PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Digging in deep: From instrumental to logical understanding in calculus
Page: 908
Calculus is a foundational sequence in mathematics and many client disciplines, such as physics and engineering. For student success both in mathematics and in these client disciplines, the mathematical background provided must go beyond simple instrumental or procedural skills to a deeper level. For success in higher-level mathematics, students must delve to the level of logical understanding, being able to articulate logical connections between two mathematical concepts. In this study we analyze students’ abilities to explain the connection between the limit definitions of derivative and definite integral, and their common geometric interpretations involving slope and area. We also determine whether a group exercise early in the term which reinforces the connection between the derivative and slope enhances students’ written responses concerning the connection on the final exam.