Study of the Representational System in Mathematics Education

点击翻译按钮获取中文摘要

In this study, we classified the modes of representaion used in mathematics teaching into five modes as follows.E1.Realistic rep. : Representations using natural objects in the real worldE2.Manipulative rep. : Representations using artificial manipulative objects1.Illustrative rep. : Representations using pictures, diagrams, and/or figuresS1.Linguistic rep. : Representations using written everyday languageS2.Symbolic rep. : Representations using mathematical symbolsMorevoer, we separated each mode of representation into children' internal representation and external representation. Based on the representational system, we examined characteristics and functional roles of each representational mode in mathematical lessons. Main findings can be summarized as :(1) E1, E2 and I are strong iconizing. S1 and S2 are week iconizing.(2) Following scheme will be suggested in the teaching-leraning process of mathematics ; E1 * E2 * I * S1 * S2(3) Manipultive rep.and Illustrative rep.play important role in problem solving and understanding processes.(4) The interactions in mathematical lessons are calssified into four types : 1.Decreased oppsition 2.Agreement 3.Integral enhancement 4.extensive enhancement.