Affective Pathways and Representation in Mathematical Problem Solving

An affective system of representation is joined with several cognitive representational systems in endeavoring to construct a realistic model for problem-solving competence. The affective states described are not global attitudes or traits, but local changing states of feeling that the solver experiences and can utilize during problem solving-to store and provide useful information, facilitate monitoring, and evoke heuristic processes. Thus affect, like language, is seen as fundamentally representational as well as communicative. Two major affective pathways-one favorable and one unfavorable-are discussed, together with conjectured relationships between affective states and useful or counterproductive heuristic configurations. Implications of the model include local affective goals for mathematics teaching related to problem-solving heuristics.