Practical Study of Constructive Approach in Mathematics Education

作为本研究的理论层面，笔者探讨了建构主义在数学教育中的发展现状，指出社会建构主义已成为数学教育的主流。我们还研究了重要的方法论原则，即反思性思维、建设性互动和建设性方法的表征模式。特别是，本研究构建了一个包含外部表征和内部表征的教学体系，明确了外部表征与其数学意义之间的关系。作为实践方面，我们对建构式教学法在小学“加法进位”、“分数基本概念”和“速度平均”教学中的应用进行了实验研究。作为实验课的主要假设，我们设定了以下几点：1.本课例说明了建构式备课模式在实践中的可行性和有效性。2.即使教师不对各种方法进行评价，儿童也可以通过反思性思维、建构性互动和表象模式自己建构、选择和使用更好的方法。作为实验课的结果，这些假设得到了验证。

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.