Teaching the Derivative through an Algebraic–Geometric Tangent Model and Dynamic Visualization
Paper Title: Teaching the Derivative through an Algebraic–Geometric Tangent Model and Dynamic Visualization Authors: Davit Kapanadze, Georgian National University SEU, Georgia Abstract: The derivative is often introduced through the limit of a difference quotient. This definition is mathematically rigorous; however, at the initial stage of learning it may be difficult for students, since it brings together several new ideas at once: increment, secant line, limit, tangent line, and instantaneous rate of change. As a result, students may learn differentiation rules mechanically without fully understanding the geometric and functional meaning of the derivative. This article presents an algebraic– geometric tangent model for the initial teaching of the derivative in the case of polynomial functions. Instead of beginning with the formal limit definition, the model first defines the tangent line by means of a double-root condition: the difference between a polynomial and its...
