Students understanding of the basis and dimensions of the solution space using the APOS theory - Mutambara, Lillias Hamufari Natsai; Makamure, Chipo (Universitas Islam Negeri Raden Intan Lampung, 2026)
The purpose of this study is to explore how in-service mathematics teachers understand the concepts of basis and dimension of the solution space as informed by the APOS theory. The data was obtained from 74 first-year in-service undergraduate mathematics teachers pursuing a Bachelor of Science Education Honours degree through the use of an activity sheet and semi-structured interviews. Employing a qualitative research approach within a case study design, the study was theoretically grounded in the APOS theory, drawing on the constructivist perspective, with the preliminary genetic decomposition serving as the basis for analysis. The study revealed that the lack of prior knowledge and related schema significantly hindered the participants' development of essential mental constructions. Most participants demonstrated a procedural understanding, signifying that a substantial number of in-service mathematics teachers were operating at the action level according to the APOS theory. Analyzing the mental constructions of in-service mathematics teachers can yield essential pedagogical strategies for enhancing understanding of the solution space. This research has implications for understanding that a structured development model based on APOS Theory enables educators to design learning sequences that gradually guide students from physical manipulation to abstract reasoning.