A Study on the Representational System in Mathematics Teachnig

点击翻译按钮获取中文摘要

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.