How Can We Understand the Relationships between the Interactions and the Learning in the Mathematics Classroom? : From One Student's Perspective

Abstract

Recent research concerning interactions in mathematics classroom suggests that a starting point for improving the everyday mathematics classroom is to have a better understanding of its unique cultural practice. The focus of this research is to gain a better understanding of mathematics classroom from students' perspectives. In particular, it aims to analysis the relationships between the nature of teacher-student or sutudent-student interactions and the students' mathematics learning. The research methodologies used in this qualitative study were hermeneutic and micro-ethnographic case studies. Four mathematics lessons were taken from an 8th grade mathematics classroom. The context was the teaching of basic triangle congruence theorems. Five students were interviewed after the lessons. This paper reports the class interactions from the perspective of one student, Yama, who was one of the more active students in the mathematics class. Yama developed his mathematical understanding in the class interactions by taking advice from the teacher and the other students, especially one of the active participants in the class, Yoshi. Yama developed his mathematical understanding and ways of participating in class through the interaction processes. An analysis of the class interactions from Yama's perspective revealed that: (1) It was very important for him to interact with another active student, Yoshi, who played the role of his adviser. They were learning from each other. Their fruitful relationship developed since they were able to complete the same task interactively in the process of the class interactions. Yama developed his mathematical understanding by reacting to Yoshi's suggestions. In this sense, the mathematical understanding itself that he developed was the result of the interactions. The fact that their fruitful human relationship influenced the mathematically rich interactions is worthy of attention. (2) Yama's "thinking with announcing" acts contributed to developing his mathematical understanding through his participation in the class interactions. The interview with the students revealed that the "thinking with announcing" activity was shared with some students in the classroom and was considered by them to be a natural process. The "thinking with announcing" represented the emergence of a classroom microculture. The classroom microculture and his mathematical knowing seemed to be developed interactively.