Characteristics of Prospective Mathematics Teachers’ Problem Solving in Metacognitive Awareness: Absolute Value Problems of Calculus Courses

Abstract

Metacognitive awareness influences problem-solving thinking. Understanding metacognitive awareness is essential in the teaching and learning process. The purpose of this research is to determine the amount of metacognitive awareness and the characteristics of each level in problem solving. The extent of metacognitive awareness of 125 prospective mathematics teacher students from four different public and private universities was revealed in this exploratory qualitative study. To acquire research data, absolute value assignments, think-aloud transcripts, and semi-structured interviews were employed. Sources and methods are triangulated to assure data validity. The data was analyzed using fixed comparison analysis. The results of this study indicate that there are six levels of metacognitive awareness of prospective teacher students: tacit use, identity use, semi-aware use, aware use, strategic use, and reflective use. The six developed levels can identify all the characteristics of metacognitive awareness that arise in solving absolute value problems. Metacognitive awareness that has been developed can supporting the development of learning models, cognitive style characterization and tracing students' process of mathematical metacognitive awareness.