Analysis of Mathematical Thinking through Interactions with a Diagram in Mathematics Education: The Meaning of a Diagram Obtained from the Networking between Semiotics and Embodiment
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- KAGEYAMA Kazuya
- Hiroshima University of Graduate Education
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- WADA Shinya
- Kagoshima University
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- IWATA Koji
- Fukuoka University of Education
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- YAMADA Atsushi
- Aichi University of Education
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- OKAZAKI Masakazu
- Okayama University
Bibliographic Information
- Other Title
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- 数学教育における図式との相互作用による数学的思考の分析 ―記号論と身体化理論のネットワーク化を通した図式の意味について―
- スウガク キョウイク ニ オケル ズシキ ト ノ ソウゴ サヨウ ニ ヨル スウガクテキ シコウ ノ ブンセキ : キゴウロン ト シンタイカ リロン ノ ネットワークカ オ トオシタ ズシキ ノ イミ ニ ツイテ
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Abstract
<p> A diagram is a kind of an inscription. In mathematics classroom, students think with different diagrams mathematically, so a diagram is considered a special type of an inscription, that is, it has an ability to enhance students’ mathematical thinking. In this research, we focus on the meaning and function of a diagram, and the goal of this article is to analyze students’ mathematical thinking with a diagram from the several theoretical perspectives - semiotics and embodiment. We assume that a diagram has a dual, complementary nature - cultural and cognitive - and it is the reason why we have chosen these theories. By standing on these theoretical perspectives, we can really understand actual students’ mathematical thinking.</p><p> The results obtained from discussions in this article demonstrate that a diagram has two important rules for construction and usage. From the semiotic perspective, these are special characters to identify an inscription as a diagram; on the contrary, from the embodiment theory, these are based on or emerged from bodily actions as a certain typical pattern.</p><p> Plus, we compared these perspectives by using the networking methodology. Comparing with each other in the term of a basic principle, research question, methodology and result, we could describe some characters of mathematical thinking with a diagram such as:</p><p>● Mathematical thinking is a process to construct and use a diagram, while it is a process of diagramming.</p><p>● Mathematical thinking is directed by mathematical signs, while it is embodied.</p>
Journal
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- Journal of JASME : research in mathematics education
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Journal of JASME : research in mathematics education 22 (2), 163-174, 2016-08-30
Japan Academic Society of Mathematics Education
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Details 詳細情報について
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- CRID
- 1390845713044991360
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- NII Article ID
- 130007580639
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- NII Book ID
- AA11141495
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- ISSN
- 24333034
- 13412620
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- NDL BIB ID
- 027849135
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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