Introduction and Key Research Questions

Females and minorities in the U.S. have made great gains in educational attainment in mathematics-related areas over the past decades. However, statistics suggesting that only 29% and 15% of Ph.D. degrees in mathematics (Andreescu, Gallian, Kane, & Mertz, 2008) and engineering (Hyde & Linn, 2006) respectively are awarded to females, are indicative that gender gaps still exist. A host of factors including biological, cognitive, motivational, and societal influences have been posited to explain the differential math achievement of genders and ethnic groups. But the relative contribution of these factors is unclear, for example, whether individual factors or specific combinations of them are responsible for differences (Royer & Walles, 2007).

The purpose of this article is to summarize the research literature relevant to two primary questions:

1. What are the differences, if any, between the mathematics performance of males and females and among different ethnic groups?
2. What factors have been hypothesized to explain these differences?

In this article, we point out that there are no simple answers to these questions. But there have been some advances made toward understanding these issues.

Recent Research Results
 
Gender Differences in Mathematics Performance
Overall, results from standardized tests of mathematics achievement reveal only small differences between the performance of girls and boys during the elementary and secondary school years (Royer & Walles, 2007). Results from the pan-Canadian School Achievement Indicators Program in 1997 and 2001 suggest a slight male advantage in mathematics achievement among 13- and 16- year-olds (CMEC, 1998; 2002), and no gender differences were found among 13-year-olds according to the 2007 pan-Canadian Assessment Program (CMEC, 2008). However, some evidence suggests that gender performance differs with respect to the complexity of mathematics. Using the results of nine test batteries that were administered throughout the U.S., Willingham and Cole (1997) found that girls showed a slight advantage in elementary grades where tests emphasized computational ability, whereas boys showed a small advantage in higher elementary and secondary grades where the emphasis was on math concepts and problem solving.

In contrast, substantial gender differences in mathematics achievement are generally found in populations of high-achieving students (Royer & Walles, 2007). For example, researchers have found large gender differences on U.S. college and graduate school admission tests (e.g., Langenfeld, 1997). Similarly, a recent study of students with a "profound aptitude for mathematics" found that the vast majority of top performers in several prestigious mathematics competitions were male (Andreescu et al., 2008). An oft-cited explanation for these findings is that the mathematics performance of males is more variable than that of females; that is, males are more likely to obtain extremely high or low scores, whereas females are more likely to obtain average scores (e.g., Hyde, Lindberg, Linn, Ellis, & Williams, 2008; Willingham & Cole, 1997). This implies that males will outperform females among top-performing students, which is supported by the findings cited above. Another implication is that females will outperform males among the lowest-performing students; however, data is difficult to obtain for low performing students (Royer & Walles, 2007).

Ethnic Differences in Mathematics Performance
Mathematics test scores for elementary and secondary school students in different ethnic groups tell a different story. According to results of the U.S. National Assessment of Educational Progress for 9-, 13-, and 17-year-olds, White students have clearly outperformed Hispanic and Black students since 1973 (NCES, 2005a, 2005b), with Hispanic students slightly outperforming Black students. Achievement gaps among high-achieving populations are more pronounced, for example, with White students outperforming Mexican-American students, and Mexican-American students outperforming Black students on a U.S. college admissions test (NCES, 2007).

A comparison of native U.S. and Canadian students with foreign-born students in high-achieving populations shows yet a different pattern. In the 2006 Putnam Mathematical Competition, which is open only to students attending universities in Canada and the U.S., Andreescu et al. (2008) found that half of the top scoring men were foreign-born, as were most of the top scoring women over the past 16 years. Many of these foreign-born top scorers represented the countries of Romania, China, and Korea.
 
Patterns of Mathematical Course-Taking
One possible explanation for the patterns of mathematics performance described above is differential patterns of course-taking. A recent study of U.S. high school students reported that males and females took similar numbers and types of math courses in 1982, 1992, and 2004 (Dalton, Ingels, Downing, & Bozick, 2007). Students of both genders were more likely to take advanced math courses and less likely to take no or low-level math courses in 2004 than in 1982. However, these increases have occurred at the same rate, so that in all three years studied, students of each gender took the same number of math credits in high school and were equally likely to take calculus or pre-calculus. The similarity of course-taking patterns between genders increases the likelihood that math test scores would approach parity. However, as noted above, a large gap nonetheless exists between the performance of females and males on U.S. college and graduate school admission tests (Langenfeld, 1997).

Data are also available for the high school course-taking patterns of 17-year-old Black, White, and Hispanic students in the U.S. (NCES, 2005c). In 1978, White students were much more likely than Black or Hispanic students to have Algebra II or Calculus as their highest math course. By 2004 however, Black and Hispanic students were taking Algebra II and Calculus only slightly less frequently than White students. Nonetheless, the performance gap between Black and White and between Hispanic and White 17-year-olds on standardized tests of mathematics has remained stable (NCES, 2007). Thus, in spite of the positive trends of course-taking patterns for females and ethnic minorities, they do little to explain the differential math achievement between genders and ethnic groups.

Motivation and Self-Esteem
How are we to explain the disconnect between the course-taking patterns and math achievement across the genders and various ethnicities? Recent research suggests that this relationship is moderated by students' motivation to achieve in math as well as self-perceptions of math competence. Eccles (1997) reported a decrease in students' general self-esteem, self-confidence in some academic subjects (particularly math and science), and a decrease in the relationship between academic performance and self-confidence as they transitioned from elementary to middle, junior, or high school. However, there is evidence to suggest that this decrease is more pronounced in minority and female students compared to males and other ethnicities (Royer & Walles, 2007). In a study of Grade 8 students, Catsambis (1994) reported that White males aspired to math and science careers with greater frequency than minority students, and that White, Black, and Latino males aspired to math and science careers and participated in extracurricular math activities with greater frequency than female peers. Further, females in all three ethnic groups were less confident about themselves as math students than their male peers; Catsambis found that these females were even less confident in themselves with respect to males when they were in Grade 10. Catsambis (2005) also noted that the attitudinal gap between genders was larger among White students than among minority students. However, Walters and Brown (2005) suggested that male attitudes toward math were substantially higher than females, regardless of ethnic group, once they entered college.

A recent review by Meece, Glienke, and Burg (2006) presents similar findings, showing that boys' and girls' competency beliefs follow stereotypes: boys judge themselves as more competent in math than girls do, but the opposite is true for competency beliefs concerning language arts. Differential competency beliefs concerning math emerge early in elementary school and persist in spite of equal gender performance in the domain. In contrast with the findings of Catsambis (1994) however, Meece et al. (2006) report that this gap in competency beliefs narrows when students enter high school. Interestingly, Meece and her colleagues found that the degree to which boys and girls value mathematics and perceive it as important is equal throughout elementary and secondary school.

Speed of Math-Fact Retrieval
A recent hypothesis for the gap in math performance between males and females in select populations is the speed of math-fact retrieval (Royer, Tronsky, Chan, Jackson, & Marchant, 1999). Math-fact retrieval is defined as an individual's ability to "automatically retrieve correct answers to addition, subtraction, and multiplication problems" (Royer et al., 1999, p. 196). If a student can quickly and automatically retrieve math facts while taking a mathematics test, for example, he or she will have more cognitive capacity to devote to higher-level problem-solving activities and will also be able to complete the test more quickly. Royer et al. (1999) demonstrated that the speed of math-fact retrieval was a significant predictor of middle school students' performance on two mathematics tests and of college students' performance on the mathematics portion of a standardized college admissions test.

Consistent with patterns of standardized test performance in the general population, speed of math-fact retrieval was similar across genders in Grades 1 through 8, and male performance was more variable (Royer et al., 1999). Also similar to previous findings on test performance in high-achieving populations, males' retrieval speed was faster than females' retrieval speed in a group of self-selected elementary students as well as in a group of college students. However, the authors note that males are not inherently faster than females. In one study, self-selected participants were allowed to practice math-fact retrieval before their retrieval speed was measured, and while this opportunity to practice did not eliminate the gender gap for a group of U.S. students, the gap seemed to disappear among both Chinese students living in the U.S. and Chinese students living in Hong Kong (Royer et al., 1999). Further, females tended to show an advantage when retrieval speed was measured for word-naming and sentence understanding tasks (i.e., verbal processing tasks instead of mathematics tasks).
 
Other Factors
A host of other factors have also been posited to explain the differential math performance of genders and ethnic groups. Some researchers have suggested that males and females have different learning styles, with females having more difficulty applying knowledge to novel problems outside the classroom, such as those found on standardized tests (Royer et al., 1999). Others have proposed biological factors; for example, a propensity for males to be more aggressive and object-oriented may contribute to their advantage in competitive upper-level math courses (Meece et al., 2006; Royer et al., 1999).

Meece et al. (2006) point out the strong influence of parents' and teachers' expectations on students' subsequent beliefs about their own math competency and career interests. Parents tend to believe their daughters need to work harder to succeed in mathematics and science courses than their sons. These influences are often reinforced at school, where most teachers are female, and many school instructional materials such as textbooks and videotapes may reinforce stereotypical gender roles (Meece et al., 2006). Andreescu et al. (2008) also suggest that many U.S.-born females and minorities who may be quite gifted in mathematics do not participate in extracurricular math activities for fear of being socially ostracized.

Socioeconomic status (SES) has been offered as an explanation for the differential performance of White and minority students; however, researchers have found that these trends persist even within groups of low-, middle-, and high-SES students (e.g., Green, Dugoni, Ingels, & Camburn, 1995). Lubienski (2002) found that regardless of SES, Black students were more likely to have limited access to calculators and have incorrect beliefs concerning mathematics than White students in the U.S., suggesting that some instructional differences were, unfortunately, related to race.

Future Directions

We have presented several lines of research intended to explain the differential math performance of genders and different ethnic groups; however, further research is needed to understand the disconnect among math performance, course-taking behavior, and attitudes including self-perceptions of mathematical competence of female and minority students (Royer & Walles, 2007). The literature indicates that early school differences between males and females and between minority groups are relatively small but it also strongly suggests that the transitional years of middle school are critical to students' development, and thus future research should aim to create both cognitive and motivational interventions targeted to produce sustained change in females' and minority students' math performance and inclination to pursue math-oriented careers (Royer & Walles, 2007).

Further, as our school systems become more ethnically diverse, it is important to conduct more research on the gender differences within ethnic groups (Meece et al., 2006). Currently, the majority of research in the area of numeracy acquisition focuses on males and females generally, but as some of the research presented here suggests, there is likely a complex interaction of gender and ethnic status.

Conclusions

In sum, the question of why females likely to attend college continue to be outperformed by their male peers is a complicated one and requires more than a simple answer. Likewise, the pattern of differences between ethnic groups is also complicated. White students outperform their Latino and Black counterparts, but are themselves outperformed by Asian students. The origin of these differences is largely unknown at this point.

The search for answers to the questions raised in this article is likely to continue for many years in the future. The need for mathematically trained workers has risen in past years and will continue to rise in the years to come. A society cannot afford to exclude females and many minority students from the pool of potential students that might meet this need.