Abstract
Students may perform matrix operations correctly while still demonstrating limited understanding of the mental constructions underlying those procedures. This study examined students’ mental constructions in learning matrix multiplication and inverse matrix concepts using the Action, Process, Object, and Schema (APOS) framework, with particular attention to transitions between adjacent constructions and associated obstacles. A qualitative study was conducted with 23 Grade XI Social Sciences students at MA Nurul Ummah, Yogyakarta, Indonesia. Data were collected from students’ written responses to two matrix activities and follow-up semi-structured interviews with three purposively selected students. The data were analyzed through APOS-guided coding using NVivo. Action was identified in 21 students (91%), Process in 17 students (74%), and Object in 4 students (17%). Four students (17.4%) demonstrated Action without corresponding evidence of Process, while 13 students (56.5%) demonstrated Process without corresponding evidence of Object. The Action-to-Process difficulty was characterized mainly by procedural reliance and limited explanations of mathematical meaning. The Process-to-Object difficulty was more prevalent and involved difficulties in coordinating procedures, representations, and the use of mathematical results in subsequent reasoning. These findings indicate that procedural performance does not necessarily reflect the development of more advanced APOS constructions. The findings also provide a basis for designing AI-supported learning as adaptive scaffolding through explanation, connection, generalization, and integration, although its effectiveness requires further empirical investigation.