数学教育における相互構成的記述表現活動に関する研究 : 内省的記述表現の規定と内省的記述活用学習の事例的分析

抄録

In this article, a type of writing activity, which has a Reflexive Nature, and enable students to be aware of "others" or the social aspects under the learning environment, is discussed. First of all, the relationship between cognition and writing is examined through the results from psychology, and it is suggested that writing activities effect on the learner's cognition or understanding. Then, considering the concept of "Reflexivity", the terms of "Mathematical Writing" and "Reflexive Writing" are defined. Reflexive writing is one type of mathematical writing, and it is formed with (1) student's own answer or solution, (2) ideas or comments from Second Personal Others, and (3) comments from First Personal Other. Because the reflexive writing activity and student's learning may develop their mutual interaction, the nature of their relation is reflexive. Also, reflexive writing is a reproduction of the class activity, which is produced from each student's viewpoint, it is the reflection of each class activity, and the nature of their relation is also reflexive. Furthermore, the social aspect of mathematics learning, especially the concept of "Others" is examined. The three types of "Others" in the learning environment are identified, and a framework of learning, "Reflexive Writing Activity", which consciously emphasizes the existence of "others", is presented. Moreover, one type of learning method in this framework, "Characters Method" has put into practice for some implications. In conclusion, Reflexive Writing Activity is not only the effective learning method which is helpful for both knowledge-understanding and the rich-fruitful learning environment, but also the aims of mathematics learning which should be regarded as one of the fundamental abilities for students.