Didactic Explanation and School Mathematical Discourse: The Case of Variation

Abstract

Context: An important area of research in educational mathematics is social communicative practices in classroom organization. Objective: To locate and analyse the forms of introduction and development of variation in teaching situations. Design: Using a qualitative - interpretive approach, specifically an ethnographic study, for the analysis of socially shared practices among teachers, when they use explanation in the classroom and its correlation in the extended classroom. Environment and participants: The research participants were three professors (one physicist and two mathematicians) who taught the subject Mathematics I. On average, thei r groups consisted of 37 students. Data collection and analysis: Information was collected through audio - recorded and transcribed classroom observations. A detailed sequential study was carried out on teaching situations to describe the work done in each i ntervention that precedes or proceeds to yet another situation and thus construct the categories of analysis. Results: Due to the interactive nature, the construction of explanations is seen as an object of analysis and this implies that the minimum units are sequences of interactions, since the construction of discursive resources and meanings for variation was addressed. Conclusions: During the classes we recorded different types of explanation, models in which the notion of variation is modelled, the tea ching representations when explaining the contents through numerical, algebraic, and natural language representation.