Junior High School Students' Conceptual Understanding of Flat-Sided Geometric Shapes through APOS Theory: A Qualitative Study

Source abstract

<p>Research on students' difficulties in geometry has mostly emphasized errors and formula mastery, while fewer studies have examined how junior high school students construct three-dimensional geometric concepts through APOS theory. This qualitative descriptive study analyzes eighth-grade students' conceptual understanding of cubes and prisms in flat-sided geometric shapes using the APOS framework. Participants were 28 eighth-grade students in Tangerang Regency who had studied cubes and prisms. Data were collected through five open-ended diagnostic questions mapped to Action, Process, Object, and Schema indicators and through semi-structured interviews. The results showed that 10 students (35.7%) were at the Action stage, 9 students (32.1%) at the Process stage, 6 students (21.4%) at the Object stage, and 3 students (10.8%) at the Schema stage. Most students could apply formulas but had difficulty explaining why formulas worked, coordinating two- and three-dimensional representations, and integrating base area, height, volume, and context. The novelty of this study lies in using APOS as a diagnostic framework for identifying were students' cognitive construction stalls in junior high school three-dimensional geometry. The findings suggest that geometry instruction should include visualization, manipulation, and reflective explanation to support transitions between APOS stages.</p>