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Problem solving: its assimilation to the teacher’s perspective. (English)
Philos. Math. Educ. J. 29, 12 p., electronic only (2015).
From the text: Most mathematics teaching remains routine and ‘instrumental’. More often than not, children are given a method for carrying out a type of task, and then many graded exercises to practice and reinforce the method. Each task has a unique correct answer. Of course such procedures do generate some ‘relational’ and well as ‘instrumental’ understanding on the part of the learner, and perhaps some strategic skills. But the primary focus of such exercises is the successful acquisition and deployment of procedures, and the acquisition of relational understanding or strategic skills is incidental. So what is going on? Why the disparity between the problem solving recommendations and the routine and convergent nature of much of school mathematics? There are many reasons, including institutional resistance to change, vested interests behind the status quo, individuals’ resistance to change, be they teachers, learners, parents or others, and so on. In this paper I want to pick out one strand to explore, which in my view has received insufficient attention. That is the assimilation of problem solving to the teacher’s perspective, by which I mean the teacher’s mathematics-related belief-system. Problem solving is understood differently by different teachers, in accordance with their beliefs. A demonstration of the lack of unique meaning and the diversity of interpretations given to the term ‘problem-solving’ by teachers and others might go some way towards explaining how widespread espousal of problem-solving can co-exist with its widespread rejection in practice.
Classification: D20 D59 C29
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