RUME 28
2026
Alexandria, Virginia
Unpacking Students’ Intuitive Limit Views Using Graphical Representational Approach
Page: 1264
Students’ intuitive reasonings of the limit of a function at a point play a role in their overall conceptual understanding of the limit concept. Some researchers have defined intuitive limit views as students’ understanding of the limit concept based on their everyday experiences (e.g., Adiredja, 2014; Adiredja et al., 2020; Rathnayake & Jayakody, 2023). In this study, I characterize limit views that are based primarily on reasonings with less emphasis on mathematizing those ideas as intuitive. Research shows that intuitive views are closely linked to students' graphical reasoning (Adamoah & Strayer, 2025). Building on the findings of Adamoah and Strayer (2025), this study explored how students’ intuitive understandings of limits are connected with graphical representations. The results of this study highlight an instructional approach to help overcome what past research identified as students’ misconceptions about the difference between limit as x→a of f(x) and f(a) (Bezuidenhout, 2001; Denbel, 2014; Fernández, 2004). Specifically, I addressed the research question: How do students’ intuitive limit views influence their reasoning with and use of graphical representations in calculus? In this study, I found that students’ intuitive limit views were linked with the graphical representational approach in two ways: (1) viewing limits with graphical representation as an object and (2) viewing limits with graphical representation as a tool. Graphical representation as an object implies students’ belief that “it shows me” and graphical representation as a tool implies students’ belief that “I’m using it to show”. Below was Jake’s explanation of how the graph with removable discontinuity showed and helped him to distinguish limit as x→2 of f(x) and f(2). The results of this study offer calculus instructors ways to integrate and effectively use graphical representations either as an object or as a tool to help deepen students’ understanding of limits in general.