Profiling junior high school students’ conceptual understanding of the Pythagorean theorem across ability levels - Nur Rahmah; T, Irma; Putri, Aisyah; Muhammad Ikram; Landy Sosa-Moguel (Universitas Islam Raden Intan Lampung, INDONESIA, 2026)
Purpose: This study aimed to map students’ conceptual understanding of the Pythagorean Theorem and to identify distinct conceptual profiles across different levels of understanding. Method: This research adopted a qualitatively driven design with a pragmatic stance. A two-item essay test was administered to 325 students aged 13–14 years (162 boys and 163 girls) to classify their levels of conceptual understanding and to determine participants for follow-up interviews. The instrument demonstrated strong psychometric properties, including content validity of 90.3%, item–total correlations of 0.72 and 0.75, and a Cronbach’s alpha coefficient of 0.83. Based on the classification results, selected students representing low, medium, and high levels of understanding participated in in-depth interviews. Data from written responses and interview transcripts were analysed using thematic analysis to identify patterns of conceptual reasoning. Findings: The results revealed three distinct conceptual profiles. Students at the low level tended to rely primarily on memorised formulas, frequently exhibited misconceptions, and provided limited justification for their solutions. Students at the medium level showed partial integration of representations but relied on constrained strategies and demonstrated inconsistent reasoning. In contrast, high-level students displayed relational understanding by integrating diagrams, symbolic representations, and coherent explanations while connecting the theorem to contextual situations. Significance: The findings provide level-specific descriptions of conceptual understanding that help explain why correct procedures may conceal conceptual gaps. These profiles offer practical guidance for diagnosing students’ thinking and for designing differentiated mathematics instruction.