Avances en la caracterización del pensamiento variacional emergente en el contexto del planteo y resolución de problemas en profesores de matemáticas en formación

Abstract

Variational thinking has been categorized from different contexts and perspectives; to some researchers, reasoning is a way of thinking and they refer to variational thinking in terms of variational, co-variational, quantitative and parametric reasoning. To other authors, thinking is functional and representational. The aim of this research was to contribute to the characterization of variational thinking arising from the formulation and resolution of problems in a group of 24 trainee mathematics professors following a qualitative perspective from a grounded theory approach. Three processes of intervention were implemented composed of ten didactic activities, one retrospective interview, three codification cycles and data analysis focused on the constant comparison method which leads up to the sampling and theory saturation. A theory was built based on the data which characterizes variational thinking as a process of formulation and problem resolution as well as a process used to understand and think about problems. Among the findings, the participants’ variational thinking is highlighted when it addresses how the values of the variable x change following a pattern while the values of the variable y change following another pattern but both values change at the same time among infinite solutions to problems that involve Diophantic equations of the form ax+by=c. Along with the evolution of students’ thinking, the results suggest that it is possible to keep moving forward in the characterization of variational thinking from the contexts studied.