Pemahaman Matematis Peserta Didik dalam SPLDV: Perspektif Teori Pirie-Kieren

Abstract

Mathematical understanding is fundamental for students, especially in mastering core topics such as the system of linear equations in two variables, which serves as a prerequisite for advanced mathematical concepts and real-life problem-solving. Despite its importance, students frequently encounter difficulties in constructing mathematical models from contextual problems, often relying on procedural approaches without deep conceptual comprehension. This study aims to analyze students’ mathematical understanding of the system of linear equations in two variables based on the Pirie-Kieren theory, which conceptualizes understanding as a dynamic, recursive, and multilayered process. Employing a qualitative case study approach, data were collected from eighth-grade students at a public junior high school in Indonesia through open-ended tests and in-depth interviews, focusing on six key indicators of the Pirie-Kieren framework: image making, image having, property noticing, formalizing, observing, and structuring. The analysis reveals that while most students demonstrated adequate ability in basic indicators such as image making and image having, significant challenges were observed in formalizing, observing, and structuring, with procedural errors and incomplete solutions being prevalent. Only a small subset of students met all the Pirie-Kieren indicators, and the phenomenon of “folding back”—returning to earlier stages to reinforce understanding—was essential for overcoming impasses, though often requiring external scaffolding. These findings underscore the need for strengthened modeling instruction, systematic scaffolding, and reflective practices to cultivate deeper mathematical understanding. The study contributes theoretical and practical insights for developing effective mathematics teaching strategies and diagnostic tools.