Problem Solving as Variational Ways of Thinking in Math Teachers in Training

Abstract

The purpose of the work was to characterize problem solving as a way of thinking manifested by a group of students who are trained to be math teachers. The research with a qualitative approach and a design from the grounded theory was focused on answering the question, how are the ways of understanding and ways of thinking of a group of mathematics teachers in training when they solve problems in discrete domains? The participants were 21 students who took a course in Number Theory in a program that trains professors of Mathematics at the Francisco de Paula Santander University (Cúcuta, Colombia). For the analysis of data from nine teaching experiments and a semi-structured retrospective interview, open, axial and selective coding processes were used. Among the findings is the way the participants interpreted necessary conditions, sufficient conditions, relationships, convergents and the infinite solutions to each problem. These ways of interpreting led students to understand relationships, patterns, and strategies for convincing and solving problems in local contexts. At the core of the theory, ways of understanding and thinking were characterized as a variational process ranging from interpretation as a way of understanding problem solving in local contexts to establishing relationships, creating strategies for generalization, and testing as ways of thinking about problem solving in a variety of contexts.