DEVELOPMENT OF TEACHING METHOD OF MATHEMATICS BASED ON OVERCOMING STUDENTS' MISCONCEPTIONS IN MATHEMATICS LEARNING

基于克服学生数学学习误区的数学教学方法的发展

• 批准号: 13680327
• 负责人: HARADA Kohei
• 金额: $ 2.56万
• 依托单位: KAWAMURA-GAKUEN WOMEN'S UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13680327/
• 关键词: MISCONCEPTION; TEACHING METHOD OF MATHEMATICS; PROOF; GEOMETRY; 証明問題

The purpose of this research is to develop of teaching method of mathematics based on overcoming students' misconceptions in mathematics learning, according to the theory of interaction in cognitive development in Genevan school. We especially apply "dialectic-didactical method" in the theory of interaction to the means of overcoming students' misconceptions in geometry learning.For the purpose of this research, we constructed a teaching method of mathematics based on Brousseau's theory of didactical situation and planned didactical experiments. The problems of experiments are two kinds of geometrical proof-problems, that one can be solved by using conditions of congruence of triangles and another one can be solved by theorem of ratios of sides of triangles. In this problem solving, we identified a student's misconception: the student realizes there are three points on one straight line based on "perceptive apprehension" for geometrical figure. In order to overcome the student's misconception, we also designed a sequence of three didactical situations: "situation for recognizing misconceptions", "situation for overcoming misconceptions" and "situation for using new knowledge".In order to demonstrate the usefulness of the teaching method, we made for didactical experiments on the second and third grade students in junior high school. From the results of experiments, we could clarify that the students could overcome their misconceptions through the teaching method and produce mathematically various actions in new problem solving. We think that the fact shows that the teaching method is useful for the students.

本研究的目的是根据日内瓦学派认知发展的互动理论，在克服学生数学学习误区的基础上，发展数学教学方法。我们特别将互动理论中的“辩证教学法”应用于克服学生几何学习中的错误观念的方法中，以布鲁索的教学情境理论为基础构建了一种数学教学方法，并进行了教学实验。实验问题是两类几何证明问题，一类可以用三角形全等条件解决，另一类可以用三角形边比定理解决。在这道题的解题过程中，我们发现了一个学生的错误观念：学生基于对几何图形的“感性理解”而认识到一条直线上有三个点。为了克服学生的错误概念，我们还设计了“认识错误概念的情境”、“克服错误概念的情境”和“运用新知识的情境”三个教学情境，并对初中二、三年级的学生进行了教学实验，以证明这种教学方法的有效性。从实验结果可以看出，通过教学方法，学生能够克服错误概念，在解决新问题时产生数学上的各种动作。我们认为，事实表明，这种教学方法对学生是有用的。

项目成果

原田耕平: "幾何の証明問題の解決における生徒の誤った推論の克服の手段"日本数学教育学会 第35回数学教育論文発表会論文集. 445-450 (2002)

Kohei Harada：“克服学生解决几何证明问题时的错误推理的方法”第 35 届数学教育论文发表会论文集，日本数学教育学会 445-450 (2002)。

HARADA, Kohei: "The means of overcoming students' errors in inference in geometrical proof-problem solving"Proceedings of the 35th Conference of Japan Society of Mathematical Education. 445-450 (2002)

原田航平：《几何证明问题解决中克服学生推理错误的方法》日本数学教育学会第35届会议论文集。