Teaching and Learning Iteration of Functions and Fixed Points

We present here lesson plans for teaching the dynamical systems topic of iteration of functions and (attractive and repelling) fixed points from three existing pedagogical viewpoints in practice: constructivism, socio--cultural theory and interactionism. In each lesson plan, it is suggested that the topic can be taught using algebraic, geometrical and computational tools. Pankaj Kamthan The study of iterations ... is central to the applications of mathematics. ---Gilbert Strang 1 Introduction Iteration is an area in dynamical systems which deals with the study of orbits of points under different functions. The idea of iteration is very general and occurs in various processes. Iteration of functions is central to the study of dynamical systems [11] --- without iteration, there will be no interplay between points and functions, and thus no (interesting!) Mandelbrot and Julia sets or dynamical behaviour of chaos which have drawn a lot of attention in recent years. But the power of itera..