Students’ Mathematical Understanding in Solving Systems of Linear Equations in Two Variables: A Pirie–Kieren Analysis
DOI:
https://doi.org/10.30862/jhm.v9i2.1075Keywords:
Mathematical understanding, Pirie-Kieren theory, Two-variable linear equation systemAbstract
This study aims to analyze junior high school students’ mathematical understanding across three levels of mathematical ability (high, moderate, and low) when solving systems of two-variable linear equations based on the Pirie–Kieren theory of understanding. It also examines differences in students’ understanding processes to provide deeper insights into the development of mathematical understanding. The novelty of this study lies in its in-depth exploration of students’ understanding processes through the Pirie–Kieren framework across different levels of mathematical ability. This study employed a qualitative descriptive design. Three eighth-grade students from SMPN 1 Pademawu were purposively selected based on mathematics achievement test results to represent high, moderate, and low mathematical ability. Data were collected through classroom observations, mathematics achievement tests, comprehension tests, and semi-structured interviews. Data were analyzed using data reduction, data display, and conclusion drawing, while methodological triangulation ensured the trustworthiness of the findings. The results revealed distinct profiles of mathematical understanding across ability levels. The student with high mathematical ability demonstrated all seven levels of understanding proposed by the Pirie–Kieren theory. The student with moderate mathematical ability demonstrated five levels: primitive knowing, image making, image having, property noticing, and formalizing. In contrast, the student with low mathematical ability demonstrated only the primitive knowing level. These findings indicate that higher mathematical ability is associated with more advanced levels of mathematical understanding, highlighting the importance of designing instruction that supports students’ progression toward deeper conceptual understanding through appropriately scaffolded learning experiences.
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