Identifying Gaps in Mathematics Preparation that Contribute to Ethnic, Gender, and American/Foreign Differences in Precalculus Performance.

Prior to a precalculus course, 2,000 Asian, Black, Hispanic, and White college students were graded on three dimensions of mathematical achievement-Early Skills, Later Skills, and Formulation. Later Skills was substantially the most important to successful completion of the course. Poor preparation in skills most needed for subsequent mathematics success may reinforce a tendency toward lack of academic striving, which Ogbu (1992) identified as contributing to academic difficulties for members of involuntary minorities such as African Americans. Black and White American students, especially Black males, learned disproportionately fewer Later Skills than their foreign-born counterparts. This study provides evidence that for both Black and White students, environment (American vs. foreign-born) can play a decisive role in the development of skills needed for academic success in precalculus. Attempts have been made to explain widely observed ethnic differences in academic performance. Lomax, West, Harmon, Viator, and Madaus (1995) found that minorities in America are receiving less quality education. In mathematics education, Tate (1997) found that "course taking was a powerful variable, often resulting in similar achievement gains across diverse groups" (p. 652). The 1995 Summer Yearbook of The Journal of Negro Education was devoted to the theme of "Myths and Realities: African Americans and the Measurement of Human Abilities. " This followed the release of Herrnstein and Murray's (1994) book, The Bell Curve, in which the authors claimed that it is implausible that environmental differences alone could explain the substantial differences in Black and White student test performance. The lead editorial of the 1995 Summer Yearbook called for "the presentation of experimental results that refute the pseudoscientific findings of such works, and the development of constructs that present a more soundly based and equitable approach to educational practice, assessment, and intellectual development" (Johnson, 1995). Viewing immigrant and American-born ethnic groups in terms of their minority status has proven effective in explaining differential performance. Ogbu (1992) cites several instances where members of an involuntary minority (a minority group that has been incorporated into a society by colonization, conquest, annexation, or slavery; Ogbu, 1987) did not perform as well as members of the same ethnic group in another country where their presence was voluntary. Moreover, he points to less academic striving as a significant impediment to school success for members of involuntary minorities. Gibson (1991) found that when both American- and foreign-born minority groups could, instead, be classified as an immigrant minority (the case where separate minority group identity is maintained beyond the first generation), more comparable performance between the American- and foreign-born minority groups could be expected. In this study, three empirical dimensions of student responses are investigated on a standardized test to determine what levels of procedural or conceptual knowledge matter most to subsequent success in a college precalculus course. Precalculus is important because it represents a gateway to careers in science, mathematics, engineering, and technology (SMET). Data on differences in mathematical preparation are gathered, comparing (a) American- and foreign-born students, (b) ethnic groups, and (c) gender groups. Analysis proceeds with an eye toward possible reforms in American educational practice that might enhance career opportunities in SMET for groups that are underrepresented in those fields. Current efforts to reform mathematics education in the United States were first introduced by the National Council of Teachers of Mathematics (1989), prompting the use of standards across the K-12 mathematics education curriculum. Of interest in the present study is Curriculum Standard 1 for K-12: Mathematics as Problem Solving. …