The development of mathematical thinking in school: a comparison of the action- psychological and information-processing approaches

Abstract

The learning and teaching of mathematics can be analyzed from different psychological points of view. Information-processing theories focus on the various information-processing mechanisms underlying mathematical competence and try to foster the development of these mechanisms in order to stimulate the growth of mathematical competence. In the action-psychological approach of the cultural-historical school, mathematics is viewed as a kind of culturally developed human activity governed by the rules that mathematicians themselves follow while doing their job. Consequently, the development of mathematical competence is regarded as the formation of a system of meaningful mathematical actions that constitute that activity. At a general theoretical level these approaches can be shown to be basically different and even incompatible. With regard to mathematics education the differences are illustrated with respect to several themes such as task-analysis, automatization, and the learning of elementary arithmetic. Considering insight and meaningful and sophisticated problem-solving as the core of mathematical thinking, the action-psychological approach appears to be the more promising candidate as an aid in the design of future mathematics education.