The Effect of the Problem-Based Learning Model with a Metacognitive Approach on Students’ Mathematical Representation Ability

Abstract

This study was motivated by students’ low mathematical representation ability, which is influenced by the suboptimal implementation of instructional approaches, resulting in a teacher-centered learning process. This condition highlights the need for a learning model that encourages active student engagement, one of which is the Problem-Based Learning (PBL) model with a metacognitive approach. This study aimed to analyze the effect of the Problem-Based Learning model with a metacognitive approach on students’ mathematical representation ability in the topic of straight-line equations among eighth-grade students at MTs Negeri 1 Kota Lhokseumawe. This study employed a quantitative approach using a quasi-experimental method with a nonequivalent control group design. The population consisted of all eighth-grade students at MTs Negeri 1 Kota Lhokseumawe, while the research sample was selected using purposive sampling. The sample consisted of class VIII-5 as the control group, which received conventional instruction, and class VIII-6 as the experimental group, which received instruction using the Problem-Based Learning model with a metacognitive approach. Data were collected using a mathematical representation ability test administered before (pretest) and after (posttest) the learning process. The normality test results indicated that the data were not normally distributed; therefore, the hypothesis was tested using the nonparametric Mann–Whitney U test at a significance level of \(\alpha = 0.05\). The analysis yielded a significance value of 0.010, which was less than 0.05. Thus, the alternative hypothesis (\(H_a\)) was accepted and the null hypothesis (\(H_0\)) was rejected. It can therefore be concluded that implementing the Problem-Based Learning model with a metacognitive approach has a significant effect on students’ mathematical representation ability.