On Intuition of the Concept of Limit: Real-life Examples Given by Secondary Mathematics Teachers

Abstract

In Sri Lankan advanced level mathematics curriculum, teachers are required only to provide the intuitive idea of the concept of limit. The purpose of this study is to explore the strategies used by mathematics teachers to achieve this. Twelve in-service secondary mathematics teachers working in government and private schools participated in the study. Data was collected through lesson observations and field notes. Video recorded lessons were transcribed and qualitatively analyzed. Teaching-With-Analogy model was used as a guiding framework to evaluate how teachers integrate real-life examples in classrooms. The analysis revealed few appealing approaches as well as various flaws and misconceptions. In fact, seven teachers took deliberate efforts to link the concept to real-life and among them, four teachers gave an intuition on how x approaches a specific value, through real-life scenarios. However, many were not successful in mapping features of the real-life example to the features of the concept. Few teachers superficially and negligently applied irrelevant metaphors, analogies and colloquial terms. There were gaps in teacher knowledge when incorporating real-life connections to the limit concept. We emphasize the importance of teachers being mindful when using real-life examples in fostering intuition since inappropriate choices of examples could contribute to misconceptions.