Metacognitive Awareness Framework for Expressions on Mathematical Work (MAFEM)
摘要
Metacognition is widely regarded as a fundamental cognitive skill, which plays a critical role in the efficacy of mathematical problem solving. This study involved an investigation of whether there is a hierarchical structure in the metacognitive expressions used by students during the process of solving mathematics problems. The discussions of a group of sixth-grade students and two fifth-grade classroom discussions during problem solving were examined. Sixth grade students’ conversations were composed of student–student interactions, and the fifth grade classroom discussions included conversations in which the teacher guided the process. When analyzing the interactions and discussions among the students, distinctions were made initially between cognitive and metacognitive expressions. The main aim of the study is to determine whether there is a hierarchical structure within the metacognitive expressions. The findings of the study suggest that there is indeed a hierarchical structure manifested within students’ expressions during mathematical problem solving. In addition, student–teacher interactions indicate that teacher may have a facilitator role in unveiling the hierarchical structure in students’ metacognitive expressions. These findings not only deepen our understanding of metacognition as a critical skill in mathematical problem solving, but also offer a framework for examining students’ metacognitive expressions of awareness in mathematical problem-solving situations.