The Social Construction of Mathematical Continuity: A Socioepistemological Approach
Abstract
In this paper we describe the empirical results of a qualitative study conducted within the theoretical framework of Socioepistemology Theory for Mathematics Education (Cantoral, 2013) in which we analyzed the role played by gesture in the processes of social construction of mathematical knowledge. It was assumed that special analysis of discourse is a mean to produce knowledge on the possible changes in the pedagogical treatment of the mathematical notion of point-continuity. The implementation of the design was carried out with eight university students between 19 and 21 years of age. The basic requirement was to have certain knowledge of the elementary functions of calculus as well as previous contact with the mathematical concept of continuity. We identify some elements that were essential in the formulation of the students’ responses, at individual as well as group level; for example, the incidence of the gesture aspect is a means that offers the possibility to articulate the visualization of mathematical concepts, so that a representation on the computer screen only establishes the scenario where the student will expand and generate new meanings even more, if these representations are articulated with gestures.
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