Benbow, C.P. and Stanley, J.C. (1980). 'Sex differences in math ability: Fact or ar~fact?' From Science, 210, 1262-1264. Reprinted with permission and copyright 1980 by the Association for the Advancement of Science.

Sex Differences in Mathematical Ability: Fact or Artifact?

C.P. Benbow and J.C. Stanley

Abstract: A *substantial sex difference in mathematical reasoning ability score on the mathematics test of the Scholastic Aptitude Test) in favor of boys was found in a study of 9927 intellectually gifted junior high school students. Our data contradict the hypothesis that differential course-taking accounts for observed sex differences in mathematical ability, but support the hypothesis that these differences are somewhat increased by environmental influences.*

Huge sex differences have been reported in mathematical aptitude and achievement (1). In junior high school, this sex dfflerence is quite obvious: girls excel in computation, while boys excel on tasks requiring mathematical reasoning ability (1). Some investigators believe that differential course-taking gives rise to the apparently inferior mathematical reasoning ability of girls (2). One alternative, however, could be that less well-developed mathematical reasoning ability contributes to girls' faking fewer mathematics courses and achieving less than boys.

We now present extensive data collected by the Study of Mathematically Precocious Youth (SMPY) for the past 8 years to examine mathematical aptitude in approximately 10,000 males and females prior to the onset of differential course-taking. These data show that large sex differences in mathematical aptitude are observed in boys and girls with essentially identical formal educational experiences.

Six separate SMPY talent searches were conducted (3). In the first three searches 7th and 8th graders, as well as accelerated 9th and 10th graders, were eligible; for the last three, only 7th graders and accelerated students of 7th grader age were eligible. In addition, in the 1976, 1978 and 1979 searches, the students had also to be in the upper 3 percent in mathematical ability as judged by a standardized achievement test, in 1972 in the upper 5 percent, and in 1973 and 1974 in the upper 2 percent. Thus, both male and female talent-search participants were selected by equal criteria for high mathematical ability before entering. Girls constituted 43 percent of the participants in these searches.

As part of each talent search the students took both parts of the College Board's Scholastic Aptitude Test (SAT)-the mathematics (SAT-M) and the verbal (SAT-V) tests (4). The SAT is designed for able juniors and seniors in high school, who are an average of 4 to 5 years older than the students in the talent searches. The mathematical section is particularly designed to measure mathematical reasoning ability (5). For this reason, scores on the SAT-M achieved by 7th and 8th graders provided an excellent opportunity to test the Fennema and Sherman differential course-taking hypothesis (2), since until then all students had received essentially identical formal instruction in mathematics (6). If their hypothesis is correct, little difference in mathematical aptitude should be seen between able boys and girls in our talent searches.

Results from the six talent searches are shown in Table 1. Most students scored high on both the SATM and SAT-V. On the SAT-V, the boys and girls performed about equally well (7). The overall performance of 7th grade students on SAT-V was at or above the average of a random sample of high school students, whose mean score is 368 (8), or at about the 30th percentile of college-bound 12th graders. The 8th graders, regular and accelerated, scored at about the 50th percentile of college-bound seniors. This was a high level of performance.

A large sex difference in mathematical ability in favor of boys was observed in every talent search. The smallest mean difference in the six talent searches was 32 points in 1979 in favor of boys. The statistically significant l-tests of mean differences ranged from 2.5 to 11.6 (9). Thus, on the average, the boys scored

about one-half of the females' standard deviation (S.D.) better than the girls in each talent search, even though all students had been certified initially to be in the top 2nd, 3rd, or 5th percentiles in mathematical reasoning ability (depending on which search was entered).

One might suspect that the SMPY talent search selected for abler boys than girls, In all comparisons except for two (8th graders in 1972 and 1976), however, the girls performed better on SAT-M relative to female college-bound seniors than the boys dW on SAT-M relative to male college-bound seniors. Furthermore, in all searches, the girls were equal verbally to the boys. Thus, even though the talent-search girls were at least as able compared to girls in general as the talent-search boys were compared to boys in general, the boys still averaged considerably higher on SAT-M than the girls did.

Moreover, the greatest disparity between the girls and boys is in the upper ranges of mathematical reasoning ability. Dmerences between the top-scoring boys and girls have been as large as 190 points (1972 8th graders) and as low as 30 points (1978 and 1979). When one looks further at students who scored above 600 on SAT-M, Table 1 shows a great dfflerence in the percentage of boys and girls. To take the extreme (not including the 1976 8th graders), among the 1972 8th graders, 27.1 percent d the boys scored higher than 600, whereas not one of the girls did. Over all talent searches, boys outnumbered girls more than 2 to 1 (1817 versus 675 girls) in SAT-M scores over 500. In not one of the six talent searches was the top SAT-M score earned by a girl. It is clear that much of the sex dmerence on SAT-M can be accounted for by lack of high-scoring girls.

A few highly mathematically able girls have been found, particularly in the latest two talent searches The latter talent searches, however, were by far the largest, making it more likely that we coub identffy females of high mathematical ability. Alternatively, even highly able girls have felt more confident to enter the mathematics talent search in recent years, our general conclusions woub not be altered unless all of the girls wHh the highest abilHy had stayed away for more than 5 years. We consider that unlikely. In this context, three-fourths as many girls have participated as boys each year; the relative percentages have not varied over the years.

It is notable that we observe skable sex differences in mathematical reasoning ability in 7th grade students. Until that grade, boys and girls have presumably had essentially the same amount of formal training in mathematics. This assumption is supported by the fact that in the 1976 talent search no substantial sex differences were found in either participation in special mathematics programs or in mathematical learning processes (6). Thus, the sex difference in mathematical reasoning ability we found was observed before girls and boys started to differ signfficantly in the number and types of mathematics courses taken. It is therefore obvious that dmerential course-taking in mathematics cannot abne explain the sex dmerence we observed in mathematical reasoning ability, although other environmental explanations have not been ruled out.

The sex difference in favor of boys found at the time of the talent search was sustained and even increased through the high school years. In a follow-up survey of talent-search participants who had graduated from high school in 1977 (10), the 40-point mean difference on SAT-M in favor of boys at the time of that group's talent search had increased to a 50-point mean dmerence at the time of high school graduation. This subsequent increase is consistent wHh the hypothesis that differential course-taking can affect mathematical ability (2). The increase was rather small, however. Our data show a sex dmerence in the number of mathematics courses taken in favor of boys but not a large one. The dmerence stemmed mainly from the fact that approximately 35 percent fewer girls than boys took calculus in high school (10). An equal proportion of girls and boys took mathematics in the 11th grade (83 percent), however, which is actually the last grade completed before taking the SAT in high school. It, therefore, cannot be argued that these boys received substantially more formal practice in mathematics and therefore scored better. Instead, it is more likely that mathematical reasoning ability influences subsequent dmerential course-taking in mathematics. There were also no significant sex differences in the grades earned in the various mathematics courses (10). .~__.__.

A possible crHicism of our results is that only selected mathematically able highly motivated students were tested. Are the SMPY results indicative of the general population? Lowering qualfflcations for the talent search did not result in more high-scoring individuals (except in 1972, which was a small and not well known search), suggesting that the same results in the high range would be observed even if a broader population were tested. In additbn, most of the concern about the lack of participation of females in mathematics expressed by Ernest (11) and others has been about intellectually able girls, rather than those of average or bebw average intellectual ability.

To what extent do girls wHh high mathematical reasoning ability opt out of the SMPY talent searches?

More boys than girls (57 percent versus 43 percent) enter the talent search each year. for this to change our conclusions, however, it would be necessary to postulate that the most highly talented girls were the least likely to enter each search. On both empirical and logical grounds this seems improbable.

It is hard to dissect out the influences of societal expectations and attitudes on mathematical reasoning

ability. For example, rated liking of mathematics and rated importance of mathematics in future careers had no substantial relationship with SAT-M scores (6). Our results suggest that these environmental influences are more significant for achievement in mathematics that for mathematical aptitude.

We favor the hypothesis that sex dmerences in achievement in and attitude toward mathematics result

from superior male mathematical abilHy, which may in turn be related to greater male ability in spatial tasks (12). This male superiority is probably an expression of a combination of both endogenous and exogenous variables. We recognke, however, that our data are consistent with numerous alternative hypotheses. Nonetheless, the hypothesis of dmerentiai course-taking was not supported. It also seems likely that putting one's faith in boy-versus-girl socialization processes as the only permissible explanation of the sex dmerence in mathematics is premature.

NOTES:

1. E. Fennema, J. Res. *Math. Educ. 5, *126 (1974); •National assessment tor educational progress,' *NAEP Nev~sl. *8 (No. 5), insert (1975); L. Fox, in *Intellectual Talent: *Research *and Development, *D. Keating, Ed., (Johns Hopkins Univ. Press, Baldmore, 1976), p. 183.

2. For example, E. Fennema and J. Sherman, *Am. Educ. *Res. J. 14, 51 (1977).

3. W. George and C. Sdano, in *Intellectual Talent: *Research *and Development, *D. Keabng, Ed. (Johns Hopkins Univ. Press, Baldmire, 1976), p. 55.

4. The SAT-V was not administered in 1972 and 1974, and the Test ot Standard Written English was required in 1978 and 1979.

5. W. Angott, Ed., *The College Eroard Admissions Testing Program (Cdlege *Entrance Examinabon Board, princeton, N.J., 1971), p. 15.

6. C. Benbow and J. Stanley, manuscript in p,reparation.

7. This was not tnue tor the acoeiefabd 8th graders in 1976. The N tor the latter comparison is only 22.

8. Cdlege Entrance Examinabon Board, *Guide to *the *Admissions Testing *Service (Educational Tesbng Service, Princeton, N.J. 1978) p. 15.

9. The l-tests and P values tor the 7th and 8th graders, respectvely, in the six talent searchers were 2.6, P < .01; P < .001; 5.1, P < .001; 5.2, P < .001; 4.9, P < .001; 7.1, P < .001; 6.6, P < .001; 2.5, P < .05; 11.6 P < .001; and 11.5, P < .001.

10. C. Benbow and J. Stanley, in preparation.

11. J. Ernest, *Am. Math Mon. *83, 595 (1976).

12. I. MacFarlan - Smith, *Spatial Ability *(Univ. ot London Press, London, 1964); J. Sherman, *Psychol. *Rev. 74, 290 (1967).

13. We thank R. Benbow, C. Breaux, and L. Fox tor their comments and help in preparing this manuscript. Supported in part by grants trom the Spencer Foundabon and the Educational Foundation ot America.