RUME 27
2025
Alexandria, Virginia
The Role of Exploring and Conjecturing When Introducing Derivatives in Calculus: To Prove or to Verify?
Page: 671
In this report, I present how eight experienced college calculus instructors used exploring and conjecturing to frame their instructional tasks for introducing derivatives. During semi- structured interviews with each instructor, I prompted them to propose instructional tasks for introducing derivatives. The tasks were broken down into their smallest calculus-specific problems, which I refer to as calculus-specific task units or CTUs. Using the notion of instructional situations by Herbst (2006), I categorized the exploring/conjecturing CTUs into a single instructional situation: Exploring or conjecturing to verify statements or relationships. I further describe how the CTUs were invoked in the tasks and the kinds of mathematical works they were expected to engage students in. To conclude, I discuss why the exploring/conjecturing CTUs revealed in the study either did not, or could not, converge to proving situations.