Exploring Students’ Mathematical Epistemic Stances in Validating Arithmetic Sequences

Abstract

This study explored the mathematical epistemology of Grade 10 students in validating arithmetic sequences, focusing on their epistemic stances in constructing and justifying mathematical knowledge. Grounded in mathematical and personal epistemology frameworks, the study examined how students use pattern recognition, trial-and-error, and example-based reasoning during validation tasks. An exploratory descriptive research design was employed involving 30 Grade 10 students from Dansalan National High School, Marawi City, Philippines. Data were collected using the Student’s Practical Epistemologies in Mathematics Questionnaire (SPEMQ), which included arithmetic sequence tasks and open-ended questions. Responses were analyzed through thematic analysis and categorized into formal and practical epistemic reasoning. Results showed that students predominantly demonstrated formal epistemic reasoning, particularly in identifying patterns, determining the common difference, and validating arithmetic sequence formulas. However, practical epistemic reasoning was also evident through students’ reliance on examples, procedural strategies, and error detection. Despite their ability to apply formulas, students’ validation processes were largely empirical rather than deductive. This study contributes to the limited empirical literature on students’ epistemic stances in specific mathematical content, particularly arithmetic sequences, by providing evidence of how students transition between practical and formal reasoning in validation tasks. The findings highlight the need for instructional strategies that facilitate students’ transition from example-based reasoning to formal mathematical justification, thereby promoting deeper conceptual understanding.