What Definitions are Your Students Learning?
Definitions are fundamental to any mathematics classroom. We consider how definitions are presented in textbooks and instructors’ lecture notes and whether students are positioned to gain a full understanding of new terms. Four textbooks, covering precalculus, calculus, and analysis, as well as three professors’ Calculus I lecture notes are compared. We found that textbooks often include two versions of definitions, formal and informal, but those definitions differ across texts. Instructors’ lecture notes do not usually have more than one version of a definition, and that version may not align with the course textbook, but they do sometimes offer intuitive or visual interpretations. We provide suggestions for being more mindful when deciding how and what definitions to present.
Capaldi, Mindy, "What Definitions are Your Students Learning?" (2019). Mathematics and Statistics Faculty Publications. 77.