Research of Mutual Relationships between Addition and Subtraction: From a Viewpoint of Algebraic Reasoning
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- WADA Shinya
- Faculty of Education, Kagoshima University
Bibliographic Information
- Other Title
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- 加法と減法の相互関係に関する研究 ─ 代数的推論の観点から ─
- 加法と減法の相互関係に関する研究 : 代数的推論の観点から
- カホウ ト ゲンポウ ノ ソウゴ カンケイ ニ カンスル ケンキュウ : ダイスウテキ スイロン ノ カンテン カラ
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Abstract
<p> This research is to approach the problem of connection of arithmetic and algebra from a viewpoint of algebraic reasoning. Therefore, in this paper, we focus on the transition from pragmatic recognition to semantic recognition from a point of view of linguistics research. The purpose of this paper is to practically examine that we constituted classes of mutual relationships between addition and subtraction from a viewpoint of algebraic reasoning and to clarify aspects of the transition based on aspects of algebraic reasoning. </p><p> As a result, the following things become clear. </p><p>(1) The classes are effective to students’ understanding of mutual relationships between addition and subtraction.</p><p>(2) Aspects of algebraic reasoning in the classes are firstly cognition of antonym by agreement of rules in diagrams and objectification of them, then cognition of synonym by interaction between inverse operation of diagram, inverse calculation, and part-whole diagrams.</p><p>(3) Aspects of the transition from pragmatic recognition to semantic recognition are firstly cognition of antonym, secondly ambiguity, finally synonym. The cognition of ambiguity, however, means not only meanings of expression but also ideas of expression. </p>
Journal
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- Journal of JASME : research in mathematics education
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Journal of JASME : research in mathematics education 20 (2), 77-91, 2014-06-14
Japan Academic Society of Mathematics Education
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Keywords
Details 詳細情報について
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- CRID
- 1390564238068276224
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- NII Article ID
- 130007580539
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- NII Book ID
- AA11141495
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- ISSN
- 24333034
- 13412620
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- NDL BIB ID
- 026193191
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- CiNii Articles
- KAKEN
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- Abstract License Flag
- Disallowed