数学学習における理解過程に関する研究(1) : 中学校第2学年「星形多角形の研究」の授業を事例として

概要

論文の詳細を見る
This is a part of the series of research on the process of understanding mathematics based on the "two-axes process model" that consists of two axes, i.e. the vertical axis implying levels of understanding such as mathematical entities, relations of them, and general relations, and the horizontal axis implying three learning stages of intuitive, reflective, and analytic at each level (Koyama, 1993, 1997). The purpose of this paper is to analyse the process of understanding in the lesson on "stellar polygon" at 2nd Grade in a lower secondary school attached to Hiroshima University in order to see the development of students' understanding of the properties of "stellar polygon" and to get some implications for the teaching and learning of mathematics in lower secondary school. The objectives of the lesson on "stellar polygon" were to improve students' understanding of how to find out the measure of an angle in a stellar polygon and to promote their mathematical thinking and attitude toward mathematics through generalising the mathematical tasks on regular polygons to regular stellar polygons. As a result of qualitative analysis of the data collected in the observation and videotape-record during the lesson, we found out the four suggestions for improving the students' understanding of mathematics in lower secondary school. First, there were three different approaches to the same task 1 in a regular nine-pointed star polygon. It means that mathematics teacher should pay attention not only to the correctness of the answer to a task but also to the process of reasoning to the answer in mathematics lesson. Second, when the students worked on the complicated task 2 in a regular nine-pointed star polygon they folded back to the image-making level. This fact suggests us the importance of teacher's decision making on what kinds of learning situation should be set up for helping students improve their mathematics understanding. Third, a questing about the reason by the teacher and the response by a student changed the development of the lesson to a higher level of understanding. It suggests the importance of social interaction among a teacher and students in mathematics classroom. Finally, the students had difficulties when they worked on the more generalised task 3 in a regular n-pointed star to formulate the measure of an angle. The fact suggests that students should reflect what they have done in the task 2 (reflective stage) and do more activities for integrating them (analytic stage) in the "two-axes process model" of understanding mathematics. Being based on these suggestions, when a teacher intends to help students develop their understanding, according to the levels of understanding and three learning stages involved in the "two-axes process model", it is suggested to set additionally the alternative tasks such as task 1' of geometrical figures in a regular nine-pointed star polygon, task 2' of the measure of an angle in a regular nine-pointed star polygon, and task 3' in a regular 12-pointed star polygon before posing the generalised task 4' in a regular n-pointed star for asking students to formulate the measure of an angle in general.
全国数学教育学会の論文

数学学習における理解過程に関する研究(1) : 中学校第2学年「星形多角形の研究」の授業を事例として

スポンサーリンク

概要

著者

関連論文

スポンサーリンク