Assessment of Mathematics Proof Construction: Preservice Mathematics Teacher Training and Upper Secondary School Students - Mohamad Waluyo; S Sutama; Nining Setyaningsih (Proceeding International Conference on Mathematics and Learning Research, 2025)
Constructing valid mathematical proofs is a fundamental yet persistent challenge for students. This study investigates the developmental trajectory of proof construction abilities among Indonesian students, spanning from upper secondary school (Grades 10-11) to undergraduate mathematics levels. Adopting a descriptive cross-sectional design, data were collected from 479 participants using open-ended proof construction tasks and a survey on proof perception. The results reveal a pervasive dominance of empirical proof schemes, where students rely on specific numerical examples rather than generalized logical arguments. Notably, formal proof construction was virtually non-existent at the secondary level, highlighting a significant pedagogical gap. While the frequency of formal proof attempts increased among university students, valid execution remained limited, indicating a disconnect between students' strategic knowledge and their normative understanding of "correct" proof. Furthermore, findings show a critical misalignment between perception and performance; students often recognized formal algebraic arguments as superior yet reverted to empirical methods in practice. The study concludes that the transition from inductive to deductive reasoning does not occur naturally and requires explicit instructional interventions to bridge the cognitive rupture between secondary calculation-based mathematics and tertiary formal reasoning.