Tracing how students make sense of convergent sequences through their preferred mathematical representations: A phenomenological exploration

Abstract

Background: Many students struggle to understand convergent sequences when they depend on only one form of mathematical representation, which limits how they interpret the idea of a sequence approaching its limit.

Aim: This study explores how students who naturally rely on symbolic, visual, or verbal representations experience the process of solving convergent sequence problems. The goal is to understand how they construct meaning, the strategies they choose, and the points at which they feel uncertain when shifting between different modes of representation.

Method: A descriptive phenomenological approach was used with seven participants selected through AHP–TOPSIS classification of Dominant Mathematical Representations. Data were gathered from written work, observations, and individual interviews, then analyzed using Colaizzi’s stages. Themes were refined through triangulation to ensure consistency and credibility.

Results: Symbolic-oriented students tended to rely on procedural steps and showed little inclination to move beyond formulas. Students who preferred visual thinking used sketches to build intuition but hesitated when expressing their ideas in symbolic form. Those with a verbal orientation explained their reasoning narratively yet were less confident when formal notation was required. Across all participants, shifts between representations occurred rarely, and emotional responses—such as hesitation or relief—often accompanied these moments.

Conclusion: The findings indicate that students’ understanding of convergence is shaped strongly by the representational mode they depend on. This limited flexibility suggests the need for instructional approaches that actively support transitions between symbolic, visual, and verbal representations so students can develop a more connected and meaningful understanding of convergent sequences