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.

作为本研究的理论方面，作者讨论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。并对建构主义教学法的重要方法论原则，即反思性思维、建构性互动和表征模式进行了探讨。特别是构建了一个包含外部表征和内部表征的表征系统，阐明了外部表征与其数学意义之间的关系，并在实践方面对小学生“进位加法”、“分数的基本概念“和“速度的平均值”的建构教学进行了实验研究。作为实验课的主要假设，我们设定了以下几点：1.实验课验证了建构主义教学模式的可行性和有效性; 2.即使教师不对各种方法进行评价，儿童也能通过反思性思维、建构性互动和表征模式，自主地建构、选择和运用更好的方法。作为实验课的结果，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。

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。

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）。

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)