Students conceptual mode and analytical thinking: Its role during mathematical problem posing and solving - Patac, Adriano Jr; Patac, Louida (Journal of Honai Math, 2025)
In mathematics education, learners frequently rely on procedural imitation when solving problems, even in contexts that demand deep conceptual understanding. This tendency can obscure underlying structural reasoning, yet the extent to which surface-level cues constrain preservice teachers’ mathematical reasoning remains underexplored. Addressing this gap, the present study investigates how third-year secondary mathematics preservice teachers engage with problems requiring conceptual insight while highlighting potential limitations of procedural imitation. The study involved 15 preservice teachers at a state university during the 2023–2024 academic year. Data were collected using multiple standardized instruments, including a Weekly Log-Journal template, End-of-Week Summary sheets, an Instructor Field-Note protocol, and post-task semi-structured interviews, all validated by experts for clarity and content. Credibility was ensured through triangulation and double coding. Analysis employed directed content analysis with theory-informed a priori codes, refined inductively, alongside reflexive thematic analysis and descriptive cross-case synthesis. Findings revealed that routine problems were predominantly addressed through familiar procedures, with learners focusing on surface similarities in equations, leading to errors and the use of spurious methods. These results suggest that superficially correct solutions may mask inadequate structural understanding, underscoring the necessity of cultivating representational fluency, critical thinking, and deeper conceptual knowledge. To address this, problem-posing rubrics should explicitly define invariant conditions and learning objectives to differentiate isomorphic from non-isomorphic situations and reduce superficial copying. The study’s implications extend to instructional design, advocating interventions that promote structural thinking and computational reasoning. Future research may include quasi-experimental investigations, longitudinal tracking of preservice teachers’ practicum performance, and the integration of tools such as GeoGebra, generative AI software, and spreadsheet packages to enhance structural reasoning and procedural flexibility.