Intelligent Diagnosis and Dynamic Differentiated Instruction for High-School Mathematics Concepts Based on APOS Theory - Model Development, Implementation Pathway, And Validation Plan

Source abstract

In high-school mathematics classrooms, conceptual understanding can usually be inferred only indirectly from students' answers, explanations, and transfer performance. A total score or a single correct-or-incorrect response rarely shows whether a student's difficulty lies in an externally guided action that has not yet been interiorized, an inability to view a process as a whole, or weak connections among concepts. To address this diagnostic problem, the study adopts a theoretical-construction and design-research orientation and proposes an intelligent diagnosis and dynamic differentiated-instruction framework grounded in APOS genetic decomposition. The framework first specifies observable evidence of Action, Process, Object, and Schema constructions for a particular concept. A Q-matrix then organizes answers, solution steps, representational transitions, verbal explanations, revision traces, and transfer tasks. Expert rubrics, cognitive diagnosis, and sequential updating are combined to produce profiles with explicit confidence estimates. Instructional groups are formed around students' current constructional difficulties and reconsidered after short task cycles, so that one assessment does not harden into a general ability label. Using the high-school function concept as an example, the paper presents a task blueprint, scoring anchors, and a classroom implementation process, together with validation requirements for construct validity, classification accuracy, calibration, fairness, and teacher usability. The framework is not intended to replace teacher judgment. Its value lies in turning APOS mental constructions into discussable classroom evidence while defining boundaries for low confidence review and responsible data use.