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Comparative analysis on the nature of proof to be taught in geometry: the cases of French and Japanese lower secondary schools

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Abstract

This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof—statement, proof, and theory—suggested by the notion of Mathematical Theorem showed differences in these aspects and also differences in the three functions of proof—justification, systematization, and communication—that are seemingly commonly performed in these countries. The results of analyses imply two major elements that form the nature of proof: (a) the nature of the geometrical theory that is chosen to teach and (b) the principal function of proof related to that theory. This paper suggests alternative approaches to teach proof and proving and shows that these approaches are deeply related to the way geometry is taught.

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Notes

  1. By “tr.” we indicate the translation in English of the French or Japanese term.

  2. All citations from French or Japanese documents are translated into English by the author.

  3. The authors of textbook add “In addition to them, the properties of equality and the formula of area or volume can be also used as arguments of proof” (Fujii et al., 2012b, p. 112).

  4. CPCTC is not proven, but is considered as a part of the definition of congruent triangles.

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Acknowledgments

The author wishes to thank Nicolas Balacheff for valuable comments on an earlier version of this paper. This work is partially supported by JSPS KAKENHI (23730826 and 22330245).

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  1. Department of Mathematics, Joetsu University of Education, 1 Yamayashiki-machi, Joetsu, 943-8512, Japan

    Takeshi Miyakawa

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Miyakawa, T. Comparative analysis on the nature of proof to be taught in geometry: the cases of French and Japanese lower secondary schools. Educ Stud Math 94, 37–54 (2017). https://doi.org/10.1007/s10649-016-9711-x

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