Saturday, February 6, 2016

Gender Gap in Math and Science

Most of the publications on the gender gap in math and science are in the fields of psychology and education. The most important questions are about the existence of the gap, what explains it, and whether the gap in early stages of education explains the subsequent career paths of men and women.
Researchers use data of standardized test scores in math and science.[i] The methodology usually compares moments (mean, median, and variance).  Benbow and Stanley (1980, 1983, and 1988), among many other papers, were the early studies to analyzing the gender gaps in mathematical reasoning ability. They presented evidence that male and female students performances in math and science are almost equal, on average, and sometimes females were even better than males, however, females are less likely to choose science and math careers.[ii] 

Recent studies include The European Commission study (2009), which analyzed TIMSS and PISA data sets to report small differences in average performance, where males’ achievements in math are greater than females at later school years, and are especially noticeable among students who attend the same teaching programs and year groups. It reports very small differences in science in favor of males. And, males are worse than females in reading.[iii] 

For the United States, Hyde et al. (2008) report that the gender gaps in math in the general population, grade 2 to 11, were trivial. On average, they found no gender gaps in test scores of 7 million students. They also found greater males’ variability, where ethnicity, i.e., whites versus Asian/Pacific Islanders, seems to matter. The causes remained unexplained.[iv]

Andreescu et al. (2008) examined data from the Study of Mathematically Precocious Youth (SMPY), Putnam Mathematical Competition, and the International Mathematical Olympiad (IMO). They found that culture is not an explanatory variable of the gender gap; and the gender gap in math is smaller in societies with more gender equality in general.

The TIMSS’ report on gender differences (2007) finds a few gender differences in average mathematics achievement at the 4th and 8th grades. At the final year of secondary school, TIMSS report that males in 18 out of 21 countries have significantly greater achievements in mathematics. In science, gender gaps in achievement favoring males were present in one-third of the countries even as early as the fourth grade. At the eighth grade in science, the gender gap was even wider with males performing significantly higher than females in nearly two-thirds of the countries.
There has been a lot of media interest in this subject because it’s a sensational issue. When Lawrence Summers, Ex-president of Harvard University, said that males are innately better than females in math the news media was on fire. He resigned his position.

There is also a tendency to jump to policy. Many want to spend more money on improving teacher’s ability, increasing teacher’s pay, reduce poverty, build better equipped schools, etc. Everyone has an agenda and search for evidence to support it.

From economic point of view, I do not think we have a problem. Maybe this is why economists were relatively less active in this area of research. It’s unclear how the ratio of male to female mathematicians (the gender gap) or scientists affects the economy.

I tested the gender gap using the TIMSS data. The data are from the study cycles 1995, 1999, 2003 and 2007 for 1,426,402 students drawn from 44090 schools representing tens of countries from all over the world. However, my test is more than testing whether the means (averages) are equal, but rather tests whether every observation in the distribution is equal.[1] Without going into the technical details, the results are summarized as follows. These are two matrices showing the 4th grade and 8th grade math and science test scores. They report the percentages of countries in the total sample, where the distribution of the scores of boys dominates; whether the girl’s dominates; and where is gender equality (zero-gap). They also report the same results for the top tail of the distribution (the top 10 percent). I kept the name of the countries in the case of gender equality because they are interesting. Boys dominate.

Gender equality is intriguing and more challenging to explain than the gender gap because equality means no gap, or no variation in the data. We simply cannot explain no-variability using conventional econometric techniques.

The only information available in TIMSS that could be used to shed light on the results of gender equality is about the type of school – the single-sex schools – or the segregated schools. This has been identified in the literature as a cultural issue and that it might explain why boys and girls do equally well in these countries. I repeated the test to test whether school segregation explains the gender equality. The test  cannot reject the null hypothesis that segregated schools distributions is equal to all non-segregated schools distributions, except in a few cases, where females clearly dominate. In math and science, Iran’s segregated schools at the 4th grade dominate. In science, El Salvador, Singapore and Dubai segregated schools dominate. Segregation explains only two of our original results for gender equality and females’ dominance (Singapore and Iran. In the 8th grade case, the test provides a little more support and explain why some countries have females’ distributions dominate, but the results do not explain that for every case where there are no gender differences or females’ domination. One wonders about the cultural common denominator between Iran, El Salvador and Singapore. I see none. Further, many of the countries, which have gender equality in math and science, do not have gender equality in general.  

Jonathan Kane, one of the authors of the paper cited above, has been reported saying that “girls living in some Middle Eastern countries, such as Bahrain and Oman, had in fact, not scored very well, but their boys had scored even worse, a result found to be unrelated to either Muslim culture or schooling in single-gender classrooms.”   

New Zealand is one of the OECD countries in addition to Canada and Sweden among all other non-OECD, Russia, and Islamic and Arabic countries, where there is gender equality. So we have no gender gap issue in New Zealand to waste our time with. Boys and girls are equally good or bad in math and science. I do not know whether this is a bad or a good outcome, but surely it could be good news for those who care about equality. However, if Kane is right then there should no reason to celebrate the gender equality result I found.    

Summary of the results
Matrix I- The 4th Grade, TIMSS, 1995, 2003, and 2007


Full sample
Top 10%
Full sample
Top 10%
Males Dominate
Females Dominate
1. Greece; 2. Ireland; 3. New Zealand; 4.Algeria; 5. Kuwait; 6. Qatar; 7.Yemen; 8. Dubai; 9. Iran; 10. Georgia; 11. Latvia; 12. Russia; 13. Ukraine; 14. Chinese Taipei; 15. Singapore; 16. Mongolia

1. Greece; 2. Ireland; 3. Algeria; 4. Tunisia; 5. Moldova; 6. Georgia; 7. Russia; 8. Ukraine; 9. Kazakhstan; 10. Philippines; 11.Thailand; 12. Mongolia

Canada (BC); 2. Israel; 3. New Zealand; 4. Sweden; 5. U.K.; 6. Algeria; 7. Kuwait 8. Morocco; 9. Qatar; 10. Yemen; 11. Dubai; 12. Iran; 13. Latvia; 14.Lithuania; 15. Russia; 16. Ukraine; 17.Kazakhstan
1. Norway; 2. Sweden; 3. Algeria4. Morocco; 5.Tunisia; 6. Dubai; 7. Moldova; 8. Georgia; 9. Russia; 10. Kazakhstan; 11.Philippines; 12.Mongolia


Matrix II - The 8th Grade, TIMSS, 1995, 1999, 2003, and 2007


Full sample
Top 10 %
Full sample
Top 10%
Males Dominate
Females Dominate
1.Finland; 2.Iceland; 3.New Zealand; 4.Norway; 5.Slovenia; 6.Sweden; 7.Egypt; 8.Kuwait; 9.Jordan; 10.Oman; 11.Palestine; 12. Qatar; 13.Saudi Arabia; 14.Syria; 15.Dubai; 16.Bosnia & Herzegovina; 17.Iran; 18.Moldova; 19.Malaysia; 20.Georgia; 21.Macedonia FYR; 22.Lithuania; 23.Romania; 24.Russia; 25.Ukraine; 26.Chinese Taipei
1. Canada (BC); 2. Finland; 3. Iceland; 4. Syria; 5. Dubai; 6.Bosnia & Herzegovina; 7.Iran; 8. Moldova; 9.Malta; 10.Cyprus; 11.Armenia; 12.Georgia; 13.Ukraine; 14.Philippines; 15Mongolia
1. Algeria; 2.Egypt; 3.Kuwait; 4.Jordan; 5.Oman; 6. Palestine; 7.Qatar; 8.Saudi Arabia; 9.Bosnia & Herzegovina; 10.Iran; 11.Moldova; 12.Malta; 13. Macedonia, FYR; 14. Serbia; 15.Philippines; 16.Mongolia
1. Canada (BC); 2.Lebanon; 3.Dubai; 4. Iran; 5.Moldova; 6.Malta; 7.Armenia.


Andreescu T., A., J. A. Gallian, M. Kane, and J. E. Mertz, (2008), Cross-Cultural Analysis of Students With Exceptional Talant in Mathematical Problem Solving, otices of the AMS, Vol. 55, no.10, 1248-1260

Benbow, C.P., (1988), Sex Differences in Mathematical Reasoning Ability Among The Intellectually Talanted, Behavioral and Brain Sciences, 11, 169-183, 225-232.

Benbow, C.P. and J. C. Stanley, (1983), Sex Differences in Mathematical Reasoning Ability: More Facts, Science, 2222, 1029-1031.

Benbow, C. P. and J. C. Stanley, (1980), Sex Differences in Mathematical Reasoning Ability: Facts or Artifacts? Science, 201, 1262-1264.

Benbow, C.P., D. Lubinski, D.L. Shea, and H. Eftekhari-Sanjani, (2000), Sex Differences in Mathematical Reasoning Ability: Their Status 20 Years Later, Psychological Science, 11, 474-480.

Hutchison, D. and I. Schagen, (2007), Comparisons between PISA and
TIMSS: Are we the man with two watches? In Loveless, T. (Ed.), Lessons learned: What international assessments tell us about math achievement, 227–261, Washington, DC: Brookings.

Hyde, J.S. and J. E. Mertz, (2009), Gender, Culture and Mathematics Performance, Proceedings of the National Academy of Science, USA, 106, 8801-8807.

Hyde, J.S., S.M. Lindberg, M.C. Linn, A. Ellis, and C. Williams, (2008), Gender Similarities Characterize Math Performance, Science 321, 494-495.

Hyde, J.S., (2005), The Gender Similarities Hypothesis, American Psychologist, 60, 581-592.

Hyde, J.S., E. Fennema, M. Ryan, L.A. Frost, and C. Hopp, (1990), Gender Comparisons of Mathematics Attitudes and Effects, Psychology of Women Quarterly, 14, 299-324



[1] First-Order Stochastic Dominance is tested using the powerful Rank Sum Test of (Wilcoxon, 1945).

[i] Commonly used data include Program of International Student Assessment (PISA) of the World Bank, Trend in International Math and Science Study (TIMSS), The U.S. SAT test scores, Study of Mathematically Precocious Youth (SMPY), Putnam Mathematical Competition, and the International Mathematical Olympiad (IMO). 
[ii] Also see Benbow and Stanley (1983), Benbow (1988), Benbow (1992), Benbow et al. (2000)

[iii] Also see for example Hutchison  and  Schagen (2007).

[iv] Also see, Hyde (2005), Hyde et al. (1990), and Hyde and Mertz (2009).