Practical Study of Constructive Approach in Mathematics Education

数学教育中建设性方法的实践研究

• 批准号: 05680219
• 负责人: NAKAHARA Tadao
• 金额: $ 1.15万
• 依托单位: HIROSHIMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05680219/
• 关键词: Constructive Approach; Construtivism; Lesson Plan; Representatinal System; Refrecteve Thinking; Addition Involving Carrying; 表現様式; 表象; 社会的相互作用

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.

作为这项研究的理论方面，作者讨论了数学教育中建构主义的当前发展，并指出社会建构主义已成为主要流。我们还研究了重要的方法论原理，即反思性思维，建设性方法的建设性互动和建设性方法的代表性模式。尤其是这项研究构建了一个销售系统，包括外部和内部表示，并阐明了外部代表及其数学含义之间的关系。作为实际方面，我们对教学中的建设性方法进行了一些实验研究，其中涉及涉及“携带分数的基本概念”和“平均速度”和“平均速度”的孩子。作为实验课程的主要假设，我们设定了以下内容。1。在建设性方法中，课程计划模型的实际可能性和有效性。作为实验课程的结果，这些假设得到了验证。

项目成果

T.Nakahara: "A Basic Study on Cognitive Processes of Mathematical Concepts (XV)" The Annals of Educational Research, Joint Research System of Faculty of Education and Attached School of Hiroshima Univ.Vol.22. 31-40 (1994)

T.Nakahara：“数学概念认知过程的基础研究（XV）”教育研究年鉴，广岛大学教育学院和附属学校联合研究系统第22卷。

小山正孝: "高校数学教育における問題解決的教授学習の展開" 『広島大学教育学部紀要』. 第42号第II部. (1994)

小山正孝：“高中数学教育中问题解决教学的发展”，广岛大学教育学部通报，第 42 期，第 II 部分（1994 年）。

Tadao Nakahara: "Study of the Representational System in Mathematics Education," Hiroshima Journal of Mathematics Education. Vol.2. 1- (1994)

中原忠雄：“数学教育中的表征系统研究”，广岛数学教育杂志。

M.Koyama: "On Transcendent Recursive Theory of Understanding of Mathematics" Bulletin of the Faculty of Education Hiroshima Univ., Part II. Vol.43. 63-72 (1995)

M.Koyama：“论数学理解的超越递归理论”广岛大学教育学院通报，第二部分。

中原忠男: "数学的概念の認識過程についての基礎研究(XV)-構成主義に立つ算数・数学教育の実践的研究-" 広島大学教育学部学部・附属共同研究体制『研究紀要』. 第22号. 2-11 (1994)

中原忠雄：《数学概念的认知过程的基础研究（十五）——基于建构主义的算术和数学教育的实践研究》广岛大学教育学部和附属联合研究系统《研究通报》第22.2-11号。 (1994)