A case of teacher and student mathematical problem-solving behaviors from the perspective of cognitive-metacognitive framework

Abstract

This study aims to investigate the problem-solving behaviors of a teacher and his students based on a cognitive-metacognitive framework. The problem-solving behaviors of 6-8th-grade students and a mathematics teacher were recorded and encoded during task-based interview sessions about solving problems, and semi-structured interviews were used to obtain information regarding the mathematics teacher's perceptions of mathematical problem-solving processes. They solved the problems in a learning environment, and their problem-solving processes were investigated using the think-aloud method. The results indicated that the students and the teacher followed a similar path involving reading, understanding, exploring, planning, and implementing. Furthermore, not all episodes occurred in each problem-solving task and the behaviors that represented given episodes changed according to the participants. Students with different problem-solving skill levels were found to exhibit different frequencies of cognitive and metacognitive behaviors while solving problems. The problem-solving behaviors of the teacher and the students revealed information related to metacognitive behaviors that are to be developed in further studies.