A Characterization of variational thinking from linear-diaphantic equation problem solving and Grounded Theory Una caracterización del pensamiento variacional desde la resolución de problemas de ecuaciones lineales diofánticas y la teoría fundamentada

Abstract

Variational thinking has been characterized from different contexts and perspectives, generally these works have been carried out from the solution of problems involving the concept of function in continuous domains. The research was focused on answering the research question, how is the nature of variational thinking manifested by mathematics teachers in training, when solving problems of diophantine linear equations? The work was guided by a qualitative approach with a strategic design based on grounded theory. As data sources, 6 learning sequences were designed and implemented to a group of 24 students who took a course of Number Theory and are training to become mathematics teachers. Among the findings, it stands out, how from particular situations, students make conjectures, discover relationships and patterns that lead them to perform actions to represent, organize and reorganize their knowledge. The simultaneous processes of data collection, codification and analysis and the method of constant comparison, led to theoretical saturation, making it possible to build the core of the theory, as a process between the variational operations of particularizing, conjecturing, relating, generalizing and proving, together with a series of actions manifested by the participants, when their variational thinking operates on problems involving diophantine linear equations of the form .