数学的問題解決における「理解」の認知的研究(III) : アナロジーの構造分析
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概要
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There are many concrete materials which we can find in school mathematics instructions. In some sense, the concrete materials are considered to be analogies from well-known objects to unknown mathematical concepts which students are going to learn. G. S. Halford and G. M. boulton-Lewis (1992) noted that "an analogy consists of a mapping from one structure, called the source or base, to another structure, called the target", and "the concrete representation is the source and the concept to be taught is the target." (pp.184-185) In this paper, the structure of analogy is analyzed on a basis of Structure-Mapping Theory by G. S. Halford and G. M. boulton-Lewis (1992), and some instructional remarks about using analogy in mathematics education are made from three features of analogy, that is, selectiveness in the mapping process, levels of analogy, and readiness to understand an analogy. 1) It is selective what properties or aspects of the source structure are mapped into the target. At the beginning of class, learners do not know what aspects of the source should be mapped into the target, because they do not yet have any knowledge about the target structure (mathematical concept to be learned), so they can not select the appropriate aspects which correspond between the source and the target. Therefore, it is necessary for teacher to give learners the point of view about what aspects of concrete materials they should consider. 2) According to Structure-Mapping Theory, there are four levels of analogy that are distinguished by the amount of categories of informations to be mapped simultaneously. A higher level analogy has more cognitive loads than lower levels, because for the higher level analogy one must deal with more informations at the same time to make sense of the link between the source and the target. We can use the structural analysis of analogy to assess the difficulty inherent in teaching materials for preparing mathematics instruction courses. 3) Whether a concrete material works well for the source structure or not depends upon the readiness of learners. Although the learners have some experiences to work with the material and is familiar with it, they can not treat that material as the source, unless they have those experiences such as they see the structure necessary for the mapping into the present concept to be learned. Then, it is important for teacher to understand the readiness of leaners to work with the materials at the beginning of using them.
- 全国数学教育学会の論文
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