Performing a Multi-Stage Mathematical and Informational Task "Dynamics of Iteration of Piecewise Linear Functions" as a Means of Developing Students' Creativity

Abstract

A multistage mathematical-informational task "Piecewise linear functions iterating dynamics" aimed at students' creativity development is examined in this paper. The stages of the assignment involve both solving mathematical tasks on determining basins of attraction of functions and developing a computer program for their construction. What acts as an important constituent of the task, are the stages of researching the dynamics of functions and conducting a computer experiment. What is used for these purposes is the method of iterating the functions under study. Students are introduced to this method when solving nonlinear equations, studying the contraction operator, proving theorems about the existence and uniqueness of a solution to a differential equation, and studying other issues. A computer experiment allows visually identifying the different basins of attraction of functions, and how they change as the power of the function increases. When performing the tasks, students understand the relation between a series of piecewise linear functions and Cantor sets. They note differences and similarities between the dynamics of different piecewise linear functions. Using information and communication technology, they conduct computer experiments; when investigating point orbits and iterating the piecewise linear functions, they estimate Lyapunov exponents. When completing the multi-step task, students act as mathematicians, programmers and experimenters, and that has a positive impact on the development of their creativity.

Keywords

• piecewise linear function
• iteration
• fractal
• point orbit
• lyapunov exponent
• cantor set
• fixed point
• creativity
• motivation
• flexibility of thinking
• originality of thinking