数学教育における「操作的証明（Operative proof）」に 関する研究（Ⅲ）

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  • A Study on Operative Proof in Mathematics Education（III）： Teaching Experiment on Operative Proof
  • 数学教育における「操作的証明(Operative proof)」に関する研究(3)操作的証明を取り入れた教授実験を通して
  • スウガク キョウイク ニ オケル 「 ソウサテキ ショウメイ(Operative proof)」 ニ カンスル ケンキュウ(3)ソウサテキ ショウメイ オ トリイレタ キョウジュ ジッケン オ トオシテ

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説明

<p>　　The purpose of this research is to consider the concept of“Operative proof”that E. Ch. Wittmann proposed as a mathematical learning activity in 1996 and to construct foundations for developing the Substantial Learning Environments with“Operative proof”.</p><p>　　In this paper, for developing the Substantial Learning Environment with“Operative proof”that used counters and place value table, I looked back on past practices on operative proof, and found out these two issues.</p><p>　　One issue is that we need some devisal for students to plan operative proof by themselves. And other one is how to develop substantial learning environment to make the shift to the formal proof from operative proof.</p><p>　　I focused on the first issue, and to obtain a certain suggestion for this issue, I carried out a teaching experiment for the 7ht grade students on operative proof that used counters and place value table. As a result, I could obtain following suggestions.</p><p>　　For planning the operative proof, it is useful for students to have some successful experience with operative proof. This suggestion was obtained from the some devisal of order of the tasks in teaching experiment. And in the process of planning the operative proof, it is helpful for students to explain own operation orally and to compare own operation with others. This suggestion was obtained from the observation of student’s activity in the teaching experiment.</p><p>　　Future tasks are to consider other type operative proofs for ANNA numbers, and to design the concrete Substantial Learning Environments that used operative proof.</p>

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