Two Types of Reflective Thinking on the Emergent Chain of Mathematical Communication

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  • 数学的コミュニケーションの創発連鎖における反省的思考と反照的思考(<特集>学習場面における他者との関わり-理論,実践,システム開発)
  • 数学的コミュニケーションの創発連鎖における反省的思考と反照的思考
  • スウガクテキ コミュニケーション ノ ソウハツ レンサ ニ オケル ハンセイテキ シコウ ト ハンショウテキ シコウ

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Abstract

The purpose of this paper is to consider cognitive and affective processes within the emergent chain of mathematical communication. From a viewpoint of reflective thinking, we analyzed exemplified expressions from each of three 5^<th> grade students. Reflective thinking is considered to be thought that occurs when we reflect on our own actions or thoughts. In this paper, we consider reflective thinking to be classified into two types of thought: the first is based on our own experience and knowledge (introspective thought), and the second is based on written expressions (reverberative thought). We consider the second type of reflective thinking to be a process of hypothesis formation employing Peirce's logic: abduction, deduction, and induction. We describe the mechanism for the emergent chain of mathematical communication as cognitive and affective processes. The emergent chain contains: (1) the first type of reflective thinking; (2) emotional experience; (3) the second type of reflective thinking; and (4) the emergence of a new idea.

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