Exploring Mathematical Epistemology of Grade 9 Students in Validating the Pythagorean Theorem

Abstract

Understanding how students justify, evaluate, and validate mathematical knowledge is central to effective mathematics instruction. This study examined the mathematical epistemology of Grade 9 students from a public national high school in Lanao del Sur, Philippines, as they validated the Pythagorean Theorem through a guided investigation. The task design intentionally utilized eight distinct side-length parity sets, including non-right triangle distractors to test the exclusionary logic of the theorem. Students’ written reflections were analyzed and categorized into two epistemic stances: practical epistemic reasoning and formal epistemic reasoning. The findings indicate that students’ mathematical epistemology is highly context-dependent and shaped by task design. While practical reasoning focused on visual representation and empirical evidence was initially dominant in initial tasks, a significant epistemic transition toward formal reasoning (theoretical justification and pattern recognition) occurred in tasks requiring the verification of universal validity. However, the study also reveals that students are prone to developing heuristic rules based on numerical patterns, such as parity (even/odd), rather than relying solely on formal mathematical properties. These results highlight the critical role of structured inquiry and the need for rigorous verification tasks that account for potential instructional-induced biases. The findings offer implications for mathematics instruction, emphasizing the importance of bridging practical engagement and formal reasoning to foster a more coherent and robust mathematical epistemological awareness.