A friend of mine recently pointed me to the ABC News report surrounding the recent study about the gender gap in mathematics. Generally I have a practice of not believing the media's representation of studies that confound strong stereotypes found within the population because naysayers come out of the woodwork. Moreover, these naysayers seem to miss what the evidence is saying, usually out of a desire to somehow prove the stereotype or an inability to read across disciplines. However, reading across disciplines reflects a skill developed over time. Generally I find that the best strategy when confronted with interdisciplinary reading is to ask a lot of questions.
Meet the naysayer of the hour: Heather Mac Donald. She recently published an article called " Math Is Harder for Girls". She brings up the "More geniuses, more idiots" hypothesis as a way to explain the representational discrepancies in math (and by extension, science and engineering).
First, let's consider what actually appears in Hyde et al. This paper reflects math test data, collected within the NCLB compliance, representative of students, grades 2-11, across 10 states spanning the regional diversity of the United States. It addresses three main arguments: 1) as a whole, girls score lower in mathematics, particularly as they reach high school level mathematics, 2) the variance for boys and girls differ significantly causing an appreciable difference at the outer tails, and 3) girls may have similar basic skills but fall behind when dealing with complicated reasoning tasks.
4 letters in the above synopsis should show us that this study cannot assess the upper echelons of mathematical ability: NCLB. Indeed, as Hyde and company found, the majority of the states had zero test items assessing a depth of knowledge characteristic of strategic thinking or extended thinking. To evaluate item #3, the researchers used a different assessment.
What do the state tests show? Well, previously the way of understanding gender gap involves looking at the mean. "On average (read: mean), boys outscore girls on this assessment." Some tests reflect some strong gender gaps like the SAT or ASVAB. Data collected in 1990 showed that while girls had higher math scores in elementary school by a narrow margin, boys displayed significantly greater mathematical aptitude in high school. Seemingly correlated to this gap was the fact that on average girls took less math classes than boys did. However, since that time, schools have actively encouraged girls to take more math classes. Looking at both sets of data, the difference favoring boys has shrunk from 0.29 to a range between -0.01 and 0.06.* There seems to be a marked shift in the nature of girls' means between 1990 and 2002.
However, Mac Donald does not contest the connection in means. She zooms in more on the question of variance. Basically, if boys have a larger variance, their scores span a greater range. In dividing male variance by female variance, Hyde and company found that all of these scores were larger than one, indicating larger male variance. However, this ratio stayed between 1.11 and 1.21 for all grades investigated. In constructing an image of the bell curve, this means that the bell curve for males is slightly flatter.
To investigate the effect of the differences in variance, Hyde and others looked at data found at +2 SD (95%) and +3 SD (99%) using the data from Minnesota testing. Interestingly, only white and Asian ethnic groupings could be analyzed because "too few students scored above the 95th percentile to compute reliable statistics for these groups: American Indians, Hispanics, and Black not Hispanic." Such a comment leads me to wonder about racial inequities. Anyway, that's not my point today. Among white students, the predictive thread holds: twice as many boys score at the 99th percentile than girls. However, among Asian students, the ratio of male to female at the 99th percentile mark is 0.91. Moreover, the Asian numbers seem considerably lower at both levels suggesting a potential cultural difference. The lack of data points for traditionally underrepresented ethnic groups also supports the idea of cultural difference.
What is more about the article's scholarly integrity, the researchers offer this observation, "If a particular specialty required mathematical skills at the 99th percentile, and the gender ratio is 2.0, we would expect 67% men in the occupation and 33% women. Yet today, for example, Ph.D. programs in engineering average only about 15% women." Given that girls earn 48% of undergraduate mathematics degrees, it could be that these highly qualified women choose between studying mathematics, sciences, and engineering for an array of reasons producing some statistical skew. (I think that undergraduate women engineering majors are somewhere around 20% but I could be mistaken.)
In considering higher order item testing as found using the National Assessment of Educational Progress data, the researchers looked only to mean consideration and did not expand on the variance data.
Personally, the closing the mean differential at all levels of tested mathematical thinking seems like a great start. However, I do wonder about the high-tail data coming exclusively from 1 state when the researchers had 9 other states. Given the discrepancy of national data reporting, it could have been as simple as what the states sent them. I'm no conspiracy theorist.
On a broader level, I am more concerned that teachers teach to tests that only ask about recall and basic skills. I support initiatives to encourage girls to take more math and science classes in high school if for no other reason that such a transcript truly does open choice.
*I'm no statistician but the data points have the same construction. I'm not sure what they mean when they say "pooled within-gender standard deviation."