Exponential Functions and Recursive Logic with Tower of Hanoi: Computational Thinking and Constructionism

Abstract

This research examines the knowledge construction process in exponential functions, employing the logical-recursive development of the Tower of Hanoi puzzle pieces and computational graphic transformations in the context of high school Mathematics education. Conducted at the Innovation Laboratory of IF-Goiano, participants crafted Tower of Hanoi representations and developed recursive computational models. Data, derived from computational tools, photography, and interviews, were qualitatively analyzed through the lenses of Computational Thinking and Constructionism. Through Data Triangulation, interdependent analysis categories were established. Results indicate that the construction of Exponential Function knowledge is a dynamic and nonlinear process, involving reflection-argumentation of intuitive-recursive and mathematical logical concepts. Construction occurs through the bidirectional transition of refining conceptual-procedural and algebraic-geometric meanings, emphasizing shared semantic aspects. These findings underscore the relevance of an intellectually active learning context, preventing students from becoming mere information reproducers.