Procedural Dominance in Students’ Reasoning on the Limit Definition: Insights from a Ways of Thinking Framework

This study explores university students’ ways of thinking about the limit concept in differential calculus and uncovers how they construct the meaning of the limit definition through their reasoning. Data were collected from 28 students in mathematics education at a university in West Java, Indonesia, through written tasks and semi-structured interviews. Thematic analysis identified dominant reasoning patterns, revealing that 71% of students exhibited procedural reasoning, 18% demonstrated conceptual reasoning, and 11% displayed formal reasoning. Based on a systematic data reduction process, these patterns were categorized into procedural, conceptual, and formal ways of thinking, and six representative participants were purposively selected for in-depth analysis. The findings show that students predominantly exhibited procedural reasoning, relying heavily on algorithmic manipulation and symbolic recall rather than conceptual understanding or formal justification. This pattern indicates that many students have not yet internalized the formal meaning of the limit definition, resulting in mechanical rather than reflective reasoning. These findings highlight the need for instructional designs that promote conceptual reflection and formal reasoning in calculus learning, enabling students to move beyond procedural competence toward a more integrated understanding of the limit concept.