Junior High School Students’ Mathematical Thinking Ability on Set Theory Material Based on the APOS Theory

Source abstract

This study aimed to describe the mathematical thinking of seventh-grade students on set material and to interpret the dominant cognitive tendencies reflected in their responses through an APOS-informed perspective. This descriptive qualitative study involved 19 seventh-grade students at Srijaya Negara Junior High School in Palembang. Data were collected through a written test organized around four mathematical thinking indicators, namely specializing, generalizing, conjecturing, and convincing, as well as semi-structured interviews. In this study, APOS theory was used as an interpretive lens rather than as a strict one-to-one measurement framework. The results showed that, within the sampled group, students’ average mathematical thinking score was in the good category (69.80). Indicator-level analysis revealed the highest achievement in specializing (81.9%) and the lowest in convincing (59.0%). Qualitative analysis of selected students from contrasting performance levels showed that the higher-performing student provided more integrated explanations, the middle-performing student relied more on procedural responses with partial justification, and the interviewed student in the less category showed difficulty in responding to the conjecture-and-proof task, although time limitation also affected task completion. These findings suggest that students tended to perform better in representational and procedural tasks than in justification-oriented tasks. The study implies that mathematics learning on set material should provide greater support for reasoning, explanation, and justification.