In a seminal chapter from 1987 entitled What’s all the fuss about metacognition?, Alan Schoenfeld discussed his observations of how undergraduate students solved problems. More than half, when faced with a non-standard problem outside a familiar context, followed the path illustrated in diagram 1. In this case, a pair of students read the problem, made a correct conjecture, but then got bogged down in calculations and ran out of time, even though they had the required knowledge to solve the problem. At no time did they stop and ask themselves “Is this getting us anywhere? Should we try something else?” If they had, Schoenfeld contends, they would have had a chance of solving the problem. As it was, their effort “is an all too typical example of the disastrous consequences of an absence of self-regulation.” |
In Inquiry Maths, students learn to regulate their activity by justifying the choice of a card to their peers and, in turn, engaging with their peers’ justifications. They also benefit from the teacher’s rejection of non-mathematical suggestions and arbitration between contending legitimate ideas. Showing the two diagrams above to students has provided a powerful learning experience. A year 7 student responded, "I've been like the student today, I need to be more like the mathematician." The diagrams help students understand why the teacher is asking them to stop exploring and to consider how to proceed. Schoenfeld asserts that the main point about self-regulation is as follows: “It’s not only what you know, but how you use it (if at all) that matters.” |
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