Exploring Mathematical Epistemology of Grade 7 Students in Validating the Multiplication of Integers

Abstract

This study investigates the mathematical epistemologies and reasoning patterns of Grade 7 students in verification of integer multiplication through trial-and-error exploration with varying side parity combinations. It was conducted at a rural area in Lanao del Sur, Philippines specifically at Ansano Memorial National High School, Municipality of Taraka. This study was employed a qualitative research design involving 28 student participants. Data were gathered through validated five item open-ended instruments designed to prompt students’ empirical reasoning. Written responses were analyzed using thematic analysis aligned with frameworks of formal and practical epistemology. Results revealed that students mainly demonstrated formal epistemic reasoning, characterized by efforts to understand conceptual foundations, identify patterns and mathematical properties, and construct generalizations. Practical epistemic reasoning was less prevalent and observed mostly in contexts focused on accuracy, error prevention, and procedural correctness. Further analysis confirmed that task design significantly shapes students’ epistemic engagement: tasks requiring explanation and generalization prompted mostly formal reasoning, while computation and application-oriented tasks caused practical thinking. The result of the study implies that early secondary students are capable of coherent, principle-based reasoning when given appropriate learning opportunities.