Theories and Practices of Thinking and Learning to Think

Abstract

One of the persisting aims in mathematics education is that students become more able in mathematical thinking. This article discusses relations between research about processes of learning and thinking, and educational practices that attempt to achieve that aim. We discuss three research perspectives that characterize thinking and learning to think differently. The associationist/behaviorist perspective views learning to think as acquisition of higher-order skills. The domain-structural/cognitive perspective views learning to think as acquiring schemata and strategies for understanding and reasoning, with concepts in subject-matter domains and with general principles of reasoning and problem solving. The situative perspective views learning to think as becoming a more effective participant in social practices of inquiry and sense-making, in which individuals develop their identities as learners and knowers. These views of thinking are reflected in educational practices that emphasize acquisition of skills, conceptual understanding and thinking strategies, and participation in practices and development of identity. The Middle-School Mathematics through Applications Project is an example of learning environments, curricula, and teaching that are designed with the situative focus. We argue that the topic of thinking provides an example in which the situative perspective can provide a framework that includes the strengths and values of the behaviorist and cognitive perspectives.