PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
“Derivative makes more sense with differentials”: How primary historical sources informed a university mathematics instructor’s teaching of derivative
Page: 866
In this brief research report, we address the recent calls to improve undergraduate mathematics instruction through our investigation of an instructor’s teaching of derivative in a Calculus course. Considering his efforts to modify the presentation of derivative in the textbook as attempts to improve his teaching as a result of his engagement with primary historical sources, we analyze his teaching to identify the changes in his practice by using Speer, Smith, and Horvath’s (2010) framework for “teaching practice.” With our analysis of instructor interviews and video-recordings of classroom sessions, we observe that Leonhard Euler’s use of differentials in defining derivative had responded to his pedagogical concerns, and had convincing power as a method, which, in turn, led him to make significant changes in how he selects and sequences content for his teaching.