VICENÇ FONT vfont@d5.ub.es
Departamento de Didáctica de las CCEE y la Matemática de la Universidad de Barcelona
This work presents a synthesis of different views about the notion of representation in the fields of epistemology, cognitive sciences and mathematics education. These views are analysed and confronted with the purpose of elaborating a theoretical proposal on the topic that seeks to keep in mind the epistemological, cognitive and instructional aspects involved in the teaching and learning of mathematical processes. It is structured in two parts. In the first part, the following issues are discussed: 1) The controversy concerning representationalism versus non-representationalism, 2) The concept of intersubjectivity as the basis for non-representationalist positions, and 3) The representationalist view in cognitive psychology.
In the second part we carry out a non exhaustive survey of different views formulated from the point of view of mathematics education. We begin with those that have been proposed by researchers in the area of Advanced Mathematical Thinking: concept definition and concept image (Dubinsky; Sfard and Tall). We go on to review more general points of view (Dörfler; Duval; Kaput; Brown) and anthropological theory and semiotic functions. The work concludes with some reflections.