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学校数学におけるaction proofの機能に関する研究:発見に焦点をあてて
http://hdl.handle.net/10091/00019486
http://hdl.handle.net/10091/00019486c942c517-a9c9-460f-bb9c-0c9264f49c2f
名前 / ファイル | ライセンス | アクション |
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Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2017-03-01 | |||||
タイトル | ||||||
言語 | ja | |||||
タイトル | 学校数学におけるaction proofの機能に関する研究:発見に焦点をあてて | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
その他(別言語等)のタイトル | ||||||
その他のタイトル | A Study on Function of "Action Proof" in School Mathematics : Focusing on Discovery | |||||
著者 |
小松, 孝太郎
× 小松, 孝太郎 |
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信州大学研究者総覧へのリンク | ||||||
氏名 | 小松, 孝太郎 | |||||
URL | http://soar-rd.shinshu-u.ac.jp/profile/ja.jNACPhLh.html | |||||
出版者 | ||||||
出版者 | 日本数学教育学会 | |||||
引用 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 日本数学教育学会誌. 数学教育学論究. 92:33-45 (2010) | |||||
書誌情報 |
日本数学教育学会誌. 数学教育学論究 巻 92, p. 33-45, 発行日 2010-03-31 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | The previous studies on "action proof" have discussed its function in the context of verifying statements or learning formal proof. However, there are any other functions of proof in mathematics than verification: explanation, systematization, discovery and communication. The purpose of this study is, however, to clarify discovery function of action proof in school mathematics among all. The reason why this study selects its discovery function is that we could achieve many productive learning activities in even primary school mathematics. Firstly, this study reviews and summarizes the previous studies on action proof and then points out that they have not discussed discovery function of action proof. Next, this study defines the concept of action proof in terms of actions on manipulative objects, the original character of the actions and a representative special case. According to this definition and to comparison between action proof and formal proof, this study points out "embodiment", "movability" and "genericity" as the characteristic properties of action proof. After that, through examining discovery function of formal proof in terms of the characteristic properties of action proof, this study clarifies two kinds of discovery function of action proof, as follows. First, in order to clarify relation between the conditions of the statement and a truth of the statement, one has to grasp not only the original character of actions on manipulative objects but also the reason why the actions can be applied to all cases of the statement; after grasping the reason, one must notice and eliminate unnecessary parts for the relation or examine the process of actions on manipulative objects with consciousness of the relation; then by interpreting facts on manipulative objects which one finds out, one can produce new statements. Second, one has to view manipulative objects from new viewpoints which are not limited to the given statement and then, if necessary, organize the actions on manipulative objects; then by interpreting facts on manipulative objects which one finds out, one can produce new statements. | |||||
資源タイプ(コンテンツの種類) | ||||||
内容記述タイプ | Other | |||||
内容記述 | Article | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0021-471X | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AN00311755 | |||||
論文ID(NAID) | ||||||
識別子タイプ | NAID | |||||
関連識別子 | 110007580077 | |||||
異版である | ||||||
関連タイプ | isVersionOf | |||||
識別子タイプ | URI | |||||
関連識別子 | http://ci.nii.ac.jp/naid/110007580077 | |||||
権利 | ||||||
権利情報 | 日本数学教育学会 | |||||
出版タイプ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 |