Mapping students’ limits conceptions: A network analysis of students’ reasoning structures in calculus

Attending to students’ reasoning and thinking about limits can reveal how they make sense of this fundamental calculus concept. Integrating these ways of reasoning into calculus instruction can create opportunities for students to develop a deeper conceptual understanding of limits. Building on past research involving students’ limit views, this sequential explanatory study identified the fine-grained limit views that contribute to students’ understanding of the limit concept from 63 Calculus II students’ responses to surveys and interviews. Twelve students were purposively selected from the surveys to represent three limit conception categories (Intuitive, Informal, and Formal; four in each category) to further explore in depth how their preferred limit views align with their understanding of limits. The findings indicated that students most frequently express intuitive limit views, which confirms findings from past research that students begin to conceptualize limits from an intuitive perspective. Additionally, themes from the study advance the field’s understanding of students’ limit views, giving a full description of students’ operational-algorithmic neighborhood understanding, dynamic-coordinated observational understanding, asymptotic-infinity contextual understanding, operational-convergence approximated understanding, and sequential-conventional neighborhood understanding. Thus, this study extended from past research by revealing how students’ limit views are structurally organized through interconnected reasoning patterns identified using network analysis.