Secondary School Calculus: Preparation or Pitfall in the Study of College Calculus?

Abstract

This study investigated the effects of various levels of secondary school calculus experience on performance in first-year college calculus, with focus on student performance on conceptual and procedural exam items. Analysis of covariance, with mathematics SAT score as a covariate, was employed to explore differences among four groups of students. Students who had a year of secondary school calculus, advanced placement or otherwise, differed significantly in performance from students who had either no calculus or a brief introduction to calculus prior to college. A brief secondary school introduction to calculus, in comparison with no secondary school calculus, provided an initial advantage in the college course. This slight advantage reappeared on the final exam and on the procedural subscale of the final exam. Students who had studied a full year of secondary school calculus performed significantly better than other groups throughout the first-semester course. The advantage was revealed more strongly in procedural than in conceptual items. There were no significant differences among the four groups of students on outcome measures in the second-semester course. Students with more secondary school calculus background were more likely to continue into the second semester of college calculus.