Prior calculus knowledge and self-selected tracking in college calculus.

Abstract

Students in a traditional beginning college calculus course who have never studied calculus are often at a disadvantage: Their course performance is typically lower than their peers who studied calculus previously. In light of this previous exposure, or "calculus," gap--the difference in course performance in beginning college calculus between those students with and without prior calculus knowledge-special sections of beginning calculus are available at a large mid-western university to students who enter college without any previous exposure to calculus. The aim of offering such "self-selected tracking" is to provide a homogeneous educational atmosphere wherein students need not be concerned that they are in any way disadvantaged because they are approaching an entirely new mathematical subject. How effective are these special sections (termed "novice" sections) in accommodating the diversity of students' mathematical preparation? Do they offer viable, alternative peer environments for certain students? Or does the resulting academic grouping merely isolate the less-prepared students from their more-prepared peers, resulting in high-track/low-track classrooms with the frequently seen harmful effects on performance and motivation for students in the low-track setting? This dissertation employs a multi-level statistical methodology--Hierarchical Linear Modelling--which simultaneously distinguishes between and estimates the individual- and classroom-level effects. In addition, the method evaluates whether or not individual-level relationships (e.g., relationships linking gender and prior calculus background with course performance) are constant across classrooms. The results suggest that such a curricular option does not lead to improved performance. Even after controlling for incoming mathematics skill level and prior calculus experience, average student performance is lower in the novice sections. In addition, the calculus-gap widens in the novice sections. Consequently, the novice environment is neither an effective nor an equitable option for students in beginning college calculus.