Sunday, August 14, 2005

Spelke on Math   posted by Razib @ 8/14/2005 01:35:00 AM

Here is a paper by Elizabeth Spelke (in press) where she argues against intrinsic differences in mathematical aptitude. I assume readers will actually read the paper before commenting. Frankly, I'm not familiar with much of the literature she draws upon to judge its veracity, so until I can dig deeper, I won't offer any comment.

Update: I am cutting and pasting Alex's comment here:

My comments:

1. She gives the impression that strategies are independent of cognitive ability (and implies that they are environmentally mediated). While it is true that people can be taught problem-solving strategies, there is no reason to believe that, taught a strategy for a given problem in a situation, one automatically generalizes it to novel problems and situations. It is akin to being taught how to answer the problem on an IQ test. Yes, people can be taught how to answer these types of questions and can score higher than what their ``true" score is, bt this does not mean that said training generalizes to the world around them.

2. The areas she lists that girls outperform males (e.g., verbal fluency, calculation) are much more memory loaded, whereas the areas she lists that boys outperform females (e.g., analogies, mathematic word problems) are much more akin to Spearman's eduction of relations and correlates. This is not a mere strategy preference, but a leaning on very different cognitive mechanisms.

3. Minor note: Gallagher's paper deals with the GRE, not the SAT-M. Moreover, my reading of the technical report (it available electronically here) is that males outperformed females on most, if not all, the item sets. I only skimmed it, though.

4. Her statement that "the SAT-M could be made to favor either males or females by suitable choice of items" is technically true, but in doing so, you would have to refine your definition of mathematics to such a degree that it no longer resembles mathematics. Robert Williams did this with the BITCH; he redefined intelligence to mean the understanding of East St. Louis Black ghetto slang, then tried to show a) how other racial groups were inferior on the BITCH and b) how biased other tests were (that were developed on the 100+ years of research into human cognitive abilities) since they didn�t correspond with his definition and instrumentation.

5. Her notion that interests and social forces w.r.t. math aptitude are inert in "real high school and college classrooms" and that only during some magic time of post-secondary instruction do they avail themselves is ass.

6. GPAs are fraught with problems when comparing within a school unless there is a very close core curriculum between the ``comparees.� Between schools, it becomes even worse. Moreover, Spearman addressed the whole issue of the foibles of using teacher perceptions of ability (grades) vs. using a standardized measurement instrument 70 years ago (see Abilities of Man). If the crux of the argument here is girls get better grades, then me thinks she needs to get a better argument.

7. "From adolescence onward, males are females show somewhat different cognitive profiles, but they are equally able to learn mathematics." What? Says who? Where? Talk about a non-sequitor (see her previous sentence)

8. My favorite absurdity in the whole paper:

American high school boys show greater variability on the quantitative SAT, but American college men and women are equally proficient at learning advanced mathematics....

Res ipsa loquitur

Further comment from Razib: #8 is the one that really seemed sketchy to me. It seemed that some of the assertions were just assertions, though there were literature reference, and I would have liked to know what she meant or how she came to some of the conclusions. How do you objectively assay proficiency at "learning advanced mathematics?" There is a wide range of variance of competency among those who graduate with mathematics degrees, even among good students, from what I have known.