Vygotskyの「複合的思考の段階」に基づく分数の生活的概念の考察 : 連合的複合を中心として
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概要
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Although it is important for researchers and teachers in mathematics education to inquire and recognize everyday concepts of children, they seem not to be examined enough. It is because of few methods that identify everyday concepts of children. Therefore, this paper is intended as an investigation of children's everyday concepts of fraction, especially from the viewpoint of complexive thinking by Vygotsky. He suggests that the theory of concept development is including three stages: unorganized congeries, complexive thinking and conceptual thinking. I think that we could use it as one of means that identify everyday concepts of fraction, because Vygotsky found out in mathematical context. At first, in this paper five different types of complexive thinking: associative complex, complex by completing collections, chain complex, diffuse complex and pseudoconcept, are summarized based on Vygotsky's 'Thinking and Speech'. Second the investigation according to complexive thinking is explained. Subjects consist of six Japanese children in third grade. They are interviewed after making to answer the questionnaire independently. The questionnaire, for example, has seven types of problem for fraction and asks children: 'which are included in the same group? And name the group based on the common feature of them.' After that, children's thinking are characterized by complexive thinking or conceptual thinking. Main findings are following: (1) Almost children's thinking were characterized by associative complex. Associative complex had two different levels: (i-A) the level based on external feature, (i-B) the level based on not-essential feature, (ii) the level based on semi-essential feature. (2) Everyday concepts that underlay acquiring fraction, one of mathematical concepts, were found out: ex.) Children had ideas of division with quantity sense as everyday concepts for fraction with division. Children were unable to recognize the object that had little divided lines as the result of division operation. (3) It was found that the process of development of acquiring concepts by children for fraction.
- 全国数学教育学会の論文
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