Cognitive Processes in Algebraic Thinking and Implications for Teaching

Abstract

Suggestions for a better achievement of the ideas and potential of algebra as well as a productive use of the algebraic code have been given by many researchers from different perspectives. Observing students’ behaviour has also induced a reflection on the nature of algebraic thinking and of its underlying dynamics. Algebraic thinking is analysed here in a semiotic perspective: the question “What does a sign represent?” is at the center of the problem between the signifier and the signified. We assume a triadic model, in which the relationship between the object and the subject is mediated by a third entity. Only by means of a semiotic act (which has an essentially triadic nature) one can really grasp the meaning of mathematical objects, but it is also by means of a semiotic act that the subject can evolve his personal senses towards a scientific and socially shared knowledge (in the sense of Vigostsky). This approach seems to be adequate for our purposes, since it is able to integrate these different standpoints into a holistic framework.