As a part of the joint research on didactics with the group of Hokkaido University, the author constructed contents of education and teaching materials on the introduction to fractions in the form of a textbook. In order to verify whether the content and materials were suitable for children, the experimental lessons (a didactical experiment) were carried out. These lessons were carried out in the 4th grade class of the Niigata Prefecture Echizen Primary School in November 1998. A teacher, Yoshimi Tateishi, taught these lessons. These lessons were linked with the "Seminar on Educational Practice Research" of the Faculty of Education and Human Sciences, Niigata University. Based on these experimental lessons, the university students and the teacher underwent a change in their perceptions that will be described below. (1) Before the experimental lessons began, the university students were negative regarding the contents of the textbook and tended to criticize the content. This reaction seems to have been caused by the fact they were comparing the theory of fractions in the textbook with the traditional and the commonly accepted theory of fractions. In this theory, only the division aspect of fractions is regarded as important. On the contrary, in the textbook, fractions are explained as unification of the division aspect and the ratio aspect. By comparison, the theory of fractions of the textbook was entirely different and high level in content. The university students, based on their perceptions, set up a negative hypothesis on children's understanding on the content of the textbook. However, in the experimental lessons, it was indicated that this hypothesis was completely untenable. The intellectual level of the children was far beyond the level of the university students and their one-sided presumption on the premise of the intellectual level of the university students. In the experimental lessons, it was concretely and clearly indicated. By participating in the didactical experiment, the university students were forced to reexamine their own understanding of fractions and themselves who persisted in their own experiences of school education. At the same time, their focus of thinking shifted to the essential meaning of fractions. (2) In the case of the teacher, the evaluation on the content of textbook was positive and supportive on the following two points. The first point was the logical consistency of the development of the definition of fractions. This was the original nature of the content of the textbook itself. The second point was a high-level-assumption on the level of intellectual curiosity of children. This was a fundamental viewpoint underlying the didactical experiment. After the experimental lessons finished, the teacher told "In these lessons, we are forced to think about the meaning of fractions logically." Especially, the ratio aspect of fractions was contained in the textbook. It was the major point of resistance in understanding the contents of the textbook in the part of both the teacher and the university students. On the contrary, in the experimental lessons, the children that were generally negative toward the usual lessons in arithmetic were the ones that understood this content (the ratio aspect of fractions) quickly and were positive in learning activities. The teacher took note of this fact. This was a major factor in bringing about a change in the perceptions by the university students. In conclusion, the most essential and important feature of this didactical experiment was the viewpoint that the aim of mathematics education is to teach mathematics as a science and the contents of mathematics education should be constructed logically. It is important that this has become the basic stance as related to organizing the teacher education curriculum.
抄録全体を表示