Enhancing Mathematical Representation and Reasoning Through Metacognitive Problem-Based Learning

Rahmat Hidayat; Rahmat Saleh

doi:10.58421/misro.v5i2.1251

DOI:

https://doi.org/10.58421/misro.v5i2.1251

Authors

Rahmat Hidayat University of People https://orcid.org/0009-0008-1240-042X
Rahmat Saleh Universitas Sahid, Jakarta

Keywords:

Mathematical Reasoning, Mathematical Representation, Metacognitive Problem-Based Learning, Secondary Education, Self-Efficacy

Abstract

Mathematical representation and reasoning are critical competencies that students often struggle to master. This study aims to evaluate the effectiveness of the Metacognitive Problem-Based Learning (MPBL) model in enhancing these abilities, while also examining the predictive roles of self-efficacy and metacognitive awareness. Using a quasi-experimental pretest-posttest non-equivalent control group design, a sample of 350 secondary students in Indonesia was selected via cluster random sampling. The experimental group (n=200) received MPBL, while the control group (n=150) followed conventional instruction. Results indicated that the MPBL group achieved significantly higher N-gains in mathematical representation (0.72, "High") and reasoning (0.68, "Medium") than the control group. Statistical analysis confirmed that the improvements were significant (p < 0.05). Furthermore, multiple regression analysis revealed that metacognition and self-efficacy jointly predicted 58% of the variance in problem-solving performance (p < 0.05). These findings suggest that integrating metacognitive scaffolding within problem-based frameworks is a potent strategy for fostering higher-order thinking in mathematics education.

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