Geometrical properties as assumptions in proofs in Japanese junior high mathematics textbooks
Geometrical properties as assumptions in proofs in Japanese junior high mathematics textbooks
In this short paper we focus on the introduction of deductive proof in Japanese junior high school mathematics textbooks. Using two major authorized textbooks with over 70% of national share of classroom use, we examined all proofs in the 8th grade textbooks where a mathematical proof was introduced. In doing so, we analysed the relationships between assumptions prescribed in the definition of a proof and properties used in the proofs in the textbooks. Through our analysis, we found that although the assumptions in these two textbooks were defined as properties that are known to be correct, some of this was without mentioning the methods of verifying the correctness. The ambiguous treatment of assumptions that we found may inhibit students’ mathematical thinking.
mathematics, education, proof
379-380
Universitätsbibliothek Paderborn
Miyazaki, Mikio
b0272598-9ddc-47c8-8d0e-8215a5cb1d5e
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
16 September 2019
Miyazaki, Mikio
b0272598-9ddc-47c8-8d0e-8215a5cb1d5e
Fujita, Taro
8564512b-09a9-498f-8fc7-0569d071f04c
Jones, Keith
ea790452-883e-419b-87c1-cffad17f868f
Miyazaki, Mikio, Fujita, Taro and Jones, Keith
(2019)
Geometrical properties as assumptions in proofs in Japanese junior high mathematics textbooks.
Rezat, Sebastian, Fan, Lianghuo, Hattermann, Mathias, Schumacher, Jan and Wuschke, Holger
(eds.)
In Proceedings of the 3rd International Conference on Mathematics Textbook Research and Development (ICMT3).
Universitätsbibliothek Paderborn.
.
Record type:
Conference or Workshop Item
(Paper)
Abstract
In this short paper we focus on the introduction of deductive proof in Japanese junior high school mathematics textbooks. Using two major authorized textbooks with over 70% of national share of classroom use, we examined all proofs in the 8th grade textbooks where a mathematical proof was introduced. In doing so, we analysed the relationships between assumptions prescribed in the definition of a proof and properties used in the proofs in the textbooks. Through our analysis, we found that although the assumptions in these two textbooks were defined as properties that are known to be correct, some of this was without mentioning the methods of verifying the correctness. The ambiguous treatment of assumptions that we found may inhibit students’ mathematical thinking.
Text
Miyazaki-etc_ICMT3_2019
- Accepted Manuscript
More information
Published date: 16 September 2019
Venue - Dates:
3rd International Conference on Mathematics Textbook Research and Development, Paderborn University, Paderborn, Germany, 2019-09-16 - 2019-09-19
Keywords:
mathematics, education, proof
Identifiers
Local EPrints ID: 446185
URI: http://eprints.soton.ac.uk/id/eprint/446185
PURE UUID: eb688a41-60d7-456a-8563-ef1b4ee9b716
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Date deposited: 26 Jan 2021 17:33
Last modified: 16 Mar 2024 10:30
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Contributors
Author:
Mikio Miyazaki
Author:
Taro Fujita
Editor:
Sebastian Rezat
Editor:
Lianghuo Fan
Editor:
Mathias Hattermann
Editor:
Jan Schumacher
Editor:
Holger Wuschke
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