Observational and experimental studies on roles of communication in mathematics learning

在信息社会中，沟通能力在教育中变得越来越重要。本研究调查了初中数学学习中课堂交流存在的问题，并寻求改善的途径。数学能力的发展包括数学话语的习得：学生应能灵活地运用符号、公式、术语、数字、表格、图形等作为交流和研究的工具。在本研究的第一年，我们对不同类型的数学课堂进行了观察性案例研究，发现了以下情况：即使学生在一节课中说话的频率很高，他们的表达也往往局限于简短的回答。计算机的使用有可能在课堂上引入新的数学交流方式，但它们尚未得到充分的重视。当教师之间的沟通组织良好时，团队教学在促进课堂交流方面具有丰富的潜力。在第二学年，运用George Lakoff的认知模型理论对学校教科书中的数学证明话语进行了分析。在美国和日本的证明教学中，分别存在模块化结构和有机结构，并普遍存在“旅程”隐喻。有人认为，数学证明应该被理解为经历或指导数学探索的旅程，以及给出旅程的说明（“讲故事”）。在此基础上，笔者在某初中进行了几何学证明学习的教学实验，提出了一种提高数学证明学习交流的教学方法：用冒险故事的比喻来解决证明问题，并要求学生保留自己的笔记本，记录自己或他人的工作并进行反思。

The ability of communication has become increasingly important in education for the information society. This research examined problems of classroom communication in mathematics learning at junior high school, and sought a way to improve the situation. Development of mathematical ability involves acquisition of mathematical discourse : Students are expected to be able to flexibly handle symbols, formulae, terminology, figures, tables, graphs, etc.as toosl for communications as well as for investigation. In the first year of this research, ovservational case studies in various types of mathematics classroom were conducted, and the following situations were identified :1. Even if the frequency of students' utterance is rather high in a lesson, their expressions are often limited to short responses.2. The use of computer has potentials to introduce new ways of mathematical communication to the calssroom, but they have not yet been fully appreciated.3. Team-teaching has rich potentials to enhance classroom communication when communication between teachers is well organized.In the second year, mathematical discourse of proof in school textbooks was analyzed using George Lakoff's theory of cognitive model. Modular structure and organic one were found in the instruction of proof in the United States and Japan, respectively, and a "journey" metaphor was common. It was argued that mathematical proof be underestood as experiencing or guiding a journey of mathematical inquiry as well as giving accout ("telling a story") of the journey. Based on this analysis, a teaching expeirment on learning of proof in geometry was conducted in a junior high school, and a teaching method to improve communication in learning mathematical proof was developed : It uses a metaphor of adventure story for solving proof problems, and asks students to keep their own notebooks for recording their own or other's works and reflecting on them.