Practical Study of Constructive Approach in Mathematics Education

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As the theoretical aspect of this study, the authors discussed the present development of constructivism in mathematics education and pointed out that the social constructivism became a main stream. We also studied on important methodological principles, that is, reflective thinking, constructive interaction and representational modes for the constructive approach. Especially this study constructed a reptesentational system including both external and internal representations as well as clarifying the relationships between the external representaions and their mathematical meanings.As the practical aspect, We made some experimental studies of the constructive approach in teaching "additions involving carrying", "elementary concepts of fraction " and "the average of speed" to the children of primary schools. As major assumptions for the experimental lessons, we set the following.1.The lessons exemplify the practical possibility and effectiveness of the lesson planning model in the constructive approach.2.Children by themselves can construct, select and utilize better methods by reflective thinking, constructive interaction and representational modes even if the teachers do not evaluate various methods. As the results of experimental lessons, these assumptions were verified.