest, Hyde, & Linn, 2010; Fredrick &
Eccles, 2002; Lindberg, Hyde, & Hirsch, 2008; Watt, 2004).
A second concern is that stereotypes can have a deleterious effect on actual performance.
Stereotype threat effects (Steele, 1997; Steele & Aronson, 1995) have been found for
women in mathematics. In the standard paradigm, half the participants (talented college
students) are told that the math test they are about to take typically shows gender differences
(threat condition), and the other half is told that the math test is gender fair and does not
show gender differences (control). Studies find that college women underperform compared
with men in the threat condition but perform equal to men in the control condition,
indicating that priming for gender differences in mathematics indeed impairs girls' math
performance (e.g., Ben-Zeev, Fein, & Inzlicht, 2005; Cadinu, Maass, Rosabianca, &
Kiesner, 2005; Johns, Schmader, & Martens, 2005; Quinn & Spencer, 2001; Spencer, Steele,
& Quinn, 1999). Stereotype threat effects have been found in children as early as
kindergarten (Ambady, Shih, Kim, & Pittinsky, 2001). Other research, measuring implicit
stereotypes about gender and math, has found that these implicit stereotypes predict
performance in a calculus course (Kiefer & Sekaquaptewa, 2007).
Stereotypes play a role in policy decisions as well as personal decision-making. For
example, schools and states may base decisions to offer single-sex mathematics classes on
the belief that these gender differences exist (Arms, 2007).
Gender and Mathematics Performance
The stereotypes about female inferiority in mathematics stand in distinct contrast to the
scientific data on actual performance. A 1990 meta-analysis found an effect size of d = 0.15,
males scoring higher, for gender differences in mathematics performance averaged over all
samples; however, in samples of the general population (i.e. national samples, classrooms –
as opposed to exceptionally precocious or low ability samples), females scored higher but by
a negligible amount (d = −0.05; Hyde, Fennema, & Lamon, 1990a). Hedges and Nowell
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(1995), using data sets representing large probability samples of American adolescents,
found d = 0.03 to 0.26 across the different data sets. Moreover, girls earn better grades in
mathematics courses than boys through the end of high school (Dwyer & Johnson, 1997;
Kenney-Benson et al., 2006; Kimball, 1989). In short, previous research showed that gender
differences in mathematics performance were very small and, depending on the sample and
outcome measure, sometimes favored boys and sometimes favored girls.
Several features of the 1990 meta-analysis (Hyde et al., 1990a) warrant more detailed
description. Using computerized literature searches, the researchers identified 100 useable
studies, which yielded 254 independent effect sizes representing the testing of more than 3
million persons. One key moderator analysis examined the magnitude of gender differences
as a function of age and cognitive level of the test (computation was considered the lowest
level, understanding of concepts was considered intermediate, and complex problem-solving
was considered the highest level). Girls performed better than boys at computation in
elementary school and middle school but the differences were small (d = −0.20 and −0.22,
respectively) and there was no gender difference in high school. There was no gender
difference in understanding of mathematical concepts at any age. For complex problem
solving, there was no gender difference in elementary or middle school, but a gender
difference favoring males emerged in high school (d = 0.29). This last gender difference,
although small, is of concern because complex problem solving is crucial for STEM careers.
A second moderator analysis examined the magnitude of gender differences in mathematics
performance as a function of the ethnicity of the sample (Hyde et al., 1990a). The striking
finding was that the small gender difference favoring males was found for Whites (d = 0.13),
but not for Blacks (−0.02) or Latinos (0.00).
Depth of Knowledge
Traditionally, researchers maintained that girls might do as well as, or even better than boys
on tests of computation, which require relatively simple cognitive processes (e.g., Anastasi,
1958). These same researchers concluded that male superiority emerged for tests requiring
more advanced cognitive processing, such as complex problem solving. The 1990 meta-
analysis by Hyde and colleagues provided some support for these ideas, although the gender
difference in complex problem solving did not appear until the high school years and was
not large even then.
Current mathematics education researchers conceptualize this issue of complexity of
cognitive processes as a question of item demand and the depth of knowledge required to
solve a particular problem. Webb (1999) developed a 4-level Depth of Knowledge
framework to identify the cognitive difficulty of mathematics items on standardized
assessments. In this framework, Level 1 (Recall) includes the recall of information such as
facts or definitions, as well as performing simple algorithms. Level 2 (Skill/Concept)
includes items that require students to make decisions about how to approach a problem.
These items typically ask students to classify, organize, estimate, or compare information.
Level 3 (Strategic Thinking) includes complex and abstract cognitive demands that require
students to reason, plan, and use evidence. Level 4 (Extended Thinking) requires complex
reasoning, planning, developing, and thinking over an extended period of time. Items at
Level 4 require students to connect ideas within the content area or among content areas as
they develop one problem-solving approach from many alternatives. This depth of
knowledge framework was used to rate the cognitive demands of the tests that assess
mathematics performance in the studies reviewed here.
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New Trends
Cultural shifts have occurred since the 1980s that call for the reexamination of gender
differences in mathematics. In the 1980s, a prominent explanation of male superiority in
complex problem solving beginning in high school was gender differences in course choice
(Meece, Eccles-Parsons, et al, 1982). Girls were less likely than boys to take advanced
mathematics courses and advanced science courses. Because mathematical problem solving
is an important component of chemistry and physics courses, students may learn those skills
in science courses as much as in mathematics courses. Today, however, the gender gap in
course taking has disappeared in all areas except physics. For the high school graduating
class of 2005, 7.7% of boys and 7.8% of girls took calculus; 57.8% of girls and 50.6% of
boys took chemistry; and 32.8% of girls and 36.8% of boys took physics (NSF, 2008c).
Insofar as courses taken by students influence their mathematics performance, we would
expect that the gender difference in complex problem solving in high school would have
narrowed.
In addition, cross-national data show that the gender gap in mathematics performance
narrows or even reverses in societies with more gender equality (e.g., Sweden and Iceland),
compared with those with more gender inequality (e.g., Turkey) (Else-Quest, Hyde, & Linn,
2010; Guiso, Monte, Sapienza, & Zingales, 2008). Insofar as the United States has moved
toward gender equality over the past 30 to 40 years, the gender gap in mathematics
performance should have narrowed.
Findings from a recent analysis of data from state assessments of mathematics performance
provide evidence that the gender gap in mathematics performance in the U.S. has indeed
diminished or even vanished (Hyde, Lindberg, Linn, Ellis, & Williams, 2008). Those data
had several limitations and raised some questions that deserve analysis in a larger study.
First, they were based just on tests administered by the states to satisfy the requirements of
No Child Left Behind Legislation. Items tapping Levels 3 or 4 depth of knowledge were
notably absent. Second, the data were derived only from students in grades 2 through 11;
trends in gender differences beyond grade 11 (age 17) could therefore not be assessed.
Third, the distributions of male and female performance were available for only part of the
sample. The available results raised intriguing questions about gender differences in
complex problem solving since in some subgroups females outperformed males at the high
end of the distribution.
Gender and Variability
Most of the research has focused on mean-level gender differences, but variability (variance)
remains an issue even when means are similar. The greater male variability hypothesis was
originally proposed in the 1800s and advocated by scientists such as Charles Darwin and
Havelock Ellis, to explain why there was an excess of men both in homes for the mentally
deficient and among geniuses (Shields, 1982). In modern statistical terms, the hypothesis is
that, independent of mean-level differences, males have a greater variance than females do
on the intellectual trait of interest. Thus, the hypothesis states that men are more likely than
women to be at both the top and the bottom of the statistical distribution of mathematics
performance. Typically the statistic that is computed is the variance ratio (VR), the ratio of
the male variance to the female variance. Thus values > 1.0 indicate greater male variability.
Based on test norming data, Feingold (1992a) found a VR of 1.11 for the DAT numerical
ability, 1.20 for the SAT-Math, and 1.02 for the WAIS Arithmetic subtest. Hedges and
Nowell (1995) found VR's ranging between 1.05 and 1.25 for mathematics tests
administered to national samples of adolescents such as the NLSY and NELS:88. The
analysis of recent state assessment data, described earlier, found VR's ranging between 1.11
and 1.21 (Hyde et al., 2008). Thus there is some evidence of greater male variability in
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mathematics performance, although the variance ratios are not terribly lopsided. The greater
male variability hypothesis, of course, is a description of the data, not an explanation for it,
but if true, it could partially account for findings of an excess of males at very high levels of
mathematical performance (Hedges & Friedman, 1993). One goal of this meta-analysis was
to re-assess the greater male variability hypothesis for mathematics performance using
contemporary data.
The Current Study
Several factors warrant a new meta-analysis of research on gender and mathematics
performance. First, approximately 18 years of new data have accumulated since the 1990
meta-analysis (Hyde et al., 1990a). Second, cultural shifts have occurred over the last two
decades. Specifically, girls are now taking advanced mathematics courses and some science
courses in high school at the same rate as boys are, closing the gap in course choice. The
magnitude of gender differences in mathematics performance is expected to be even smaller
than it was in the 1990 meta-analysis; of particular interest is the gender difference favoring
boys in complex problem-solving in high school, and whether this difference has narrowed
in recent years. Third, statistical methods of meta-analysis have advanced. At the time of the
1990 meta-analysis, only fixed-effects models were available. Fixed-effects models have
since been criticized, and random-effects and mixed models have been developed (Hedges
& Vevea, 1998; Lipsey & Wilson, 2001). The current meta-analysis used a mixed-effects
model, the advantages of which are detailed below.
Our goals in these meta-analyses were to provide answers to the following questions:
1. What is the magnitude of the gender difference in mathematics performance, using
the d metric?
2. Does the direction or magnitude of the gender difference vary as a function of the
depth of knowledge tapped by the test?
3. Developmentally, at what ages do gender differences appear or disappear?
4. Are there variations across U. S. ethnic groups, or across nations, in the direction or
magnitude of the gender difference?
5. Has the magnitude of gender differences in mathematics performance declined
from 1990 to 2007?
6. Do males display greater variance in scores and, if so, by how much?
Study 1 addressed these questions using traditional methods of meta-analysis that involve
identifying all possible studies using article databases. Study 2 addressed the questions using
an alternative method advocated by Hedges and Nowell (1995), which involves the analysis
of recent large, national U.S. data sets based on probability sampling. Cross-national,
probability sampled data sets have been analyzed by others (Else-Quest, Hyde, & Linn,
2010; Guiso et al., 2008; Penner, 2008).
Study 1
Method
Identification of studies—Computerized database searches of ERIC, PsycINFO, and
Web of Knowledge were used to generate a pool of potential articles. To identify all articles
that investigated mathematics performance, the following search terms were used: (math* or
calculus or algebra or geometry) AND (performance or achievement or ability) NOT
(mathematical model). This broad term was selected to capture the widest range possible of
research conducted on this topic while avoiding studies that used computational modeling
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methodology to study unrelated phenomena. Search limits restricted the results to articles
that discussed research with human populations and that were published in English between
1990 and 2007. The three database searches identified 10,816, 9,577, and 18,244 studies,
respectively, which were considered for inclusion. Given the tremendous volume of studies
identified, we decided to rely solely on this method of identification, a potential limitation.
Abstracts and citations were imported into RefWorks citation manager, and then each article
was evaluated for inclusion based on the following criteria: (a) the title or abstract alluded to
a measure of mathematics performance; (b) the study appeared to contain original data; (c)
the study was conducted on a human population; (d) the sample included at least five males
and five females. 3,941 studies met the aforementioned criteria. These articles were then
printed and examined to determine whether they presented sufficient statistics for an effect
size calculation. The final sample of studies included in study 1 utilized data from 242
articles, comprising 441 samples and 1,286,350 people.
Although the final sample of studies is large, some readers may wonder why so many
potential studies were lost during the coding processes. Most cases of exclusion were based
on one of three reasons: (1) Many of the articles identified in our search reported on data
from the large national datasets included in Study 2 (NAEP, NELS, LSAY, NLSY) or from
large international datasets (SIMS, TIMSS, PISA) that had been covered by other meta-
analyses of gender differences in mathematics performance (Else-Quest, Hyde, & Linn,
2010; Guiso et al., 2008; Penner, 2008). Those articles were excluded from study 1 to avoid
redundancy. (2) The searches also picked up reports published by state, local, and federal
educational organizations, few of which contained individual-level data. (3) Finally, many
articles did not contain enough data to compute effect sizes (e.g., results were not
disaggregated by gender) and additional data could not be obtained from the study authors.
Coding the studies—If studies reported data from large datasets or longitudinal studies
that were likely to create multiple publications, this was noted so as to avoid inclusion of
non-independent effect sizes.
Several characteristics of each sample were coded as potential moderators: (a) age of the
participants; (b) nationality of participants (American, Canadian, European, Australian/New
Zealander, Asian, African, Latin American, or Middle Eastern); (c) for US samples, majority
ethnic group of participants (Euro-American, African American, Asian American, Hispanic,
other; mixed; or unreported), and (d) ability level of the participants (low ability, general
ability, selective, highly selective).
Several aspects of the mathematics tests were also coded as potential moderators: (a)
whether the test was time-limited; (b) whether the test included each of several problem
types (multiple choice, short answer, open ended); (c) which types of mathematical content
were included in the test (numbers and operations, algebra, geometry, measurement, data
analysis and probability); (d) depth of knowledge (level 1 recall, level 2 skills/concepts,
level 3 strategic thinking, level 4 extended thinking; levels are described in greater detail
above, see also Webb, 1999) and (e) whether the test was specific to the local curriculum
(i.e. based on published curricular standards for the region or developed in collaboration
with local teachers, textbooks, and syllabi) or was relatively independent of the curriculum.
Publication year was also coded as a potential moderator.
50 articles were double coded to determine inter-rater reliability. Percentage agreement for
coding of the moderators was > 95% for all variables.
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Effect size computation—Cohen's d (Cohen, 1988) is the effect size for the standardized
mean difference between two groups on a continuous variable (e.g., the mean difference
between males and females on a continuous measure of mathematics performance). Thus,
for each independent sample within an article, d was computed, with d = (Mm − Mf) / sw
and Mm = the mean for males, Mf = the mean for females, and sw = the pooled within-
gender standard deviation. Whenever possible, separate effect sizes were computed for
independent groups within each sample (e.g., different age groups, Blacks and Whites). If
means and standard deviations were not available, the effect size was computed from other
statistics such as t or F, using formulas provided by Lipsey and Wilson (2001). The
complete list of samples, with corresponding effect sizes and variance ratios, can be found in
the supplemental online material for this article.
In a few cases, more than one effect size was available for the same sample. When that
happened, the following decision rules were used to select or calculate a single effect size
for inclusion in the analyses: (1) If a study used a longitudinal design, we used the effect
size from the most recent measurement. (2) If multiple effect sizes were available from the
same time point but missing data produced different sample sizes for different measures,
then the effect size with the largest corresponding sample size was selected for inclusion in
the analyses. (3) If there were multiple effect sizes from the same time point with the same
sample size, means and standard deviations were pooled, and the pooled values were used to
compute the composite effect size that was included in the analyses.
Raw effect sizes were corrected for bias, and standard errors were calculated. Specifically,
estimated population effect sizes were used, which adjust for upward-bias of effect sizes
among small samples (Hedges, 1981). In addition, inverse variance weights were calculated
for each effect size so that analyses could be weighted by inverse variance, a procedure that
allows large samples to have more leverage in the analyses than small samples have (Lipsey
& Wilson, 2001).
Variance ratio computation—Variance ratios were also computed for each study, with
VR = variancemales / variance females. Thus, a VR >1 denotes greater male variability, and a
VR < 1 denotes greater female variability. Standard errors and inverse variance weights
were calculated for each variance ratio. Analyses of the variance ratios were conducted as
outlined by Katzman and Alliger (1992).
Data analyses—Results were analyzed using a mixed-effects model (Lipsey & Wilson,
2001) and SPSS macros by Wilson (2005). The mixed-effects model assumes that variability
among effect sizes can be explained by both fixed factors (i.e. systematic differences due to
moderators) and random factors (i.e. error variance). This approach is preferable to fixed-
effects or random-effects models, which assume that all variability among effect sizes is
accounted for by moderators or by error, respectively. In mixed-effects models, a random-
effects variance component is computed based on the residual homogeneity after moderator
effects have been accounted for. Then, inverse variance weights are recalculated with the
random-effects variance component added, and the model is refit.
To measure heterogeneity of variance of the effect sizes, Q statistics were computed using
weights based on the mixed-effects model. When homogeneity analyses indicated that there
was significant heterogeneity among the effect sizes, moderator analyses were conducted to
test whether characteristics of the mathematics assessments or characteristics of the samples
could explain the variability among effects. These moderator analyses allowed us to explore
whether systematic differences among the studies led to reliably different effects.
Moderators were tested for significance using an analog to ANOVA in the case of
categorical moderator variables (e.g., ethnicity), or an analog to multiple regression in the
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case of continuous moderator variables (e.g., publication year). The level of missing data for
moderator variables (due to vague descriptions of mathematics measures and study
procedures) made it untenable to conduct a simultaneous analysis of all moderators. The
piece-wise approach is not ideal, but we believe that it is warranted in this case, because we
were testing a priori hypotheses based on the findings of previous meta-analyses.
Results
Magnitude of gender differences—The overall weighted effect size, averaged over all
studies, was d = +0.05, representing a negligible gender difference. Figure 1 shows the
distribution of effect sizes, which is approximately normal and centered around 0.
Heterogeneity analysis revealed that the set of effect sizes was significantly heterogeneous,
Qt (427) = 11478.74, p < .001. The random effects variance component was .070.
Moderator analyses—Given the heterogeneity among the effect sizes, we conducted
analyses for suspected moderator variables. Table 1 displays the analyses for variations in
effect size as a function of characteristics of the tests. Problem type (presence of multiple
choice, short answer, and open ended questions) was the only aspect of the tests that
significantly predicted heterogeneity among the effects, Qb (3, 178) = 8.11, p < .05. The
presence of multiple choice questions on exams predicted relatively better performance by
males (β = .16), whereas the presence of short answer and open ended questions predicted
relatively better performance by females (βs = −.02 and −.06, respectively).
The magnitude of the gender difference did not depend on whether there was a time limit for
the test Qb (1, 136) = 2.21, p = .14, or whether the test was curriculum-focused, Qb (1, 422)
= 3.01, p = .08. Similarly, there were no variations in the magnitude of the effect size as a
function of problem content (numbers and operations, algebra, geometry, measurement,
probability), Qb (5, 204) = 8.55, p = .13, or depth of knowledge, Qb (3, 119) = 1.51, p = .68.
Table 2 displays the analyses for variations in effect size as a function of characteristics of
the sample. The magnitude of the gender difference varied significantly as a function of the
selectivity of the sample, Qb (3, 424) = 27.06, p < .001. For samples of the general
population, d = +0.07, but d = +0.40 for highly selective samples.
Nationality was not a significant predictor of effect sizes, Qb (7, 421) = 10.12, p = .18. All
effects were small or negligible. Among US studies, effect sizes varied as a function of
ethnicity, Qb (1, 89) = 10.00, p < .01. Samples composed mainly of Whites showed d =
+0.13, whereas for ethnic-minority samples, d = −0.05. Although we would have preferred
to report results from these groups separately by ethnicity, the number of samples was too
small to permit this.
The analysis also indicated that age was a significant moderator, Qb (5, 423) = 44.75, p < .
001. Gender differences were negligible in elementary-school and middle-school-aged
children and reached a peak of d = +0.23 in high school. The gender difference then
declined for college-age samples and adults.
To test for trends over time from 1990 to 2007, an analog to multiple regression was
performed, using year of publication to predict effect size. This analysis indicated that
publication year was not a significant predictor of effect size, Qb (1, 427) = 1.05, p = .31.
A final analysis explored the interaction of age and depth of knowledge. Thus, our next
analysis focused on both depth of knowledge and different age groups. This analysis was
limited by the fact that many articles identified in our original search provided insufficient
information to be able to code depth of knowledge, so they were not useable in this analysis.
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Furthermore, of those that had usable information about test content, only a small proportion
of tests included items that tapped complex problem solving (Level 3 or 4). Some studies
located in the literature search involved problem solving at Level 3 or 4 but reported only
qualitative data on students' approach to the problem, with no data on actual performance.
Although these studies could not be included in the meta-analysis, they suggest the value of
looking at more complex tasks. Table 3 provides a breakdown of effect sizes by age and
depth of knowledge. Of particular interest in this analysis was whether a gender difference
in complex problem solving would be seen among high school and college students, as was
found in Hyde's 1990 meta-analysis. Our results showed that there was a small gender
difference favoring high school males on tests that included problems at Levels 3 or 4 (d =
+0.16), but the effect was reversed among college students (d = −0.11). However, these
findings are based on small numbers of studies, and therefore cannot be considered robust.
Gender differences in variability—A mixed-effects analysis of gender differences in
variance was conducted in parallel to the effect size analyses reported above. The overall
weighted variance ratio, averaged over all studies, was VR = 1.07, indicating a slightly larger
variance for males than for females. The residual variance component was .073.
Study 2
Method
Large United States datasets—Study 1 excluded articles that reported secondary data
analyses from large national datasets, because original data from those studies were acquired
directly for a separate analysis, which constitutes Study 2. Datasets were included in Study 2
if (a) they included relevant information about math performance, (b) represented data
collected after 1990, (c) were nationally representative with a large sample size, and (d)
provided statistics for both males and females. International datasets were excluded from
Study 2 because they have been thoroughly reviewed elsewhere in the literature (see Else-
Quest, Hyde, & Linn, 2010). The following large U.S. datasets were analyzed in Study 2:
The National Longitudinal Survey of Youth - 1997 (NLSY97, U.S. Bureau of Labor
Statistics, n.d.), The National Educational Longitudinal Study (NELS88, National Center for
Educational Research n.d.a), The Longitudinal Study of American Youth (LSAY, n.d.), and
the National Assessment of Educational Progress (NAEP, National Center for Education
Research, n.d.b).
The NLSY - 97 began data collection in 1997 and followed students each year until 2002. At
the first assessment 58.3% of participants were White, 27.0% were Black, 1.7% were Asian
American, 0.8% were American Indian, and 12.4% did not report ethnicity. Math
achievement was measured using the PIAT-R (Markwardt, 1998). During round one of data
collection, the test was administered to all participants who were in the ninth grade or lower.
During round two of data collection, the test was administered to all participants who had
taken the test during round one, as well as those who were at least 12 years old on December
31, 1996. The PIAT-R consists of multiple choice items about three areas of math content:
1) foundations (i.e. number, size, and shape discretion), 2) basic facts (i.e. addition,
subtraction, multiplication, division), and 3) applications (i.e. algebra, geometry, fractions,
word problems, and numerical relationships). The PIAT-R math assessment begins with an
age-appropriate question and increases or decreases in difficulty until the youth establishes a
“basal,” that is, when the youth correctly answers five consecutive questions. Once a basal is
reached the questions increase in difficulty until a “ceiling” is reached when the youth
incorrectly answers five of seven consecutive questions. The ceiling is then adjusted for
incorrect responses given between the basal and the ceiling and is standardized with a mean
of 100 and a standard deviation of 15. The current study determines math achievement using
the standardized score of the PIAT-R math for each assessment.
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The NELS88 is a longitudinal study which began examining 8th graders in 1988 and
followed these youth in 10th and 12th grade in 1990 and 1992. At the first assessment
67.0% of participants were White, 12.2% were Black, 12.7% were Latino, 6.3% were Asian
American, and 1.6% did not report ethnicity. The NELS math assessment was developed by
Educational Testing Services and consisted of multiple choice questions. Item content
included arithmetic, algebra, geometry, data and probability, and advanced topics. One
version of the test was administered at the base year, and three versions of the test were
administered at the first and second follow up. Based on their performance on the math test
in the base year, students were divided into three groups (low, moderate, and high ability)
and were assigned versions of the math test at the first and second follow up in accordance
with their ability. Each test, regardless of ability, assessed skill/knowledge, comprehension,
and problem solving in all five content areas described above. In addition to the multiple
choice test, a constructed response test was given to 12th graders at the 1992 assessment;
this test involved items examining measurement, geometry, and data analysis.
The LSAY followed youth from 1987 to 1992 with assessments at each year from grades 7 to
12. At the first assessment 70% of participants were White, 11% were Black, 9.2% were
Latino, 3.5% were Asian American, 1.5% were American Indian, and 4.8% did not report
ethnicity. At each assessment students completed a multiple-choice math test that assessed
skills in geometry, measurement, data analysis, algebra, and simple operations (for a
complete list of problems, see http://lsay.msu.edu/instruments_006.html).
The NAEP math assessment was the only large U.S. database in the current study that was
not longitudinal. It consisted of two different studies: the long-term trend assessment, and
the main assessment.
The NAEP long-term trend assessment was given every four years from 1992 to 2004 to
students aged 9, 13, and 17. Ethnic diversity was different for each assessment and age
group, but consisted of Whites (M = 74.07%, SD = 4.87), Blacks (M = 14.78%, SD = 1.31),
Latinos (M = 7.82%, SD = 3.31) and those who did not report ethnicity (M = 3.29%, SD =
1.38). The math assessment in this study has remained virtually unchanged since its
inception in 1978. It included both multiple-choice and short constructed response items
which focus on math skills including number operations, measurement, algebra, and
geometry.
In contrast to the long-term trend data, the NAEP main assessment selected students by
grade rather than by age. The main assessment was given to 4th and 8th graders every two
years from 1990 to 2007. Twelfth graders were included in 1990 through 2000. Ethnic
diversity was different for each assessment and age group, but consisted of Whites (M =
67.07%, SD = 6.43), Blacks, (M =15.94%, SD = 0.99), Latinos (M = 11.89%, SD = 4.89),
Asian Americans (M = 3.17%, SD = 1.66), American Indians (M = 0.94%, SD = 0.42) and
those who did not report ethnicity (M = 3.29%, SD = 1.38). The math portion of the NAEP
main assessment used multiple choice, short constructed response, and long constructed
response items. In addition to the math skills assessed in the long-term trend analysis, the
main analysis also included skills in data analysis and probability.
A unique aspect of the NAEP assessments is that performance scores are constructed via
IRT (item response theory). Thus, they are not a direct reflection of the number of problems
any student got right or wrong. Rather, the pattern of correct responses is used to construct a
“probable value” score that reflects the student's overall understanding of mathematics. See
Mislevy, Johnson, and Muraki (1992) for a further discussion of this approach and its
advantages in estimating population values. Our analyses are based on these probable value
scale scores, along with the corresponding weights and standard errors reported by NAEP.
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Data analysis—Data analysis for Study 2 was similar to Study 1. All effect sizes were
calculated, and a mixed effects model was used to determine whether the effect sizes within
each dataset were heterogeneous. If effect sizes were heterogeneous, a weighted ordinary
least squares regression was applied to predict gender differences in math performance.
Moderating variables used in Study 2 were age, publication year, percentage of each type of
problem (number sense, algebra, geometry, measurement), percentage of problems in each
type of format (multiple choice, short answer, open ended), and percentage of Whites,
Blacks, and Latinos in each sample. Similar to Study 1, variance ratios were also computed.
More information about sample and test characteristics were available for the large datasets
than were available for the studies uncovered in the literature reviews in Study 1. Therefore,
with the exception of depth of knowledge, we were able to code moderator variables with
more detail and many moderators that were coded as categorical variables in Study 1 were
considered continuous variables in Study 2. For example, Study 1 coded whether the tests
used multiple choice, short answer, or open ended questions, whereas Study 2 coded the
percentage of question in each format.
Results
Across all datasets in Study 2, the average weighted effect size was d = +0.07. The average
weighted variance ratio across all datasets was 1.09. The effect sizes were heterogeneous,
Qt(55) = 393.04, p < 0.001, with a random effects variance component of .001. Differences
among the national datasets were a significant source of heterogeneity Qb(4, 55) = 43.12, p
< .001; therefore we describe findings from each dataset in turn.
Effect sizes for each assessment of the NLSY are presented in Table 4. The mean weighted
effect size for all six assessments of the NLSY was d = +0.08. The average weighted
variance ratio was 1.05. Effects sizes for NLSY-97 were homogenous, Qw(5) = 5.72, p = .
33.
Effect sizes for each assessment of the NELS:88 are presented in Table 5. The average
weighted effect size across all eight assessment was d = +0.10. The average weighted
variance ratio for the NELS:88 was 0.94. Effect sizes within the NELS:88 were
heterogeneous, Qw(7) = 18.66, p < 0.01.
Effect sizes for each assessment of the LSAY are presented in Table 6. Results for the
LSAY indicated small or negligible gender differences for each assessment. The average
weighted effect size for all six assessments was d = −0.07. The weighted average variance
ratio was 1.26. Effect sizes were homogenous, Qw(5) = 2.50, p = .78.
Effect sizes for each assessment of the NAEP are presented in Table 7. Results for NAEP
indicated small or negligible gender differences at all grades. The average weighted effect
size across all 18 assessments of the long-term trend data was d = +0.09. The average
weighted effect size across all 18 of the main assessments was d = +0.06. The average
weighted variance ratio for the long-term trend data was 1.13 and for the main assessment
was 1.04. Effect sizes for both the long-term trend data and the main assessment were
homogenous, Qw(17) = 16.05, p = .52 and Qw(17) = 12.88, p = .74, respectively.
The heterogeneity of the effect sizes across datasets indicates that these studies are not
replications of each other but rather vary along some dimension(s). We therefore conducted
additional moderation analyses to examine whether sample characteristics or test
characteristics could explain the heterogeneity among effect sizes across datasets. These
analyses were conducted using an analog to multiple regression, in which each level of each
moderator was entered as a separate predictor of the studies' effect sizes. The resulting betas
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can be interpreted much like correlation coefficients, with positive values indicating an
increase in effect size as the value of the moderator increases (relative advantage for males)
and negative values indicating a decrease in effect size as the value of the moderator
increases (relative advantage for females).
As seen in Table 8, two aspects of the tests accounted for heterogeneity among studies:
problem type and mathematical content. With regard to problem type, tests with a higher
proportion of multiple choice and open-ended items yielded smaller gender effect sizes,
whereas tests with a higher proportion of short answer items yielded larger gender effect
sizes. This finding surprised us, given that three of the big datasets (LSAY, NLSY, NELS)
were 100% multiple choice, and only one of them had a negative overall effect size; if
multiple choice items confer a significant female advantage, we might have expected
negative effects across all three of those studies. Therefore, we conducted an additional
analysis, looking just at the 36 NAEP effect sizes, which have variation in the proportion of
multiple choice, short answer, and open-ended questions. When looking at just the NAEP
effect sizes, we found a different pattern of results, such that males did better on tests with a
greater proportion of multiple choice items (β = +.29), and females did better on tests with a
greater proportion of short answer and open-ended items (βs = −.32 and −.19, respectively).
Thus, problem type had a similar effect on gender differences in the NAEP as were found in
study 1.
With regard to mathematical content, tests with a higher proportion of algebra items yielded
smaller effect sizes (females performed relatively better), and tests with a higher proportion
of measurement items yielded larger effect sizes (males performed relatively better). The
other three types of mathematical content were not significant predictors of effect size in this
analysis.
With regard to depth of knowledge, tests containing items at levels 3 or 4 yielded larger
effect sizes (males performed better or females performed worse). All of the tests contained
items at levels 1 and 2, and therefore we were not able to examine the specific effects of
items at those levels.
The ethnic composition of the samples did not have an effect on the magnitude of the gender
difference in mathematics performance. However, age was a marginally significant predictor
of effect size (p = .0516), with older samples yielding relatively larger gender differences
favoring males.
Discussion
We proposed to answer six questions with these meta-analyses. We take up each question in
turn.
First, what is the magnitude of the gender difference in mathematics performance, based on
contemporary studies? Taking Study 1 and Study 2 together, the answer appears to be that
there is no longer a gender difference in mathematics performance. For Study 1, d values
averaged +0.05 based on data from 1,286,350 persons. For Study 2, d values averaged +0.07
based on data from 1,309,587 persons. These results are consistent with a recent analysis of
U.S. data from state assessments of youth in grades 2 through 11, which found that girls had
reached parity with boys in math performance (Hyde, Lindberg, Linn, Ellis, & Williams,
2008).
Second, does the direction or magnitude of the gender difference vary as a function of the
depth of knowledge tapped by the test? By itself, depth of knowledge was not a significant
predictor of differences in effect sizes in study 1. However, study 2 indicated that there may
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be a modest effect of depth of knowledge on gender differences in mathematics
performance, with those containing a greater proportion of items at levels 3 or 4 favoring
males. These results are inconsistent with a recent analysis of NAEP data, examining gender
differences for items categorized as difficult by NAEP, and as at Level 3 or 4 Depth of
Knowledge; at 12th grade, the average d = +0.07, or a negligible difference (Hyde et al.,
2008). However, an examination of depth of knowledge and age simultaneously in Study 1
(Table 3) indicates a male advantage (d = 0.16) in Level 3 or 4 problems in high school, a
finding that is consistent with the earlier meta-analysis by Hyde and colleagues (1990). This
finding, however, is based on only 3 studies, so it should be interpreted with caution. Very
few studies used items requiring this greater depth of knowledge, yet it is precisely the skill
that is required for high-level STEM careers.
Third, developmentally, at what ages do gender differences appear or disappear? Consistent
with previous meta-analyses, are gender differences larger in high school than in elementary
or middle school? The data sets reviewed in Study 2 showed a marginally significant
increase in effect sizes as age increased (β = +.24). This is consistent with the results of
Study 1, which found gender differences close to 0 for elementary and middle school
students, and small effects favoring males for high-school and college students (ds= +0.23
and +0.18, respectively). These results, too, are inconsistent with the Hyde et al. (2008)
analysis of data from state assessments, which showed no gender difference in performance
at any grade level through grade 11. Again, though, it is important to consider age and depth
of knowledge required by the test simultaneously.
Overall, we conclude that a small gender difference favoring males in complex problem
solving is still present in high school. Multiple factors may account for this gender gap. As
noted earlier, girls are less likely to take physics than boys are, and complex problem
solving is taught in physics classes, perhaps even more than in math classes. Gender
differences in patterns of interest may play a role (Su, Rounds, & Armstrong, 2009),
although these patterns, too, are shaped by culture. Moreover, even in very recent studies,
parents and teachers give higher ability estimates to boys than to girls (Lindberg, Hyde, &
Hirsch, 2008), and the effects of parents' and teachers' expectations on children's estimates
of their own ability and their course choices are well documented (Eccles, 1994; Jacobs,
Davis-Kean, Bleeker, Eccles, & Malanchuk, 2005).
Fourth, are there variations across U.S. ethnic groups, or across nations, in the direction or
magnitude of the gender difference? In regard to ethnicity, Table 2 shows that, for Study 1, a
small gender difference was found favoring males among Whites, d = +0.13, but for all
ethnic minorities combined, d = −.05. This result is similar to the one found in the 1990
meta-analysis (Hyde et al., 1990a), which found a small gender difference favoring males
among Whites, but no difference for ethnic minority groups. Table 2 also shows variation in
effect sizes according to nationality or region of the world. The largest gender difference
favoring males was found in studies from Africa, d = +0.21, but even this difference is
small. The largest difference favoring females was found in Central/South America and
Mexico, d = −0.06. These variations in the magnitude and direction of the gender difference
in math performance are consistent with those found in analyses of international data sets
such as PISA and TIMSS. These other studies have, in addition, found that values of d for
nations correlate significantly with measures of gender inequality for those nations (e.g.,
Else-Quest et al., 2010; Guiso et al., 2008; Penner, 2008).
Fifth, has the magnitude of gender differences in mathematics performance declined from
1990 to 2007? Study 1 found no relation between year of publication and effect sizes,
indicating no discernible trend over time toward smaller gender differences. This may be
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because of the fact that, even in 1990, gender differences were already small (Hyde et al.,
1990a), leaving little room for further decline.
Sixth, do males display greater variance in scores and, if so, by how much? The overall
variance ratio in Study 1 was 1.07. That is, males displayed a somewhat larger variance, but
the VR was not far from 1.0 or equal variances. In Study 2, the average variance ratio was
1.09, again not far from 1.0. In addition, the NELS:88 data (Table 3) show several VR's that
are < 1.0, indicating that greater male variability is not ubiquitous. Variance ratios less than
1.0 have also been found in some national and international data sets (Hyde et al, 2008;
Hyde & Mertz, 2009).
Overall, to put these findings in a broader context, gender can be conceptualized as one of
many predictors of mathematics performance. Other factors include socioeconomic status
(SES), parents' education, and the quality of schooling. Melhuish and colleagues (2008)
compared the effect sizes of 9 predictors of children's mathematics performance at age 10:
birth weight, gender, SES, mother's education, father's education, family income, quality of
the home learning environment, preschool effectiveness, and elementary school
effectiveness. The striking finding was that gender was the weakest of these 9 predictors,
i.e., it had the smallest effect size. Mother's education, quality of the home learning
environment, and elementary school effectiveness were far stronger predictors. Our findings
are consistent with those of Melhuish and colleagues; gender is not a strong predictor of
mathematics performance.
Implications
Overall, the results of these two studies provide strong evidence of gender similarities in
mathematics performance. The heterogeneity of the findings suggests that there are
moderator variables that might clarify the pattern of effect sizes. Detecting consistent
moderators of gender differences would be strengthened by measures that tap the full range
of mathematical reasoning, including items that require sustained reasoning about complex
problems. The existence and magnitude of gender differences in mathematics performance
varies as a function of many factors, including nation, ethnicity, and age.
These findings have several policy implications. First, these findings call into question
current trends toward single-sex math classrooms. Advocates of single-sex education base
their argument in part on the assumption that girls lag behind boys in mathematics
performance and need to be in a protected, all-girls environment to be able to learn math
(e.g., Streitmatter, 1999). The data, however, show that girls are performing as well as boys
in mathematics, based on 242 separate studies (Study 1) and 4 large, well-sampled national
U. S. data sets (Study 2). The great majority of these girls and boys did their learning in
coeducational classrooms. Thus, the argument that girls' mathematics performance suffers in
gender-integrated classrooms simply is not supported by the data. If we wish to improve
students' mathematics performance, we would do better to focus not on gender, but on
factors that have larger effects, such as the quality and implementation of the curriculum
(Tarr et al., 2008) as well as the quality of the elementary school and the quality of the home
learning environment (Melhuish et al., 2008).
Second, the dearth of Level 3 or 4 items in assessments has a serious consequence. Given
the importance of mathematics tests for school evaluation under the No Child Left Behind
legislation, it is common for teachers to teach to the test (Au, 2007). If the test fails to
emphasize the skills that citizens need, American students are disadvantaged. In addition,
without evidence concerning student progress on these important forms of mathematical
reasoning, teachers, administrators, and policy makers cannot determine which curriculum
materials or teaching strategies contribute to mathematical proficiency. Finally, tests that fail
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to emphasize complex problem solving or sustained reasoning communicate an inaccurate
picture of mathematics to students.
These findings also have implications for dispelling stereotypes. Overall, it is clear that, in
the U.S. and some other nations, girls have reached parity with boys in mathematics
performance. It is crucial that this information be made widely known, to counteract
stereotypes about female math inferiority held by gatekeepers such as parents and teachers,
and by students themselves.
Supplementary Material
Refer to Web version on PubMed Central for supplementary material.
Acknowledgments
This research was funded by the National Science Foundation (REC 0635444 to Hyde) and the Eunice Kennedy
Schriver National Institute of Child Health And Human Development (T32 HD049302 to Lindberg). The content of
this paper is solely the responsibility of the authors and does not necessarily represent the official views of the
funding organizations.
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