Tecnología y educación matemática: construcción de una trayectoria hipotética de aprendizaje en el juego de las Torres de Hanói

Abstract

This document presents the analysis of learning trajectories during the solution of the Tower of Hanoi game. The concept of learning trajectories was proposed by Simon M. to describe the path that a subject follows during the solution of a problem (Simon, 1995). Investigating learning trajectories is helpful because it enables better decisions to be made during the scaffolding process. In addition, it allows students to have a better knowledge about learning. To investigate learning trajectories, a coherent categorization system was developed to identify the routes and game strategies used by several players and the keys to thinking enunciated by 6 players. The Tower of Hanoi game was also implemented on the web. To establish game patterns, an algorithm was implemented in Matlab. The algorithm in Matlab filters the data, generates the graph that represents the space of the game problem and on each node it assigns the value of the absolute frequency of the movements of all the players. The result of the algorithm is a heat map that allowed establishing four hypotheses and four levels of development along with two general processes that are described in the work methodology.