The Mozambican students understanding of the concept limit of a function: a case study

Abstract

The limite concept, a basic concept for calculus courses has been reported as a difficult concept for the students around the world. As a teacher at a secondary school and as a lecturer at the Eduardo Mondlane University I perceived the students'difficulties when encountering this concept. The present study scrutinizes the students'understanding of the concept of limit of a function. I borrowed the concepts "concept image and concept definitions"from Tall and Vinner (1981) to establish the students'mental images and definitions of the limit concept. Since mental images can only come into being within a representation, I concerned myself with how the students worked the numerical, algebraic and graphical representations and how they switched from one representation to another, drawing on Douady's (1986) work. Two classes of two schools, one in Maputo and other in Quelimane were chosen for the present study. A task was administerd and nine students, four from Maputo and five from Quelimane, were interviewed with the goal deeping the students'thinking when tackling the limit concept. The results of the research showed tha students'concept definitions of a limit of a funtion might be split into two broad categories. The first category encompassed the defitions that suggested a dynamic nature which were classified as approach and continuity. Alternatively, the students'definitions indicated a staatic concept definition, using the words interval, neighborhood or the formal definition with the simbols and were included in the categories notations/algebraic calculation, boundary and formal definition. Similarly, the students'images included the asymptotic and the motion picture. Adding to these two categories three static concept images were classified: the barrier, the value correspondence and the procedural. moreover , i established the relationship between the different representation systems and students'concept images used in the solution process. in addition, I ascentained students'connections between images associated to the context and those generated from the mathematics in a daily life problem.