Abstract

Proof construction is central to mathematics learning yet remains a persistent challenge for preservice teachers. This study examined the proof-construction struggles of seventy-three mathematics teacher education students (MTES) enrolled in a specialization course at a state university in northern Philippines. Using a qualitative exploratory design supported by descriptive statistics, the study analyzed students’ written proofs of five propositions alongside follow-up interviews. Responses were classified into six categories: lack of reasoning and definition errors, limited knowledge of proof techniques, reliance on numeric examples, use of verbal statements, incomplete proofs due to insufficient setup, and proficient systematic proof construction. Findings revealed that 88.6% of MTES failed to produce valid proofs, relying heavily on empirical reasoning and struggling to apply axiomatic methods. Interview data confirmed difficulties in abstract thinking, logical structuring, and generalization, highlighting the influence of teacher-centered instructional traditions and procedural emphases on prior schooling. The study recommends strengthening proof-based instruction through scaffolded tasks, explicit teaching of proof techniques, and structured opportunities for reflection. Situated within Toulmin’s argumentation model and proof schemes theory, these results underscore the urgent need for teacher education programs in the Philippines to integrate reasoning-focused approaches that build metacognitive awareness and prepare future teachers for the demands of formal mathematics.