数学教育における直観ルールの研究 : その数学指導上の意味について

抄録

Through the work in mathematics and science education, it has been observed that students react in a similar way to a wide variety of conceptually nonrelated problems which share some external, common features. Tirosh, D., Stavy, R. who have studied students' comprehension of specific notions have also found that often their responses are in line with intuitive rule. The intuitive rule SameA-SameB relates to comparison tasks. Typically, the students are asked to relate to two systems or two entities which are equal with respect to one quality or quantity (A1=A2), but may differ with regard to another quality or quantity, either B1=B2 or B1=⃥B2. The students are asked to compare the two systems or entities with respect to quality or quantity B. It was found that students often claim that B1=B2 because A1=A2. In the present article, I describe the model of intuitive rule. I consider how intuitive rule has something to commit an error and what meaning intuitive rule has in mathematics teaching. The result of this research are as follows: (1) The missconception is sometimes caused by intuitive rule. (2) Intuitive rule revitalizes in various domain. (3) Intuitive rule is relevant to constitute conservation and proportion. (4) Intuitive rule restricts and facilitates children's recognition. (5) The presentation of the opposite opinion has an effect to restrain from revitalization of intuitive rule. (6) It is necessary to explore the way of coexistence together intuitive rule. (7) Intuitive rule has a strong predictive power about children's responses to the task.