Abstract
This article explores aspects of a unified psychological model for mathematical learning and problem solving, based on several different types of representational systems and their stages of development. The goal is to arrive at a scientifically adequate theoretical framework, complex enough to account for diverse empirical results but sufficiently simple to be accessible and useful in mathematics education practice. Some perspectives on representational systems are discussed, and components of the model are described in relation to these ideas¿including constructs related to imagistic thinking, heuristics and strategies, affect, and the fundamental role of ambiguity.