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

本研究的目的是根据Genevan学校认知发展中的交互作用理论，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“辩证法-教学法”应用于克服学生在几何学习中的误区。为达到本研究的目的，我们构建了一种基于布鲁索的教学情境理论和有计划的教学实验的数学教学方法。实验问题是两类几何证明问题，一类可用三角形同余条件解决，另一类可用三角形边比定理解决。在这次解题中，我们发现了一个学生的误区：学生基于对几何图形的“知觉理解”而意识到一条直线上有三个点。为了克服学生的误解，我们还设计了三个教学情境：“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”。为了证明该教学方法的有效性，我们对初中二、三年级学生进行了教学实验。从实验结果可以看出，通过这种教学方法，学生可以克服误解，在新问题的解决中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。

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.