| Co-Investigator(Kenkyū-buntansha) |
YAMAGUCHI Takeshi Fukuoka University of Education, Faculty of Education, Associate Professor, 教育学部, 助教授 (60239895)
IWASAKI Hideki Hiroshima University, Graduate School for International Development and Cooperat, 大学院・国際協力研究科, 助教授 (50116539)
TAKESHITA Masanori Faculty of Literature, Yasuda Women's University Professor, 文学部, 教授 (80188177)
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| Research Abstract |
The ultimate purpose of this research is to propose the adequate theory of teaching and learning mathematics based upon "The New View of Learning Ability, " which emphasizes children's interests, will, and attitude. As a first step to achieve this purpose, we have noted on the generalization process which seems to be one of the specific and essential matures of mathematical thinking and learning. For the analysis of the generalization process, Dorfler's generalization model provides us the fruitful suggestions. This model, however, has some issues about the explanation of the cognitive process promoting the generalization. Therefore, in this research, we have firstly set up a theoretical framework for the analysis of cognitive activities in generalization in terms of critical consideration on Dorfler's model from the metacognititive viewpoint and Skemp's director system.
Secondly, in order to illustrate the advantage of our theoretical framework, we have designed two mathematics classes which are both problem-solving oriented, and normal. One is "Numbers on the Calendar" to examine the change of forms in algebraic signs in generalization. The other is "The Sum of Five Angles in Pentagram" to research the change of meaning in geometric figures in generalization. A close observation, comparison, and analysis of these two practice based upon the above framework, especially focusing on "Symbols as Objects" in Dorfler"s model, has shown that there are two types of generalization : one is the generalization of objects, the other is that of method.
Thirdly, we have designed and evaluated new teaching materials, which aim to develop "The New View of Learning Ability", by incorporating Wittmann's Teaching Units into our theoretical framework. To put it concretely, we have developed a teaching experiment "Star Patterns" based on the above theoretical framework and have proved its effectiveness.
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