Characterizing variational thinking from problem resolution and the grounded theory
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Keywords
Variational Thinking, Problem Solving, Grounded Theory, Diophantine Linear Equations
Abstract
The purpose of the research was to contribute to the characterization of the variational thinking manifested by a group of 24 students who are training to become mathematics teachers, when they solve problems involving linear diophantine equations of the form ax+by=c. The study had a qualitative approach with a grounded theory design. The methodological strategy was composed of a parallel work between three interventions that grouped 11 didactic activities as data sources, the processes of open, axial, selective coding and data analysis always permeated by the method of constant comparison, which led to sampling and theoretical saturation. The findings show the variational way of thinking of the participants when from substitutions and combinations of integers in the equation, they establish links and relationships that lead them to formalize, generalize and prove. As a result, variational thinking was characterized as a process in problem solving, made up of the subprocesses transforming, formalizing, generalizing and proving variationally. The results imply that it is possible to continue advancing in characterizing variational thinking from different contexts and different domains.
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Luis Fernando Mariño, Francisco de Paula Sanatander University, Colombia
Graduate in Mathematics and Computing. Magister in Mathematical Education. Francisco de Paula Sanatander University.
Rosa Virginia Hernández, Francisco de Paula Santander University, Colombia
Degree in Mathematics and Computing. Magister in Mathematical Education. Francisco de Paula Santander University.