Conceptual profile of equation and mathematical knowledge for teaching: establishing relationships in a study with prospective teachers

Abstract

Given the centrality of the concept of equation in mathematics and other areas, a research was developed that aimed to identify and understand the conceptions of equation of prospective mathematics teachers. In this paper, in particular, we seek to identify prospective teachers’ different conceptions of equation and to understand how these conceptions are related to their mathematical knowledge for teaching. The research was based on the Theory of Conceptual Profiles, on the Conceptual Profile of Equation and on the Mathematical Knowledge for Teaching. The research was developed under a qualitative approach, from an interpretative perspective and used as a method of analysis some elements of the Content Analysis. The conceptions of equation of the prospective mathematics teachers investigated are related to some of the zones of a conceptual profile of equation under construction, and the different meanings of equation mobilized by the prospective teachers of this study are related both to the common knowledge and to the specialized knowledge of the content equation.