A Study on the Representational System in Mathematics Teachnig

本研究的目的概括如下：1.研究目的。对数学教学中的各种表征进行分类和系统化。研究儿童对各种表征的理解过程。研究表征在数学课中的功能作用及其实践原则。本研究的主要结果和发现如下：(1)将数学教学中的表征模式分为五大类，即“现实表征”、“操纵表征”、“图画表征”、“语言表征”和“符号表征”。(2)从符号和认知的角度阐明了每种表征模式的特点。(3)阐述了表征在数学课中的功能作用及其实践原则。例如，原则上，五种表征方式在数学课中的使用顺序依次为“现实表征”、“操纵表征”、“图画表征”、“语言表征”和“符号表征”。(4)儿童对“长短”等反义形容词的理解不同。(5)设计了“图形操作表”和“图形证明法”。

The aims of this research are summarized as follows.1. To classify and systematize various representations in mathematics teaching.2. To research children's understanding process about various representations.3. To study functional roles of representations and their practical principles in the lessons of mathematics.The main results and findings in this study are as follows.(1) The representational modes in mathematics teaching are classified into the five categories - namely, "Realistic representation", "Manipulative representation", "Pictorial representation", "Language representation" and "Symbolic representation".(2) The characteristics of each representational modes are clarified in view of symbolic and cognitive stand.(3) The authors showed functional roles of representations and their practical principles in the lessons of mathematics.For example, in principle, the five representational modes are used by the order of "Realistic representation", "Manipulative representation', "Pictorial representation", "Language representation" and "Symbolic representation" in the lessons of mathematics.(4) Children understand differently the antonymous adjectives such as "long - short".(5) "Operative sheets of figures " and "Method of figurative proof" are devised.