Abstract
In this paper, we analyze and compare two didactical designs for introducing primary school pupils to proportional reasoning in the context of plane polygons. One of them is well-documented in the literature; the other one is based on our own data and is accordingly presented and discussed in more detail in this paper. The two designs come from different cultural and intellectual environments: lesson study in Japan (implicitly based on the “open approach method”) and “didactical engineering” in France (based on the theory of didactical situations). The general aim of our paper is to compare these two environments and their approaches to didactical design, basing our discussion on the concrete designs mentioned above. Clear differences among them are presented, while we also identify links which hold potential for integrating research and practice.
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Notes
Editor-in-chief’s note: There are different views on the meaning of proportion in various countries. The notation a:b, where a and b denote merely quantities and not variables, may simply be taken as another expression of ratio, because one would not say “a is proportional to b” in this case. Proportion would then require equivalence of ratios, e.g., a:b :: c:d, i.e., a is to b as c is to d. However, these different definitions of proportion do not affect the substance of the issues in the rest of this paper.
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Acknowledgements
We would like to thank Mr. Chikara Kobayashi and his colleagues who generously provided us with materials from a lesson study. We acknowledge as well the anonymous reviewers and the editor for their fruitful comments on earlier versions of this paper.
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Takeshi Miyakawa and Carl Winsløw contributed equally to this paper.
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Miyakawa, T., Winsløw, C. Didactical designs for students’ proportional reasoning: an “open approach” lesson and a “fundamental situation”. Educ Stud Math 72, 199–218 (2009). https://doi.org/10.1007/s10649-009-9188-y
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DOI: https://doi.org/10.1007/s10649-009-9188-y