Combined conceptualisations of metacognitive knowledge to understand students’ mathematical problem-solving

Abstract

This study examined the metacognitive knowledge of Finnish comprehensive school students and explored whether grade-based differences in metacognitive knowledge exist among 6th, 7th and 9th graders. Integrating qualitative (declarative, procedural, conditional) and contextual (person, task, strategy) frameworks, the research aims for a comprehensive understanding. We employed mixed-methods approach; qualitative data from 225 student interviews underwent qualitative theory-driven analysis, followed by quantitative methods to explore variations and relationships. Results showed prevalent procedural and strategic metacognitive knowledge. Utterances on problem-solving often linked to task-specific knowledge, emphasising the need for a varied metacognitive knowledge set. 9th graders excelled in explaining strategy use, while 7th graders demonstrated proficiency in understanding when and why to employ specific strategies. Although a qualitative level approach can aid in understanding the development of metacognitive knowledge, combining qualitative and contextual conceptualisations provides a better overview of metacognitive knowledge. This study suggests that metacognitive knowledge-supporting elements are needed in math learning materials and teachers’ pedagogical actions.

Keywords

• Metacognitive knowledge
• math education
• comprehensive school
• student
• problem-solving
• Ana Paula Lopes, Polytechnic Institute of Porto: Instituto Politecnico do Porto, Portugal