A Post-constructivist Perspective
Chapter 4. Understanding*-in-the-Making
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In painting, as elsewhere, the invisible is received, but not produced. (Marion, 1996, p. 46, emphasis added)
The purpose of this chapter is to work towards a theory of learning that makes a radical commitment to the fact that students cannot see or comprehend what is the knowledge they are to learn until after they have learned it. A fragment from a fourth-grade mathematics curriculum – intended for the students to arrive at a generalization of the type y = 3·n + 6 – is used to think and think about learning given that the students cannot aim at the future knowledge outcome precisely because they do not know (a) the generalization, (b) that they are supposed to generalize, or (c) from which aspects of their experience to generalize something. Because students do not know what they will know until after the learning event*-in-the-making has been finalized, I suggest that this future knowledge may be better thought of as the (initially) foreign/strange, which affects students before they can grasp what is happening to them or what/that they have learned. Before that we have to think understanding*-in-the-making, where we do not know what the nature of the (at least temporarily) finalized knowledge will be (which is why the term is marked by an asterisk). ← 85 | 86 →
In A Cultural-historical Perspective on Mathematics Teaching and Learning (Roth & Radford, 2011), the authors present an extended description and analysis of a student...
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