This empirical study examines the variety of materials used and the myriad of teaching strategies employed by U.S. high school mathematics teachers in their effort to prepare students for later success in college calculus, a requirement for most STEM majors. Designed as a retrospective cohort study, we use 12,000 college calculus students' histories to predict performance while controlling for demographic differences. This study has the capability to both reveal the most promising educational practices in mathematics, including technological innovations, and to assess the degree of match between high school math and college calculus courses, both traditional and reform based.
(FICSMath) project has been to investigate the factors that contribute to students' success in their first college calculus course, with a special focus on the students' educational experiences during high school. College calculus is required for students intending to pursue a STEM career and, for some, a major impediment to furthering their studies. To that purpose, a large, nationally representative survey of college students was carried out. The stratified national random sample contained 10,437 students taught by 336 college instructors at 134 institutions. Among the research outcomes, the project found that: The "achievement gap" between black and white students, a hotly debated topic in mathematics and science education, also existed among the FICSMath participants, where black students earned college calculus grades that were, on average, more than 5 points lower than those of the white students. However, this gap can be accounted for by socio-economic and other background differences between black and white students, particularly parental attitudes about mathematics and the availability of math homework support at home prior to college. Recently, identity has been discussed as an important ingredient in young persons' career choices in STEM. The FICSMath data showed that the elements of mathematics identity (interest, performance/competence, and recognition) predicted the participants' interest in an engineering career. Importantly, recognition by parents, relatives, peers, and teachers of a student as a "math person" played a larger role for females than for males—a finding with obvious policy implications. There was a large disparity between what college mathematic professors and high school mathematics teachers viewed as the best preparation for student success in taking college calculus. Professors placed greater emphasis on the learning of algebra skills and functions than did teachers. By contrast, teachers focused on a positive and cooperative classroom environment and on teaching real-life problems more strongly than did professors. The calculus performance of students of immigrant backgrounds was compared with those of non-immigrant students. Students born abroad and having attended high school abroad did extraordinarily well, on average. Students born abroad and educated in the U.S. and students with immigrant parents performed similarly to their non-immigrant counterparts. Students are typically admonished to "work harder," but the amount of effort students exerted in their most advanced high school mathematics class was not always associated with better grades in college calculus. Spending more time reading the mathematics textbook in high school uniformly predicted a more negative outcome in college calculus, whereas spending more time studying was associated with positive outcomes under most, but not all conditions. Students who had studied hard in a non-calculus high school class and had received a weak grade in it earned a worse college calculus grade than did students with the same high school grade who had not studied in that non-calculus high school class. This suggests deep-seated problems in the group of students exerting "desperate efforts" that cannot be resolved simply by increasing study time. The road to college calculus was once a matter of simply moving through a predetermined sequence of high school mathematics courses (Algebra I, Geometry, Algebra II, Precalculus, and Calculus) for four or five years depending on whether one started algebra in the eighth or ninth grade. However, the variety of pathways has expanded to include Integrated Math, statistics, several forms of high school calculus, and opting out of a year of high school mathematics. A surprising finding was that nearly 30% of students enrolled in college calculus had also taken precalculus at the college level. This was after they had taken and passed a precalculus or calculus course at the high school level, but performed poorly when taking their college’s placement exam in mathematics.
