GeoGebra as a Means for Understanding Limit Concepts

Abstract

Limit is a major concept in calculus that underpins the concepts of derivatives and integrals. The common misconception about limits is that students treat the value of a limit of a function as the value of a function at a point. This happens because usually the teaching of limit only leads to a procedural understanding (Skemp, 1976) without a proper conceptual understanding. Some researchers suggest the importance of geometrical representations to a meaningful conceptual understanding of calculus concepts. In this research, GeoGebra as a dynamic software is used to support students’ understanding of limit concepts by bridging students' algebraic and geometrical thinking. In addition to this, realistic mathematics
education (RME) is used as a domain theory to develop an instructional design regarding how GeoGebra could be used to illustrate and explore the limit concept of so that students will have a meaningful understanding both algebraically and geometrically. Therefore, this research aims to explore the hypothetical learning trajectory in order to develop students’ understanding of limit concepts by means of GeoGebra and an approach based on RME.
The results show that students are able to solve limit problems and at the same time they try to make sense of the problem by providing geometrical representations of it. Thus, the use of geometric representations by GeoGebra and RME approach could provide a more complete understanding of the concepts of limit. While the results are interesting and encouraging and provide some promising directions, they are not a proof and a much larger study would be needed to determine if the results are due to this approach or due to the teachers’ enthusiasm, the novelty effect or what is known as the Hawthorne Effect.