Students’ Misconceptions of the Limit Concept in a First Calculus Course

Abstract

Misconceptions of the limit concept were examined in 130 pre-engineering students in Dilla Universities. Questionnaire and Interview were deigned to explore students understanding of the idea of a limit of a function and to explore the cognitive schemes for the limit concept.The study employed a quantitative-descriptive or survey design. The empirical investigation was done in two phases. A questionnaire on the idea of a limit was given to 130 students during the first phase. During the second phase 14 interviews were conducted. Then, the results indicated that students in the study see a limit as unreachable, see a limit as an approximation, see a limit as a boundary, view a limit as a dynamic process and not as a static object, and are under the impression that a function will always have a limit at a point. Regarding the relationship between a continuous function and a limit were: Students think that a function has to be defined at a point to have a limit at that point. A function that is undefined at a certain point does not have a limit; Students think that when a function has a limit, then it has to be continuous at that point. Other misconceptions were: The limit is equal to the function value at a point, i.e. a limit can be found by a method of substitution, when one divides zero by zero, the answer is zero, Most of the students know that any other number divided by zero is undefined. The study concluded that many students’ knowledge and understanding rest largely on isolated facts, routine calculation, memorizing algorithm, procedures and that their conceptual understanding of limits, continuity and infinity is deficient. The outstanding observation was that students see a limit as unreachable. This could be due to the language used in many books to describe limits for example ‘tends to’ and ‘approaches’. Another view of a limit that the students have is that a limit is a boundary point. This could be because of their experience with speed limits, although that could always be exceeded. Lecturers ought to become aware of their students’ understanding and possible misconceptions. Diagnosing the nature of students’ conceptual problems enables lecturers to develop specific teaching strategies to address such problems and to enhance conceptual understanding.Finally, the study suggested that concepts such as limit, involves a construction process, students build on and modify their existing concept images. Lecturers, in teaching the topic of limit, could develop concepts first before embarking on techniques in problem solving. Students need to conceptualize first before applying the formula.

Keywords: Limit Concept, Misconceptions; Limits of functions; Concept Image; Concept Definition