DIFFERENCES IN LEARNING OUTCOMES: CALCULUS & MATHEMATICA VS. TRADITIONAL CALCULUS

Abstract

ABSTRACT This study, conducted -at The Ohio State University, compared students from the calculus-reform course sequence Calculus & Mathematica with traditional students in two areas: conceptual and procedural understanding of calculus, and achievement in calculus-dependent courses. Task-based interviews were conducted with students from both groups after they had completed one of the two calculus sequences. These interviews were used to investigate understanding of calculus. An analysis of grades collected from the university database was conducted to investigate student achievement in calculus-dependent courses. Results from the interviews showed that the Calculus & Mathematica students were more likely to approach problems from a conceptual viewpoint of calculus knowledge, whereas the traditional students were more likely to approach problems procedurally. The Calculus & Mathematica group also demonstrated a more general understanding of the derivative and integral than the traditional group. Results from the analysis of grades show a significant difference in the introductory differential equations course favoring traditional students, and a significant difference in the first course of the calculus-based physics sequence favoring the Calculus & Mathematica students. Other significant differences, favoring the top third of Calculus & Mathematica students, were found in the introductory physics courses and in an introductory engineering mechanics course.