John Tierney has annoyed me before on the subject of women in science. And now he’s back, this time recapping the conventional wisdom that math departments like mine are 90% male because of the inborn boyish math power we men possess. He styles this as “daring.” The chutzpah!

Anyway, this time around he presses some perfectly respectable social science into service. Here’s a fact: more boys than girls get perfect scores on the math SAT. And a recent study by Jonathan Wai, et al found that that among students who scored over 700 on the math SAT in 7th grade — just 1/10,000 of their sample — boys outnumbered girls by about 13 to 1 in the 1980s, a figure which dropped to 4:1 by the early 1990s and has stayed roughly constant since.

Now here’s how the standard — oops, sorry, I mean “daring” — argument goes: mathematicians surely possess a math aptitude among the top 1 in 10,000 of the population. That segment of the population is mostly men, as proven by science. Ergo, most mathematicians should be men.

A mistake here, or at least a potential mistake, is thinking of success in mathematics as something driven by a variable called “aptitude”, which can be measured on a scale — as if getting tenured at Harvard were something like getting a 10 million on the math SAT. Wai et al find that girls make up a substantial majority of extremely high 7th grade scorers in the English and writing sections of the exam. Should one conclude on aptitudinal grounds women should be a majority among English professors? It’s easy to mistake your operationalizations for reality, as when Wai et al write:

Giving the SAT-M in the 7th grade allows individual differences in the extreme right tail of the distribution (i.e., the top 1% which includes over one third of the ability range) to be captured adequately

I can think of lots of things they might mean by “one third of the ability range” but none which have any content.

Not that I’m saying it’s meaningless to ace the SAT before getting your driver’s license. It’s a vanishingly small proportion of people who get a 700 on the math SAT at 13. But I’d think it would be a very small proportion of mathematicians too! If 10% of mathematicians were extreme child math prodigies, and those extreme child math prodigies are 80% boys, one hasn’t gone far towards explaining why US math research faculties are overwhelmingly male.

There’s actually an empirical question here which I know nothing about. So let’s contribute to my know-nothingness by undertaking a brutally unscientific survey. If you’re a working mathematician — say, a Ph.D. student in good standing or a faculty member at a university — did you score above 700M on the SAT when you were 13 or younger? Since I think it’s a fairly small proportion of the world that takes the exam that early, let’s ask a more widely applicable question as well: if you took the SAT as a senior in high school, did you get 800 on the math section? (If you answer this, you might mention whether you took the exam before or after the 1995 recentering.)

When I was in 7th grade (before 1995), I got a 610 on the math part and a 680 on the verbal part. In 12th grade (after 1995), I got an 800 on both parts.

I was smart enough as a kid, but very far from a math prodigy. I doubt I was even among the top 5 math students in my (public and not very wealthy) high school.

I took it once as a senior and got 790.

I didn’t take the SAT in 7th grade. When I took it at the end of 11th grade I did get an 800 (recentered) on the math section.

I took the SAT once, when I was a senior in high school (after 1995). I got 800 on the math section.

What’s the SAT?

(Seriously, can one expect to obtain evidence for physiological human features by studying a test that is so highly specific to a certain country and time period?)

I think Kowalski captured the main fallacy of such studies. Mathematics is studied since the dawn of civilization in all cultures and nations. Compared to other scholarly disciplines: what is the proportion of women in different historical periods? Is that proportion rising with the recent emancipation of women?

790 as a junior in 1993. Also took it in 7th grade, but don’t remember my score…600? Anyway, definitely below 700.

Yes to 700+ when 13 or younger. (Took it to qualify for CTY, though in fact I never went.) This would’ve been around 1988.

I got a 710 I think at 13, and a 790 I think at 17, both before 1995. The whole idea of taking the SAT before you need to now seems kinda perverse.

I took the SATs officially after 1995 when I was a senior, and I got 800 on the math section. I *think* when I took a practice exam the first time when I was 14, I got a 780.

I’m not sure why people hold so staunchly to this hypothesis that aptitude in mathematics must be innate. (Could this be tied into our math phobic culture so the majority feel a need to explain that the reason they feel they’re not as good is an innate talent that they’re not born with as opposed to maybe they just didn’t try as hard?) I mean, I find it pretty ridiculous for people to assert that their inquiry of gender difference as “purely scientific.” What leads somebody to hypothesize in the first place that differences on achievement of the SATs must be innate rather than oh, say at least 13 years of societal messages that girls can’t and don’t need to do math. is purely based on their own biases and NOT science. This is often what frustrates me the most about these claims. Why should we be working to prove that women are just as capable instead of them working to prove that we are not?

I also can’t help but wonder if Tierney would “dare” to make the claim that intelligence and aptitude is also racially based. After all, just look at the shape of my skull! Everybody knows asians are better at math. I must’ve gotten an above 700 score on the math portion of the SATs because I “overcame” my gender with my race.

Okay, I’ll quit with the sarcasm.

800 in 1974 or 1975. Now an active tenured mathematician.

I did not take the SAT in 7th grade. I took it in 1994 and got a 760.

680 in 7th grade, 800 in 11th grade. Both well before 1995.

Not a mathematician, but in 7th grade (after 1995), I scored a 1280, of which I think around 680 was math. In junior year (also, coincidentally, after 1995), I scored a 790. (I could never execute that much simple math without making a stupid mistake.)

Sadly, I think John Tierney will continue to annoy us for many years — it takes a special talent to turn proof positive that social forces effect relative academic performance (13 : 1 -> 4:1 in the course of two decades) into an argument that one gender is fundamentally better at math.

Emmanuel: the SAT is the most commonly used college admissions exam in the US. At least when I took it, the math part test quite elementary algebra, geometry, and logical reasoning skills (there’s no calculus or statistics).

Survey: I did take the SAT in middle school. I don’t remember my score, but I think it was in the 600s. When I took the SAT for college admission, I think I got 700 or 720. In both cases, as a percentile I did much better on the verbal portion than the math. Therefore, by Tierney I should be an English professor…

680 at 14, 800 at 15 (in 1985). Now tenured.

There _might_ be a reporting bias in these comments…

But I have no idea which direction the bias would go! Thus, the numbers are completely reliable. SCIENCE!

Sounds more like SOCIAL SCIENCE than SCIENCE to me.

Ob xkcd: Stand back, I’m going to try SCIENCE!

I suspect that anyone who has already developed an interest in mathematics before high school and eventually becomes a mathematician is highly likely to have an SAT math score of 800. For anyone who has learned to think mathematically, the test is just too easy. I therefore conjecture that most mathematicians who did not get an 800 developed their interest and skills in math later.

In the 7th grade (~1994) I got a 640. Freshman year I got a 780. Junior year I got a 780 again, and angrily called it quits.

I got an 800 on the math SAT when I took it as a senior. At 13, I think I got a 590 (after 1995).

There were a handful of other students in my high school classes who had comparable aptitude for math (at least as I perceived it then), but AFAIK none of them were interested enough to do pure math. Funnily enough, last time I went back to talk to some of my high school teachers, they told me they’d expected me to become a physicist.

I took the SATs in 7th grade. I scored 680 on math and 650 on verbal (which would be a 720 on verbal now, post-centering), which qualified me for SET (where I assume they’re getting their data from), but in verbal not math. Took SATs again in 9th grade and got an 800 math (I was trying to convince local colleges to let me take classes, and dropping high SAT numbers opened doors) which then went down thereafter.

I don’t think it’s that I was way smarter in 9th grade than in 7th, what had happened was that I took Algebra II, Geometry, Trig, and Calculus in the intervening time. So an early 700 in math means *someone let you take good math classes early.* It’s a very poor proxy for mathematical aptitude *even at the 7th grade level* which is itself a poor proxy for adult mathematical aptitude (granting, ad arguendo, that such a thing exists).

Yes, over 700 by 13; yes, 800 in high school; both before 1995.

The quickest way to deflate the argument Tierney regurgitates, namely that standardized tests in the US show that boys are innately more likely to be math-awesome than girls, is to simply check the analogous data in other countries. If the difference is genetic, it will show up all around the world, right? … oops, game over.

I can’t remember my exact numbers, but I think it was something like

640 in 7th grade

790 my junior year

I wish I could have taken more math when I was younger. From what I remember my dad gave me a crash course in the elementary geometry on the SAT before I took it in 7th grade. In those 45 minutes I gleaned enough to answer all of the geometry problems on the test, though I guess I have no idea if they were correct *laughing*

I took the SAT’s in 7th grade (to qualify for CTY) and I remember that I got at least 650, and it might have been above 700 in math. If I had to guess, I’d say 690. Clearly knowing where I fell is vital to predicting how good my future research will be. And clearly, if it was 690, I’m another woman who can’t quite cut it at the top end of mathematics.

Got 800 on SAT math in high school, or maybe 790. All of this was in the 80’s.

730 at age 13 (before recentering), 800 at age 16 (after recentering). It feels a little weird discussing this online; am I the only one who grew up under the impression that it was taboo to mention precise test scores?

Did not take in 7th grade. Scored 800 in high school, pre-1995.

740 at age 10 (after recentering) — and having never gone to school, in case that’s relevant. Never retook the SAT. Now a Ph.D. student.

I received a 700 Verbal and 680 Math circa 1987 and ended up with a PhD in experimental physics from MIT (Math-Physics ScB from Brown). Never was any good at SAT math… much better at BC Calculus AP exam… got a 5.

It seems the numbers here are in favor of strong 7th grade scores correlating with careers in math. Not me (currently a research I postdoc).

7th grade (pre 95) was 460 math (before taking algebra I).

Although I’m a lay reader, I’m pretty interested in the women in academia issue and I know of some studies that look at the empirical question Prof. Ellenberg posed. This paper by David Lubinski includes a review of a lot of findings in relatively limited space. Among the youths in the Study of Mathematically Precocious Youth, the mean score of students who eventually tenure track faculty in math, science, or engineering was 696 with the lowest score being 580. (There were eighteen kids who eventually did this).

Lubinski, D. (2009). Exceptional cognitive ability: The phenotype. Behavior Genetics, 39, 350-358.

The data is interesting, but there are some problems (it seems to me) with Tierney’s assertions. There isn’t much direct evidence concerning genetic and hormonal linkages to high ability, as measured by scoring really well on the SAT or ACT as a young person. Twin studies suggest a strong role for genes in the development of cognitive ability, and the SMPY has looked for genes for high ability by comparing some of their participants to control groups in the population. The studies have yet to find any replicable linkage between any gene and high ability, though. There are hypotheses out there as to why more males score at the highest levels of aptitude tests, but some of them are quite speculative (http://pps.sagepub.com/content/4/6/622.full.pdf+html).

Another recent review found there aren’t any hypotheses about the relationships between mathematical ability and genes or hormones with strong, consistent empirical support.

Ceci, S.J., Williams, W.M., & Barnett, S.M. (2009, March). Women’s underrepresentation in science: Sociocultural and biological considerations. Psychological Bulletin.

Tierney takes an awful lot for granted in assuming the figures from the study simply reflect innate characteristics, especially because there isn’t an expansive literature that links a specific pattern of genes or hormones to performing at the right tail of quantitative ability.

I really don’t understand why people believe in intelligence/aptitude tests so much. In my case, I took the PSAT around 1990 and got a 72 on the math portion. Since I wanted to go to a good college and major in a science area I decided to work hard to improve my score. I ended out getting an 800 on the math part. My improvement on the AHSME (another supposed aptitude-type test) was even more dramatic, I increased 40 points in one year and ended out in the top 10 in my (large) state. Did I suddenly become more intelligent? I certainly had covered the material when I had taken the earlier exams. But I had been working on my math pretty hard since then.

Surely many people 13 or younger who are capable of hitting 700 don’t. A lot of the “exam prodigies” have parents who are teachers or who are otherwise overly interested in these benchmarks and push their kids. I find them annoying and I think this whole discussion just reinforces the idea that intelligence or mathematical ability can be measured, and encourages this type of parental behavior. My kid got a 750 and he’s only 12!! What has your kid done???

800 in 2001 and 2002 (7th and 8th grade), 800 in 2005 (11th grade).

800 on the SAT as a senior in 1967. Taking tests has always been my greatest ability.

I don’t think anyone took it in 7th grade back then.

770 age 12 (1991), 800 age 15 (1994), not tenured. I think as far as factors for high performance go, the easy access to puzzles, algebra, and academic role models during my youth may have been a significant contributor. I can’t reasonably say anything concrete about how my XY chromosomes helped or hurt my performance individually.

I wonder if we can characterize the sort of cognitive dysfunction that lies at the root of Tierney’s style of argumentation. There seems to be a big heap of just-world hypothesis at work: all is right with the way people make their way along career paths, and anyone saying otherwise is trying to spoil the great machine. Perhaps he also thinks men are “his team” and that they deserve to “win”. Finally, there should be a word for the way he casts himself as the maverick hero, bucking “political correctness” by defending popular prejudices.

I took the SAT in 7th grade and I don’t remember my score but it was well below 700. I was involved in the CTY program and, because there was some indication that better scores could result in priority in placement in summer courses, I retook them in 9th grade: 700 V, 690 M. I last took the SATs as a junior in high school (before recentering): 750 V, 780 M. Even on the GRE, I only scored a 790 M.

I don’t technically fall under the auspices of the survey (undergraduate, though one with a decent amount of grad coursework under his belt) — but I got an 800 on the SAT at 13, and was one of only a tiny handful of students to do so under that program that year. This was post-95, obviously.

@Jordan: I worry that this survey is not very scientific in that people with high scores are more likely to respond. (In fact, the only reason I responded myself is that my scores were lower than those that most other people were posting, whereas I imagine some of your readers will recognize me as a moderately successful mathematician.)

[…] I realized, as I was writing this, that I am really sick of having this argument. Anyway, Jordan Ellenberg, who I have never met but heard plenty of awesome things about, is apparently not sick of it, and posted about it on his blog. […]

I think I agree with the above comment by Pete Clark.

Or maybe this is wishful thinking? Taking the SAT in 8th grade, I believe I got something around 600, and junior year of high school, I got 710.

However, I half-follow satisfy the conditions DY put out. I did not become interested in mathematics until college; until then, I thought I would become a physicist.

[…] ways in areas beyond just math and science. The science Tierney cites is light: mathematician Quomodocumque and his commenters do a good job of deconstructing the […]

This article is annoying, but equally annoying is the assumption amongst you academic mathematicians in discussions here and on facebook is that the ultimate successful career goal for someone excelling at math is that they become an academic mathematician. Especially silly since the math SAT has no proofs, and I’ve seen that mathematicians have a certain verbal skill not seen in engineers. Mathematicians are always explaining that the math they do has nothing to do w/ the math in high school , so the whole thing is doubly annoying.

(I got 740 in 10th grade, even though re-took it later, and have PhD in engineering).

Wait, I don’t think “the ultimate successful career goal for someone excelling at math is that they become an academic mathematician!”

True – I read too much into these comments, but I deleted my FB account and had to vent here. However, in posting your survey, you were focusing on the link between mathematicians and early math test scores. It’s possible that your goal was to invalidate one of the many logical jumps that Tierney makes in his article. I would conduct a survey asking readers who had exceptional early math test scores about their current professions.

(actually a reply to Idith’s followup below, but reply-threading only goes two deep:)

“I would conduct a survey asking readers who had exceptional early math test scores about their current professions.”

In fact, that kind of research has been done! See the work of Benbow et al.

http://www.vanderbilt.edu/Peabody/SMPY/camilla_benbow.htm

which features extensive longitudinal study of one high-early-SAT cohort. Executive summary: lots of scientists, but certainly these folks don’t _exclusively_ become scientists.

I think you have the logic backwards. Getting an 800 on the math SAT definitely does not imply that you should strive to be an academic mathematician. But becoming an academic mathematician does tend to imply you got an 800 on the math SAT.

More discussion of John Tierney here:

http://ilaba.wordpress.com/2010/06/17/an-entirely-positive-approach-or-something/#more-1597

When I took the SAT in high school in the 1960s, I did not have any idea what the test would be like or what sort of math problems would be in it. I remember doing extremely well in the mathematics part, but beyond that all I remember was that it was not 800. I wonder how much even minimal coaching prior to the exam improves one’s score. Also, I’ve never liked racing through problems under time pressure. I probably did much better doing problem sets involving harder problems of the kind that got me into summer NSF math programs for high school students at Notre Dame and Berkeley.

I just read about some very interesting psychological research that is relevant here. In one study, boys and girls were given some kind of test of quantitative ability. When they were told the test was merely a research tool, boys and girls scored equally well. When another group was told the test was a measure of their quantitative aptitude, the girls did worse than the boys. Related studies found similar effects in other areas, and with racial instead of gender differences.

Conclusion: test scores that appear to confirm widely held stereotypes may instead be an artifact of some belief in those stereotypes.

A helpful addition to your NYTimes.com (Firefox) browsing experience:

never accidentally click on a “Science” article again onto to discover

that the author is Tierney: http://userstyles.org/styles/30674

790 in 1998. 760 verbal. I went on to major humanities, studied for the verbal and writing portions of the GRE, aced them both, still got 790 on math. Ended up switching to math and am now a postdoc. Female.

Oh yeah and I took it as a senior. I didn’t know people who took the SAT before that in my milieu… Why?? Anyways, for once on a blog post, the comments put me in a better mood than the article. Who is this Tierney character x-(? I’m going to go back to the Grothendieck post and reread it to cleanse my mind :)