The relationship among metacognitive knowledge, metacognitive calibration accuracy and mathematical problem solving performance

Abstract

The purpose of this research was to investigate relationships among metacognitive knowledge, metacognitive calibration accuracy and mathematical problem solving performance. In order to measure metacognition more holistically, metacognitive knowledge and metacognitive calibration (both prospective and retrospective) were taken into consideration together. Mathematical problem solving performance was assessed through three mathematical word problems. In the analyses, judgment bias and different levels of performance of students were taken into consideration. There were 200 participants in the study obtained from seventh grade students from public (N=90) and private (N=110) schools. The convenient sampling method was used in the data collection process of the study. Results demonstrated a significant relationship between prospective and retrospective monitoring accuracy. Another significant relationship was found between problem solving performance and metacognitive monitoring calibration. In terms of judgment bias, students tended to be overconfident in their prospective judgments compared to retrospective ones. Moreover, there is a significant difference between overconfident and underconfident students' performances. High performers tend to be underconfident while low performers are generally overconfident. Lastly, metacognitive knowledge was a differentiating factor for low performers in prospective judgments not in retrospective judgments.