A quantitative analysis of the near transfer of learning from calculus to subsequent engineering courses

Abstract

In this longitudinal study, we track student answers to a question from the Calculus Concept Inventory (CCI) pre- and post-instruction in Calculus I as well as an analogous question in the next semester framed in the context of Aerospace Engineering or Chemical Engineering. Nearly 88% of the students who answered the post-CCI question correctly answered the context question correctly, suggesting that students are able to transfer learning from Calculus I to subsequent engineering courses. Moreover, nearly 43% of the students who incorrectly answered the post-calculus question were able to correctly answer the applied context question. During the semester when the students took the engineering courses, they also answered two questions from the Student Assessment of their Learning Gains instrument to assess their mathematical confidence and the degree to which they make connections between mathematics courses and other courses. Students who were more confident in their mathematical ability were more successful in transferring their understanding from the mathematics to the engineering context.