Observational and experimental studies on roles of communication in mathematics learning

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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.