Características de la actividad matemática en torno a la enseñanza del análisis de los patrones numéricos haciendo uso de la conjetura de Collatz: Una mirada desde la teoría de la objetivación

Abstract

This thesis investigates the characteristics of mathematical activity that emerge when teaching numerical pattern analysis using the Collatz Conjecture. The research approaches this from the perspective of Objectivation Theory. The study aims to understand how, through exploring the Collatz Conjecture (a seemingly simple but complex problem involving numerical sequences), students develop and deploy diverse forms of mathematical thinking and action. Objectivation Theory, which focuses on how individuals make sense of mathematical objects and integrate them into their knowledge, provides the theoretical framework for analyzing this process. In essence, the work examines the types of interactions, reasoning, representations, and discussions generated when students attempt to understand and predict the behavior of Collatz sequences. By doing so, the goal is to identify the key elements that define mathematical activity in this context, which could offer valuable insights for designing more effective pedagogical strategies in the teaching of numerical patterns.