Representations of Mathematics, their teaching and learning: an exploratory study

Abstract

This work describes an exploratory study, the first of the four phases of a more inclusive research, which aims at understanding the way to promote, in a Mathematics teachers’ group, a representational evolution leading to a practice that allows a Mathematical meaningful learning of Mathematics. The methodology of this study is qualitative. Data gathering was based on questioning; all the subjects of the sample (n=48) carried out a projective task (a hierarchical evocation test) and answered a written individual questionnaire. Data analysis was based in a set of categories previously defined. The main purpose of this research was to identify, to characterize and to describe the representations of Mathematics, their teaching and learning, in a group of 48 subjects, from different social groups, in order to get indicators for the construction of the instruments to be used in to the next phases of the research. The main results of this study are the following: (1) we were able to identify and characterize different representations of the teaching and learning of Mathematics, in what respects its epistemological, pedagogical, emotional and sociocultural dimensions; (2) we were also able to identify limitations, difficulties and items to be included or rephrased in the instruments used.