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Gender, culture, and mathematics performance

Edited by Randy Schekman, University of California, Berkeley, CA, and approved April 2, 2009 (received for review February 5, 2009)
Abstract
Using contemporary data from the U.S. and other nations, we address 3 questions: Do gender differences in mathematics performance exist in the general population? Do gender differences exist among the mathematically talented? Do females exist who possess profound mathematical talent? In regard to the first question, contemporary data indicate that girls in the U.S. have reached parity with boys in mathematics performance, a pattern that is found in some other nations as well. Focusing on the second question, studies find more males than females scoring above the 95th or 99th percentile, but this gender gap has significantly narrowed over time in the U.S. and is not found among some ethnic groups and in some nations. Furthermore, data from several studies indicate that greater male variability with respect to mathematics is not ubiquitous. Rather, its presence correlates with several measures of gender inequality. Thus, it is largely an artifact of changeable sociocultural factors, not immutable, innate biological differences between the sexes. Responding to the third question, we document the existence of females who possess profound mathematical talent. Finally, we review mounting evidence that both the magnitude of mean math gender differences and the frequency of identification of gifted and profoundly gifted females significantly correlate with sociocultural factors, including measures of gender equality across nations.
 exceptional talent
 gender gap index
 greater male variability hypothesis
 International Mathematical Olympiad
 Programme for International Student Assessment
Researchers first began investigating gender differences in abilities and behaviors in the 1880s (1). The scientists of the time concluded that women's smaller brains were sadly deficient. For example, George Romanes declared in 1887 that mental abilities were secondary sex characteristics attributable to brain size (2). Twentyfirst century scientists have vastly better research methods available to them. Moreover, the behaviors and performance of women and men in 2009 are substantially different from what they were in the Victorian era. This article reviews and synthesizes the current evidence on gender differences in abilities, focusing on mathematical skills because of the crucial role they play in success in careers in science, technology, engineering, and mathematics, i.e., STEM fields. The review is organized around 3 questions: Do gender differences in mathematics performance exist in the general population? Do gender differences exist among the highly mathematically talented? Do females exist who possess profound mathematical talent? Last, we consider the evidence concerning the contribution of sociocultural factors to the gender differences observed in measured mathematical performance.
Do Gender Differences in Mathematics Performance Exist in the General Population?
In influential reviews published in 1966 and 1974, the noted developmental psychologist Eleanor Maccoby concluded that gender differences in mathematics performance were scientifically well established, with males scoring higher (3, 4). She documented that boys and girls acquire early number concepts similarly in the preschool years, a conclusion fully supported by contemporary data (5), and that their performance throughout elementary school was similar; however, boys' skills in mathematics increased faster than girls' beginning around 12 or 13 years of age, creating a significant gender gap in performance by high school.
The technique of metaanalysis became available by the 1980s. It provides a powerful statistical method for synthesizing the results of numerous studies on a given question. In research on gender differences, the metaanalyst computes the effect size, d, for each study and then computes a weighted average effect size across all studies (6). The effect size is computed as d = (M_{M} − M_{F})/S_{w}, where M_{M} is the mean score for males (M), M_{F} is the mean score for females (F), and S_{w} is the withingroups standard deviation. Thus, it is a measure of the distance between the male and female means in standard deviation units. Positive values represent better performance by males, whereas negative values represent better performance by females. According to standard guidelines, an effect size of 0.20 is small, 0.50 is moderate, and 0.80 is large (7).
Hyde and colleagues reported a 1990 metaanalysis on gender differences in mathematics performance involving 100 studies representing the testing of >3 million individuals, most from the U.S. but some from other nations such as Australia and Canada (8). Overall, they found d = −0.05 for samples of the general population, an effect so small as to be considered no gender difference. Further analyses explored effects of age and cognitive level of test items on the magnitude of gender difference. Test items were coded as assessing simple computation (i.e., memorized math facts), deeper understanding of concepts, or, at the highest level, complex problem solving. The results indicated a slight female advantage in computation in elementary and middle school, and no difference in high school. There were no gender differences in understanding of concepts at any age. Complex problem solving displayed no gender difference in elementary school and middle school, but a gender difference favoring males emerged in high school, with d = 0.29. This latter finding is of concern because complex problem solving is an essential skill for success in life and in STEM careers.
These findings were largely replicated in a 1995 metaanalysis using large datasets based on the testing of excellent probability samples of U.S. adolescents (9). For high school students, d values ranged between 0.03 and 0.26 for mathematics performance, that is, boys performed better than girls by a small amount.
One prominent explanation for this measured gender difference in math performance in high school has been differential patterns of course taking (10, 11), that is, girls were less likely than boys to take advanced mathematics courses in high school. They were also less likely to take chemistry and physics, other courses where complex problem solving is taught. Lacking this training, girls, not unexpectedly, performed less well than boys on standardized tests.
However, gender patterns had changed by the beginning of the 21st century. Girls are now taking calculus in high school at the same rate as boys, although they still lag behind boys in taking physics (12). In this new environment, do boys' and girls' math scores still differ? Massive amounts of data relating to this question are available because No Child Left Behind (NCLB) legislation in the U.S. mandates that all states test all children in all grades on their proficiency in mathematics. In one recent study, researchers obtained useable data from 10 states representing the testing of >7 million youth (13). Averaged across these 10 states, gender differences in performance were close to zero in all grades, including high school, with d values ranging between −0.02 and 0.06 (Table 1). When analyzed by ethnicity, the same pattern of gender similarities was found for all ethnic groups studied, that is, African Americans, Latinos, Asian Americans, American Indians, and Whites. Thus, girls have now reached parity with boys in mathematics performance in the U.S., even in high school where a gap existed in earlier decades.
However, coding of the test items on these examinations for cognitive level indicated that none of them tapped complex problem solving at most grade levels for most states (13). Thus, it was impossible with these NCLB datasets to investigate whether a gender gap existed in complex problem solving. Therefore, the researchers also examined data from the National Assessment of Educational Progress (NAEP), a federally managed program that tests a random sample of U.S. students each year (14). Items from 12th grade data categorized by NAEP as hard and by the researchers as requiring complex problem solving were analyzed for gender differences; effect sizes were found to average d = 0.07, a trivial difference. These findings provide further evidence that U.S. girls have now reached parity with boys, even in high school, and even for measures requiring complex problem solving.
Some have argued that the absence of gender differences in mathematics performance in the general population is irrelevant to the advancement of STEM fields; rather, researchers should focus on the mathematically talented, a topic discussed below. However, Weinberger found that <1/3 of the collegeeducated white U.S. males in the STEM workforce had high school quantitative SAT scores >650 (15). Thus, progress in STEM fields is fueled, not only by the highly talented, but also by the millions of laboratory technicians and other bachelors and masterslevel scientists whose mathematics skills might place them below the 75th percentile, but whose contributions are still essential.
Moreover, numeracy is important for everyone, with mathematical competency being crucial to anyone shopping for a home mortgage, investing their savings for retirement, or deciding among several treatment options for a serious medical ailment. The recent example of consumers' failure to comprehend adjustablerate mortgages is a sobering case in point. Mathematical skills are essential, not only for accountants, economists, and physicists, but also for teachers, nurses, politicians, and the lay public in general.
Do Gender Differences Exist Among the Mathematically Talented?
The hypothesis that the variability of intellectual abilities is greater among males than females was originally proposed by Ellis in 1894 to explain a phenomenon that seemed obvious at the time: There were both an excess of males among the mentally defective and very few female geniuses (1). If this Greater Male Variability Hypothesis were valid, it could account for the existence of a preponderance of males at the highest levels of performance even when a mean gender difference does not exist, as shown schematically in Fig. 1. This is the hypothesis to which Lawrence Summers was referring when he stated at the National Bureau of Economic Research Conference held on January 14, 2005, “There are issues of intrinsic aptitude, and particularly of the variability of aptitude, and that those considerations are reinforced by what are in fact lesser factors involving socialization and continuing discrimination. It's talking about people who are 3 ½, 4 standard deviations above the mean in the onein5,000, onein10,000 class. Even small differences in the standard deviation will translate into very large differences in the available pool substantially out.”
The statistic used nowadays to test this hypothesis is called the variance ratio (VR), that is, the ratio of male variance to female variance in a distribution. Thus, variance ratios >1.00 indicate greater male variability. Variance ratios calculated from the state math assessments (13) are shown in Table 1. All are >1.00, but the discrepancy in variances from gender similarity is not great, with VRs ranging between 1.11 and 1.21.
Theoretical models have been used to examine the consequences of greater male variance based on the assumption that the scores are normally distributed (16). For example, if d = 0.05 and VR = 1.12, values representative of the ones found in the state assessments, then the ratio of malestofemales scoring above the 95th percentile would be 1.34. At a very high cutoff, the 99.9th percentile, the M:F ratio would be 2.15. Even for a STEM specialty that requires mathematics skills at the latter level, we would expect workers in the occupation to be 68% male and 32% female if math talent were the only factor that mattered. Yet in recent years, for example, women accounted for only 18% of the Engineering Ph.D.s awarded in the U.S. (17). If d = 0.00 and VR = 1.20 as shown in Fig. 1, a field would need to require workers who are at least 4 standard deviations (SDs) above the mean, the 1in20,000 level, to be only 18% females and 5 SDs, the 1inone million level, to be only 9% females.
Theoretical models are, of course, just that. Actual distributions rarely conform exactly to normal ones. Thus, gender ratios in the upper tails of actual distributions were calculated using data from the Minnesota state assessments (13). Results were analyzed separately by ethnicity to ensure that the findings were not limited to the predominantly White samples that have been the mainstay of U.S. research. For students scoring above the 95th percentile, the M:F ratio was 1.45 for Whites, close to theoretical prediction. At the 99th percentile, the M:F ratio was 2.06, again close to theoretical prediction. However, the M:F ratio was only 0.91 for AsianAmericans, that is, more girls than boys scored above the 99th percentile. Analysis of data from 15yearold students participating in the 2003 Program for International Student Assessment (PISA) likewise indicated that as many, if not more girls than boys scored above the 99th percentile in Iceland, Thailand, and the United Kingdom (18). The M:F ratios above the 95th percentile on this examination also fell between 0.9 and 1.1 for these abovenamed countries plus Indonesia, that is, were not significantly different from equal variances (19). These findings challenge the Greater Male Variability Hypothesis, which, if valid, should hold for all representative populations, regardless of ethnicity or nationality.
Two recent studies directly address the question of whether greater male variability in mathematics is a ubiquitous phenomenon. Machin and Pekkarinen (19) reported that the M:F VR in mathematics was significantly >1.00 at the P < 0.05 level among 15yearold students in 34 of 40 countries participating in the 2003 PISA and among 13yearold students in 33 of 50 countries participating in the 2003 Trends in International Mathematics and Science Study (TIMSS). However, these data also indicated that the math VR was significantly less than or insignificantly different from 1.00 for some of the countries that participated in these assessments (e.g., Table 2), a finding inconsistent with the Greater Male Variability Hypothesis.
Penner has performed a detailed analysis of the distributions of math scores obtained by boys compared with girls in each country that participated in the 1995 TIMSS (20). Striking was his finding of considerable countrytocountry variation, not only in the magnitude of the difference between mean male and female scores, but also in the shapes of the distributions, ratios of malestofemales scoring in the right and left tails of the distributions, and difference in standard deviation (SD) between males and females. We have normalized these latter differences to overall within SD for each country such that the numbers >0 in the rightmost column of Table 2 indicate greater male variability. Notable is the fact that numerous countries had a normalized SD difference that was insignificantly different from zero, with 3 even having a negative value, that is, greater female variability. Neither the 10thgrade 2003 PISA nor 12thgrade 1995 TIMSS data gave any indication of greater male variability in mathematics for either Denmark or the Netherlands. As Penner concluded, “The common assumption that males have greater variance in mathematics achievement is not universally true.” Given the absence of universality, the occurrence of greater male variability and scarcity of topscoring females in many, but not all, countries and ethnic groups must be largely due to changeable sociocultural factors, not immutable, innate biological differences between the sexes.
Some studies have focused specifically on the mathematically talented. The best known example is the Study of Mathematically Precocious Youth (SMPY) or Study of Exceptional Talent (SET), an ongoing study originally begun at The Johns Hopkins University in the 1970s (21). These researchers administer the SAT to children <13 years of age who have been identified as mathematically advanced. Their sample is voluntary, and the sampling frame is not well defined. It has also changed over time with respect to sample size and ethnicity, including large numbers of children of immigrants from Eastern Europe and Asia in recent years. In 1980–1982, they reported a very lopsided M:F ratio of 13:1 among students scoring ≥700 on the quantitative section of the examination (21). However, here too, the gender gap has dramatically narrowed with time. The M:F ratio was down to 2.8:1 by 2005 (22, 23). Thus, females now represent at least 1/4 of the mathematically precocious youth being identified in this U.S. talent search. This fairly rapid and dramatic change occurred coincident with enactment of Title IX, the second wave of the women's movement, and greatly increased immigration of Eastern Europeans and Asians to the U.S., points further discussed below.
Do Females Exist Who Possess Profound Mathematical Talent?
No woman to date has been awarded a Fields Medal, the socalled “Nobel Prize of mathematics.” Nevertheless, over the centuries women have made many profound contributions to mathematics, from Hypatia of Alexandria in ca. 400 CE to Professor Maryam Mirzakhani of Stanford University in the 21st century. Notables in between have included MarieSophie Germain, Ada Lovelace, Emmy Noether, Dame Mary Cartwright, Grace Hopper, and Julia Robinson (see www.maa.org/pubs/posterW.pdf for brief biographies of these and some other outstanding female mathematicians). Ingrid Daubechies, Dusa McDuff, Marina Ratner, and Karen Uhlenbeck are among the current members of the mathematics section of the U.S. National Academy of Sciences. Thus, the answer to the above question is emphatically “Yes,” that is, females with profound mathematical talent do, in fact, exist.
With women prohibited from pursuing doctoral studies in mathematics at essentially all universities in the world before the 1890s, let alone being mathematics professors at major research universities, their extreme scarcity before the 20th century was, undoubtedly, largely due to very few women having had the opportunity to develop and use their mathematical talents. Once opportunities began to open up, women accounted for 14%–15% of the Ph.D.s awarded in mathematics in the U.S. during the decades before World War II (refs. 24 and 25 and Fig. 2). However, by the 1950s, this number had plummeted to 5% and did not return to its previous level until the 1980s. In the past decade, the percentage of U.S. mathematics Ph.D.s awarded to females among both U.S. citizens and noncitizens has been hovering at ≈30% (ref. 26 and Fig. 2), a number consistent with the M:F 2.8:1 ratio observed in recent SMPY cohorts (23) and the ≈2:1 ratios for students scoring above the 99th percentile on standardized tests (13, 18). However, U.S. research universities hired many of their STEM faculty in the 1960s postSputnik era when federal funding for science greatly increased and large numbers of baby boomers began to attend college, but Ph.D.level female mathematicians were scarce. These professors have only recently begun to retire, accounting in part for the current large disparity between percentage of female professors in topranked research departments (27, 28) and students of mathematics.
All students identified in the SMPY or who achieve a Ph.D. in mathematics possess both a gift for mathematics and the will to study it intensively. However, only a small subset of this group is truly profoundly gifted in mathematics. To identify the latter, Andreescu et al. (28) examined data on high school and college students who excel at the very highest level in extremely difficult competitions in mathematical problem solving where solutions require the writing of rigorous proofs. One such competition is the International Mathematical Olympiad (IMO) (www.imoofficial.org). The top scorers on the IMO have truly exceptional skills in mathematics, that is, at the 1inamillion level. Because the IMO is taken by 6member teams consisting of very top mathematics students from ≈95 countries, it also provides information regarding cultural differences among nations.
Table 3 lists the names of some female high school students who scored among the very top in the world on the IMO. Some of them (e.g., Ana Caraiani) have also scored among the very top on the intercollegiate William Lowell Putnam Mathematical Competition (ref. 28 and www.maa.org/awards/putnam.html), an examination open only to students who have matriculated to colleges in the U.S. and Canada. Some (e.g., Maryam Mirzakhani) have become tenured professors in very topranked mathematics departments and won prestigious awards for their accomplishments in mathematics research. Thus, females of this profound caliber in mathematics exist.
Table 4 indicates the percentages of students on IMO teams who were female during the past 3 decades for countries whose teams achieved a median rank among the top 30 in recent years. Some of these highranked countries (e.g., Russia, Serbia) had >20% female team members during some decades, a number that should be considered a lower bound on the percentage of the population with profound intrinsic aptitude for mathematics who are female. Noteworthy, however, are the facts that the frequency with which females are members of IMO teams can dramatically change with time, differs quite significantly among countries, and, even, can differ 20 to 60fold among ethnic groups within countries (Table 4 and ref. 28). For example, the U.S. had zero females on its teams throughout the first 23 IMOs in which it participated, finally having 3 females on 5 of its teams during the past 11 years. Likewise, the United Kingdom fielded only 1 female on its teams from 1967 to 1988, yet has had 10 different females on its teams during the past 2 decades, with several participating more than once. During the 13year period immediately before reunification, the German Democratic Republic had 5 females on its teams, whereas West Germany had zero. Since partitioning, Slovakia has fielded 3 times as many females on its teams as has the Czech Republic (28). During the past decade, the Republic of Korea has had 6 female participants versus Japan's zero. Such large differences among genetically related populations and rapid changes over time within countries in the frequency of identification of females with extreme talent in mathematical problem solving cannot be primarily due to biological factors.
Role of Culture in Nurturing Mathematical Talent
Current research provides abundant evidence for the impact of sociocultural and other environmental factors on the development and nurturing of mathematical skills and talent and the size, if any, of math gender gaps. The evidence comes from both crossethnic and crossnational studies and the abovecited changes observed within countries over time in the general, SMPY, and IMOlevel populations.
Several researchers have investigated crossnational patterns of gender differences in math performance, studies that also provide clues as to the specific cultural factors that most affect outcomes. Baker and Jones (29) found that the magnitude of the mean gender difference in mathematics performance on the Second International Mathematics Study (SIMS) significantly correlated, across nations, with measures of gender inequality. For example, the size of the math gender gap correlated −0.55 with the percentage of women in the workforce in those nations. Likewise, Guiso and colleagues (18), using 2003 PISA data testing 15yearolds from 40 countries, found that gender inequality as measured by the World Economic Forum's Gender Gap Index (GGI) (30) significantly correlated with the magnitude of the mean math gender gap. The GGI provides a measure of the gap between men and women in economic participation and opportunity, educational attainment, political empowerment, and health and survival; the closer it is to 1.00, the smaller the gender gap on these measures. In other words, Guiso et al. (18) concluded that the math gender gap varies across nations; nations with greater gender equality typically have a smaller math gender gap.
Regarding change over time, the likeliest explanation for the dramatic improvement in math performance by U.S. females lies in 2 recent cultural trends: (i) girls in general taking more mathematics and science courses during high school due, in part, to changes in requirements for graduation and admission to colleges, and (ii) the opening up to females shortly before or after enactment of Title IX in 1972 of STEMintensive specialty high schools, colleges, and graduate schools along with career opportunities in STEM fields. These 2 trends are intimately connected.
The increase in women pursuing careers in STEM has been quite dramatic in some STEM fields. For example, only 14% of the U.S. doctoral degrees in the biological sciences went to women in 1970, whereas this figure had risen to 49% by 2006 (31). Entry into other STEM areas has been slower, yet substantial. For example, 5.5% of U.S. doctoral degrees in the physical sciences were awarded to women in 1970, compared with 30% in 2006; the percentages in mathematics and statistics were 8% in 1970 and 32% in 2006 (26, 32). Clearly, numerous women are willing and able to learn the mathematics needed for advanced degrees in these areas when provided with an appropriately nurturing sociocultural environment along with educational and career opportunities.
The Guiso study (18) also provides data relevant to the Greater Male Variability Hypothesis discussed earlier. Whereas the U.S. ranked a dismal 36th out of 40 countries in the ratio of 15yearold femalestomales scoring above the 99th percentile in the 2003 PISA, the United Kingdom had equal numbers of girls and boys scoring above this percentile, and Iceland and Thailand actually had more girls than boys above this cutoff. These authors concluded that a strong correlation exists between a country's measures of gender inequity and the size of the math gender gap both at the mean and the right tail of the distribution.
In new analyses, we calculate a Pearson correlation of −0.34 (P < 0.05) between the ratio of malestofemales scoring above the 95th percentile on the 2003 PISA (supplementary online material accompanying ref. 19) and the 2007 GGI (30). Likewise, we find a correlation of 0.44 (P < 0.05) between the percentage of girls on a country's IMO teams during the past 2 decades (Table 4) and its 2007 GGI (Table 5 and Fig. 3). These findings stand in distinct contrast to Machin and Pekkarinen's (19) claim that no correlation exists between GGI and VR for mathematics.
Noteworthy in this context is the fact that the U.S. ranked only 31st best, between Estonia and Kazakhstan, among the 128 countries included in the 2007 Global Gender Gap Report (30). Countries such as the U.K. and Iceland, where the ratio of girlstoboys scoring above the 99th percentile in the 2003 PISA was close to 1.0 or favored girls, had a GGI rank of 11 and 4, respectively. Likewise, Denmark and the Netherlands, where the VR was essentially 1.00, had GGI ranks of 8 and 12, respectively.
Similarly, Penner's crossnation analysis of the 1995 TIMSS data (20) showed that the proportion of girls scoring above the 95th percentile positively and significantly correlated with several measures of female equality and status, including equity in educational opportunities and representation in the labor force and political offices. Numerous findings in Penner's recent study contradict the Greater Male Variability Hypothesis for mathematics. Our finding that the percentage of girls on a country's IMO team significantly correlates with its GGI, but not with its median IMO team rank or percentage of world population (Table 5), is also inconsistent with the Greater Male Variability Hypothesis. If this hypothesis were valid, these latter factors should inversely and significantly correlate with percentage of girls because (i) the best 6member IMO teams consist of multiple students gifted at the 1inamillion level where females would be rare, and (ii) countries with larger populations would be more likely to have several such 5SDabovethemean students; the GGI would be largely irrelevant.
Thus, we conclude that gender inequality, not greater male variability, is the primary reason fewer females than males are identified as excelling in mathematics at the high and highest levels in most countries. Of course, gender inequity is complex and multifaceted. It can encompass dynamics in school classrooms leading teachers to provide more attention to boys; guidance counselors, biased by stereotypes, advising females against taking engineering courses; mathematically gifted girls not being identified and nurtured; scarcity of women role models in mathintensive careers leading girls to believe they do not belong in them; unconscious bias against females in hiring decisions; and hostile work environments leading qualified women to drop out in favor of friendlier climes. The data reviewed here did not determine which of these and other genderrelated factors are most influential; all likely contribute to some degree.
Conclusions and Future Directions
This review was organized around 3 questions: Do gender differences in mathematics performance exist in the general population? Do gender differences exist among the highly mathematically talented? Do females exist who possess profound mathematical talent? The answer to the first question is that U.S. girls now perform as well as boys on standardized mathematics tests at all grade levels. Among the mathematically gifted, there may be as many as 2 to 4fold more boys than girls depending on precisely where the cutoff is set. However, this gender gap, too, has been closing over time at all levels, including even in the IMO. Thus, there is every reason to believe that it will continue to narrow in the future. Moreover, the gender ratio favoring boys above the 99th percentile is not ubiquitous and correlates well with measures of a country's gender equity, strongly indicating that the gap is due, in large part, to sociocultural and other environmental factors, not biology or gender per se.
One serious policy concern that arose from the Hyde et al. study (13) is that the tests developed by states in the U.S. to comply with the mandates of NCLB include almost no questions requiring complex problem solving. NCLB puts pressure on teachers to try to get all their students to pass, thus leading them increasingly to teach to the test (32). With complex problem solving not covered, mathematics teachers will be tempted to neglect teaching it in favor of teaching computation and other lowerlevel mathematics skills. Yet problem solving and highlevel mathematical reasoning are essential skills for success in life and STEM careers. This neglect of problemsolving skills could place U.S. students at a disadvantage compared with their peers in countries where teaching and tests emphasize more challenging content (33). Therefore, it is crucial to address this issue.
Importantly, the U.S. also needs to do a better job of identifying and nurturing its mathematically talented youth, regardless of their gender, race, or national origin. Doing so is vital to the future of the U.S. economy as documented in Thomas Friedman's The World Is Flat: A Brief History of the TwentyFirst Century (34). Beyond Bias and Barriers: Fulfilling the Potential of Women in Academic Science and Engineering (35), Rising Above the Gathering Storm: Energizing and Employing America for a Brighter Economic Future (36), Foundations For Success: The Final Report of the National Mathematics Advisory Panel (37), and Identifying and Cultivating Extraordinary Mathematical Talent (38) outline numerous steps the U.S. can and should take to ensure we have the welleducated labor force needed to fill the STEM jobs of the future.
Acknowledgments
We thank Jonathan Kane and Jennifer Petersen for help with making figures and performing statistical analyses and Marcia Linn and Cathy Kessel for comments on the manuscript. This work was supported by National Science Foundation Grant REC 06354444 (to J.S.H.) and funds from The Wisconsin Alumni Research Foundation (to J.E.M.).
Footnotes
 ^{1}To whom correspondence should be addressed. Email: jshyde{at}wisc.edu

Author contributions: J.S.H. and J.E.M. analyzed data and wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.
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 Article
 Abstract
 Do Gender Differences in Mathematics Performance Exist in the General Population?
 Do Gender Differences Exist Among the Mathematically Talented?
 Do Females Exist Who Possess Profound Mathematical Talent?
 Role of Culture in Nurturing Mathematical Talent
 Conclusions and Future Directions
 Acknowledgments
 Footnotes
 References
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