Framing Instructional Tasks for Interaction with Content: Introducing Derivatives Graphically with Inquiry

In this study, I present how eight U.S. college calculus instructors with different patterns of inquiry practices used instructional situations to frame instructional tasks for introducing derivatives graphically to students. During four interviews, the instructors proposed up to eight tasks for introducing derivatives physically, graphically, verbally, and symbolically (Zandieh, 2000). The findings focus on the two tasks proposed by each instructor that centered the graphical representation of the derivative: derivative at a point as the slope of a tangent line, and derivative as a function presented by its graph. While no two instructors proposed the same tasks with the same instructional situations for teaching these concepts, they relied on graphing, conjecturing, and calculating situations to frame their tasks. [For the complete proceedings, see ED658295.]