THEORIES AND PRACTICES OF THINKING AND LEARNING TO THINK

One of the persisting aims in mathematics education is that students b ecome more able in mathematical thinking. This article discusses relat ions between research about processes of learning and thinking, and ed ucational practices that attempt to achieve that aim. We discuss three research perspectives that characterize thinking and learning to thin k differently. The associationist/behaviorist perspective views learni ng to think as acquisition of higher-order skills. The domain-structur al/cognitive perspective views learning to think as acquiring schemata and strategies for understanding and reasoning, with concepts in subj ect-matter domains and with general principles of reasoning and proble m solving. The situative perspective views learning to think as becomi ng a more effective participant in social practices of inquiry and sen se-making, in which individuals develop their identities as learners a nd knowers. These views of thinking are reflected in educational pract ices that emphasize acquisition of skills, conceptual understanding an d thinking strategies, and participation in practices and development of identity. The Middle-School Mathematics through Applications Projec t is an example of learning environments, curricula, and teaching that are designed with the situative focus. We argue that the topic of thi nking provides an example in which the situative perspective can provi de a framework that includes the strengths and values of the behaviori st and cognitive perspectives.