数学教育におけるアナロジーの研究(1) : 数学の理解に果たすアナロジーの機能

概要

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We can see analogy as a cognitive process in which one finds some similarity among two different objects and transfers some information of one side to another. Although mathematics is presented in certain reasoning which is made from purely logical formations, we must rely on the uncertain reasoning of analogy during we learn mathematics. Analogy consists of two basic elements: base domain and target domain. Our knowledge about base domain is applied into target domain. In this framework, analogy can be seen as a mapping of information from base domain to target domain. In this paper, I make the following remarks to analyze analogy in mathematics education. a) There are two kinds of base domain: model and analog. b) We must consider user and producer of analogy. A base domain of producer is a target domain of user, and vice versa. C) Associations of base domain are mapped into target domain, then new concepts might occur in the target domain. Based on the above remarks, I illustrate some roles of analogy in understanding mathematics. i) Analogy develops new mathematical concepts. ii) Analogy makes misunderstanding of mathematical ideas. iii) Analogy creates some mathematical words.