Enhancing the Learning of Limits of Functions Using Multiple Representations

Abstract

This is an exploratory study considering instructional methods in mathematics education. The study examined misconceptions arising from selected assignments undertaken by sixty-five students. The students were attending a calculus mathematical course unit on limits of functions, in different academic areas offered at selected tertiary institutions in Western Uganda. In this study, forms of expressing ideas on limits of functions are considered as far as they facilitate access to underlying mathematical principles. We explored the use and application of tools for representing mathematical ideas to enhance students’ conceptual understanding and problem solving skills. A small-scale pilot of interventions using readily available GeoGebra dynamical computer software was applied. The diagnostic assignment on limits of functions was used for data collection. The main objective was to examine whether or not students preferred the application of multiple representations to the analytic approach. The semi-structured interview protocol was also conducted to probe further and correlate students’ responses and their problem-solving abilities. The results showed that multiple representations-based instructions significantly changed students’ understanding of the limits of functions. The results promise better access and understanding of more abstract mathematical concepts and may support students’ problem solving abilities. The semi-structured interviews conducted indicated that multiple representations supported and, therefore, enhanced students’ understanding and solving of the limits of functions. This study highly recommends that mathematics educators should adapt multiple representations based instructions to enhance students’ critical thinking, and problem-solving.