Reasoning-and-proving in geometry in school mathematics textbooks in Japan
Reasoning-and-proving in geometry in school mathematics textbooks in Japan
In Japan it is in Grades 7-9, and primarily in geometry, that school students are introduced to the significance and methodology of proof in mathematics. As textbooks play a central role in everyday lessons in Japan, this paper presents an analysis of the geometry chapters of a selected mathematics textbook currently in common use with students aged 13-14 in Grade 8. We show that the emphasis in the textbook is on ‘direct’ proofs of geometrical statements, accompanied by activities which encourage students to form conjectures. Based on our analysis, we raise critical issues related both to the strengths and weaknesses of such a textbook design on students’ understanding of reasoning-and-proving. The strengths, as evidenced by Japanese national data, are that most Grade 8 students in Japan are able to construct suitable proofs – usually based on congruent triangles. The weaknesses, as verified by other research, are that the same students may not fully appreciate the necessity or generality of mathematical proof.
mathematics education, school textbooks, geometry education, reasoning-and-proving, Japan, congruent triangles
81-91
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
2014
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Fujita, Taro and Jones, Keith
(2014)
Reasoning-and-proving in geometry in school mathematics textbooks in Japan.
International Journal of Educational Research, 64, .
(doi:10.1016/j.ijer.2013.09.014).
Abstract
In Japan it is in Grades 7-9, and primarily in geometry, that school students are introduced to the significance and methodology of proof in mathematics. As textbooks play a central role in everyday lessons in Japan, this paper presents an analysis of the geometry chapters of a selected mathematics textbook currently in common use with students aged 13-14 in Grade 8. We show that the emphasis in the textbook is on ‘direct’ proofs of geometrical statements, accompanied by activities which encourage students to form conjectures. Based on our analysis, we raise critical issues related both to the strengths and weaknesses of such a textbook design on students’ understanding of reasoning-and-proving. The strengths, as evidenced by Japanese national data, are that most Grade 8 students in Japan are able to construct suitable proofs – usually based on congruent triangles. The weaknesses, as verified by other research, are that the same students may not fully appreciate the necessity or generality of mathematical proof.
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Fujita&Jones-Reasoning-proving_geometry_textbooks_Japan_2014
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Accepted/In Press date: 16 September 2013
e-pub ahead of print date: 5 November 2013
Published date: 2014
Keywords:
mathematics education, school textbooks, geometry education, reasoning-and-proving, Japan, congruent triangles
Organisations:
Mathematics, Science & Health Education
Identifiers
Local EPrints ID: 369503
URI: http://eprints.soton.ac.uk/id/eprint/369503
ISSN: 0883-0355
PURE UUID: 741a0f49-b5a7-4e3a-956c-53a7f28f432e
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Date deposited: 02 Oct 2014 12:20
Last modified: 14 Mar 2024 18:04
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Author:
Taro Fujita
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