Mathematical Working Spaces in schooling: an introduction

Abstract

The theoretical and methodological model of Mathematical Working Space (MWS) is introduced in this paper. For over 10�years, the model has been the object of collaborative research among various researchers, generally coming from French and Spanish speaking countries. Articulating epistemological and cognitive aspects, the MWS model is aimed at providing a tool for the specific study of mathematical work in which students and teachers are effectively engaged during mathematics sessions. The abstract space thus conceived refers to a structure organized in a way that allows the analysis of the mathematical activity of individuals dealing with mathematical problems. Thus, analyzing mathematical work through the lens of MWS enables tracking down how meaning is progressively constructed, as a process of bridging the epistemological and the cognitive perspectives—these being modelled as two planes at different levels in the diagrammatic structure—in accordance with different specific yet intertwined genetic developments. Each is identified as a genesis related to a specific dimension in the model: semiotic, instrumental and discursive geneses. A general overview of the different papers included in this issue is given, and shows how the model can be used to study different tasks, teaching situations and activities set in specific mathematical fields or domains. Some perspectives are finally drawn, while reflecting on the possibility of ‘networking’ different theoretical frames with the MWS framework. Indeed, the latter is not proposed as a holistic theory, but rather should function as a tool interacting strongly with other approaches.