# Mathematics and Education

A slow blog

## Who is the Most “Mathematically-intensive” of Them All?

Well, mathematics, of course. But what comes after that? Engineering, computer science, or economics perhaps? Answers differ, even according to the same definition of “mathematically intensive.”

In their article “Women in Academic Science: A Changing Landscape,” Ceci, Ginther, Kahn, and Williams categorize “mathematically-intensive” fields “on the basis of the mean GRE quantitative scores of graduates [sic] students in each field,” resulting in the figure below.

Figure 9. Percentage of PhDs awarded to females across STEM fields as a function of fields’ average GRE Quantitative Reasoning scores. Data shown here are drawn from Educational Testing Service (http://www.ets.org/s/gre/pdf/gre_guide.pdf) and the WebCASPAR database (https://ncsesdata.nsf.gov/webcaspar/).

Their summary: “the more math, the fewer women.”

This is not the case when computer science and mathematics are disaggregated. Moreover, other aspects of Figure 9 are puzzling. Here’s a quick plot of average GRE scores from the GRE Score Guide (the source cited by Ceci et al.) against percentages of female PhDs from the National Science Foundation.

It’s understandable why some names in Figure 9 might differ from those in the GRE Score Guide because Figure 9 combines statistics from NSF and ETS. Names and classifications of fields are not the same at each. Not so understandable are some differences between the scores in Figure 9 and GRE Score Guide.

 Name and score in Figure 9 Score and name in GRE Score Guide, Table 4 Psychology 149 149 Psychology Life Science 151 151 Life Sciences Social Science 152 150 Social Sciences Geoscience 154 154 Earth Sciences (? no scores given for Geosciences) Economics 159 160 Economics Physical Sciences 159 158 Physical Sciences Engineering 160 159 Engineering Mathematics/Computer Science 160 157 Computer and Information Sciences 162 Mathematical Sciences

Reasons for some discrepancies are easy to guess. In the ETS classification, Physical Sciences includes Computer and Information Sciences, and Mathematical Sciences. The score listed may be a weighted average of other fields that ETS lists under Physical Sciences. Similarly, the score computed for Social Sciences might have excluded scores for Psychology and Economics.

In the GRE Score Guide, Mathematical Sciences are composed of Actuarial Science, Applied Mathematics, Mathematics, Probability, Statistics, Mathematical Sciences—Other. Also, Computer Science is a subcategory of Computer and Information Science. However, the Guide does not give scores for these categories. Perhaps the GRE scores did not come from the GRE Score Guide, but from some other ETS source. But, if that’s the case, why not report scores separately for Mathematics and for Computer Science? (And why ignore the more general categories?)

Reasons for the discrepancies in scores for Economics and Engineering are harder to guess. Suggestions are welcome.