PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
The Generation and Use of Examples in Calculus Classrooms
Page: 941
In this paper, we analyze video data of five instructors teaching the Mean Value Theorem in a first-semester calculus course. Throughout the lessons, graphical examples were provided by the instructors and/or the students of functions that satisfied or did not satisfy the conclusion of the Mean Value Theorem. Through the use of thematic analysis, we identified four themes related to emergence and use of examples: who generated the example, who evaluated the example, for what purpose the example was used, and the richness of the example. We emphasize that instruction that leverages student generated examples can provide a great deal of richness in a mathematics lesson and create opportunities to engage students in authentic mathematical activity. This work contributes to an evolving notion of what is entailed in students’ active learning of mathematics and the role of the instructor.