CHAPTER 24: A Constructivist Approach to Teaching Mathematics

Over the last few years, psychologists and educators have been interested in going beyond behavioristic and Piagetian views to new conceptualizations of learning, especially in using the computer as a “model” of how we think and learn. One of the new conceptualizations has been “information processing.” Proponents of this view claim that when we think, we basically process information; it’s as simple as that. This, however, leads to a further question: How do we manage this processing? To account for the management of processing, it is suggested that the learner engages other processes called metacognitive processes. But, still we might ask: What manages the metacognitive processes? Although this is not a trivial question, most proponents presently do not differentiate between levels of management, simply naming all those processes above the cognitive level metacognitive processes. In fact, the difference between cognitive and metacognitive is not always clear. For the time being, let us say that strictly mathematics propositions, procedures, and processes are called cognitive, while management decisions about such matters as when to use them, in what order, and with what degree of confidence are called metacognitive processes.