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Additional info for Lesson Study: Challenges in Mathematics Education
Was it best to pause to discuss why 0 is even? Helen could have just asserted that 0 is even and moved the lesson back on the track of investigating the fairness of the spinners game. When reflecting on this question, Helen asserted that the diversion was useful because it enabled her to clarify some fundamental misunderstandings about zero and to show how mathematical concepts are determined by definitions. Here, we see that Helen justifies her choice in terms of her understanding of important principles of doing mathematics – in this case the role of definitions in mathematical reasoning.
Stacey K. (1982). Thinking Mathematically, London: AddisonWesley. Pirie, S. & Kieran, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26, 165 –190. Pólya, G. (1945/1973). How to solve it. Princeton, NJ: Princeton University. Schoenfeld, A. (1985). Mathematical Problem Solving. New York: Academic Press. Skemp, R. R. (1976). Relational Understanding and Instrumental Understanding. Mathematics Teaching, 77, 20–26.
What seems to the experienced mathematician as a steady extension of number systems is, for the growing child, a succession of changes of meaning which need to be addressed in teaching. We will return to this shortly. The symbolic world develops through increasingly sophisticated number systems which are given an embodied meaning through the number-line. These are extended further into the plane through cartesian coordinates, graphs relating symbolism to embodied visualization, with subjects such as trigonometry being a blend of geometric embodiment and operational symbolism.