Constructing the Concept of Geometric Transformation through APOS Theory: A Perspective on Learning Readiness

Concept construction is essential for developing mathematical abilities such as conceptual understanding and problem-solving. The APOS theory (Action, Process, Object, Scheme) offers a framework for conceptual development through mental activity sequences. A key factor influencing concept construction is students’ learning readiness, which is strongly tied to their initial abilities. This study investigates the relationship between learning readiness and concept construction, as well as describes students’ concept construction profiles based on APOS theory. Employing a mixed-method approach with an explanatory sequential design, the study involved 34 eleventh-grade students from a public high school in Gresik. Data collection techniques included cognitive diagnostic assessments, written tests, think-aloud protocols, interviews, and classroom observations. Quantitative data were analyzed using regression and correlation analyses, while qualitative data were processed through reduction, display, and conclusion drawing. Findings revealed a very strong, positive correlation (r=0.9046) between learning readiness and concept construction, suggesting that higher readiness aligns with more complex conceptual structures. Additionally, three profiles emerged: students with advanced readiness displayed complete analytical constructions; those developing readiness showed pseudo-complete constructions; and newly developing students exhibited incomplete geometric constructions. Future studies should explore APOS-based instructional models tailored to readiness levels and validate findings across broader mathematical topics and grade levels.