Towards a Cognitive Theory of Practice
As I view it, the topic of the relations between practice and theory in mathematics education conveys two main problems. The first problem concerns the relationship between mathematics as a practical activity, and mathematics as a theoretical body of knowledge. The second problem concerns mathematics education, and the relationship between the teacher’s activity in the classroom and research in mathematics education and psychology. I think that, for both problems, we need a theory of practice and of articulation between theory and practice. This theory must be quite general since it does not concern mathematics or mathematics education alone, but all human activities. To do this, we also need some practice of theory, or theorizing. And we need examples, since theory without examples is usually incomprehensible.
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