<![CDATA[Understanding algebraic concepts is an important prerequisite for advanced mathematics learning because it involves a transition from symbolic manipulation to structural thinking and proof. This study analyzes students’ understanding of algebraic concepts in a Linear Algebra course using the APOS (Action, Process, Object, Schema) theoretical framework. The method is descriptive qualitative, with systematic application of APOS indicators in the domain of Linear Algebra. Data were collected through conceptual tests and analysis of proof and problem-solving tasks. Data analysis involved reduction and categorization based on APOS development. The results showed three patterns of understanding: (1) students in the low-ability category failed to meet the criteria for the Action, Process, Object, and Schema stages; (2) the medium category showed partial comprehension—reaching the Process stage and parts of the Object stage on routine problems but failing at the Action stage for abstract constructive problems; and (3) the high category generally reached the Schema stage on constructive problems but showed failure at the Action stage on problems requiring proofs of basic axioms, or vice versa. The findings suggest emphasizing development of the Action stage and the process–object linkages to strengthen transfer to the Schema. Practical recommendations include gradual constructive tasks, mediated proof-of-concept learning, and APOS-indicator-based formative assessment.]]>
