Predicting undergraduate students' mathematical thinking about derivative concept: A multilevel analysis of personal and institutional factors

This cross-sectional study examines the determinants of mathematical thinking aspects at two levels: within-classroom level and between-classroom level. We hypothesized that personal factors (gender, socioeconomic status (parents' educational attainment), current cumulative grade point average, prior mathematic achievement (high school mathematics achievement)) and institutional factors (faculty/school affiliation, grade level) have concomitant associations with students' mathematical thinking about the derivative. The sample consisted of 2424 undergraduates from 130 classrooms. Multilevel modeling showed that students' mathematical thinking about the derivative varied primarily as a function of their gender and cumulative grade point average (within-classroom level) and of their faculty affiliation (between-classroom level). Parents' educational attainment and high school mathematics achievement at the within-classroom level, and grade level at the between-classroom level were only moderately associated with different mathematical thinking aspects. Methodological and practical implications of the findings are further discussed.