Differentiation in three easy, GeoGebra-style, lessons

Abstract

Why is calculus difficult? It required a conjunction of geometric and algebraic thinking to invent or discover its concepts. What makes GeoGebra exciting as a tool for calculus is that it offers an opportunity to represent differentiation as both an algebraic and geometric process simultaneously. My experience of working with teachers is that the software is sufficiently straightforward and user-friendly that it doesn’t take a lot of practice, or insider-knowledge about how it works, to give the teacher, or even the learner, the tools to discover the hidden treasures of calculus, and to develop insights which do not require the towering genius of its originators or discoverers, Newton and Leibnitz. Take differentiation. First, we have the geometric image of a point moving round a curve, with its tangent varying in gradient…