Approaching Calculus with SimCalc: Linking Derivative and Antiderivative

Abstract

The purpose of this chapter is to present the integration of SimCalc into a new approach to calculus. This is the way in which the freshman course of math at ITESM, Mexico is currently being taught. SimCalc offers, through movement, the image of the derivative (velocity) and its antiderivative (position). This feature allows integrating SimCalc into a teaching approach in the classroom that puts together both core subjects of calculus: derivative and integral. Its mediator role is translated into contextual versions of these concepts at an early stage of the course. Then, situated proofs in this environment are produced and from there, new approaches to develop meaning about the mathematics of variation and change emerge. I describe elements of our experience in the classroom; since it is there, in the classroom, where the students have lived their experience and have triggered a symbolization process that includes body gestures to visual images. The learning objective is set to interpreting the graph of a function through the behavior of its derivative.