Study of the Representational System in Mathematics Education

在本研究中，我们将数学教学中使用的表征模式分为以下五种模式。写实再现：使用现实世界中自然物体的再现。操纵性代表：使用人工操纵性对象的表示。说明性代表：使用图片、图表和/或数字的表示。语言表征：使用日常书面语言的表征。符号表征：使用数学符号的表征。然而，我们将每种表征模式分为儿童的内部表征和外部表征。基于表征系统，我们考察了数学课堂中每种表征模式的特点和功能角色。主要发现如下：(1)E1、E2和I具有较强的符号化。S1和S2是周图标。(2)在数学教学过程中提出以下方案；(3)操纵性再现和说明性再现在问题的解决和理解过程中起着重要作用。(4)数学课堂中的互动可以分为四种类型：1.课堂互动；2.减少反对。协议3。积分增强4。广泛的增强。

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.