Exploring common errors, challenges, and strategies of solving limits in calculus

This paper presents findings from a case study examining undergraduate students’ common errors when solving limit problems, the challenges encountered, and the strategies employed in enhancing their understanding and performance in this topic. A mixed-methods approach was utilised, combining quantitative and qualitative data collection. Common errors were assessed by analysing students’ assessment work solutions, while challenges in learning limits and strategies for improvement were investigated through surveys conducted among students and lecturers. Additional qualitative feedback from lecturers provided insights into the challenges and effective strategies for improvement. The results identified three common types of errors, where conceptual errors (misunderstandings of the fundamental principles and concepts underlying limit problems) contributed to the highest percentage of errors at 67.6%, followed by procedural errors (incorrect steps or algorithms in the mathematical process of solving limit problems), and factual errors (mistakes in recalling or applying mathematical facts related to limits), with 18.9% and 13.5% error percentage, respectively. While most students expressed positive feelings towards learning limits of functions, a significant number reported being hesitant or moderately confident when solving limit problems. The study identified insufficient pre-requisite knowledge, conceptual confusion, as well as procedural and factual inaccuracies as the most significant challenges students face in understanding limits, with consulting resources, revisiting foundational concepts, and collaborative learning being the most effective strategies for improvement. Frequent practice, constructive feedback, and addressing misconceptions and common errors were emphasised as critical methods to enhance students’ comprehension and performance in solving limit problems. Limitations of the study included a small sample size and a focus on specific programmes, prompting recommendations for broader studies with diverse samples and exploration of teaching interventions in future research.