INVESTIGATING SOCIAL SCIENCE STUDENTS’ UNDERSTANDING OF LIMITS THROUGH THE LENS OF THE PROCEPT THEORY

Abstract

The idea of limit is central to both differential and integral calculus. It is also applicable in other disciplines such as physics, engineering, economics, etc.  Because of this, conducting a study to further improve teachers’ knowledge about how social science students (whose major is economics) understand limits is of utmost importance. The reported study sought to find out how students understand the idea of limit with regard to the use of its symbolism. Sixty first year university students in the social sciences acted as the sample of the study. An adapted procept theory was used to analyse data obtained from these students through their solution to tasks on limit and explanations on their thinking and solution processes. Qualitative analysis of data indicated that some students understood the limit symbolism  to be a procept while others did not. When solving the mathematical tasks, students’ difficulties emanated from: (i) their inability to coordinate the two processes,  and , or  and  (ii) the proper use of the limit operator,  and (iii) inability to realise that the simplification has led to the same response as they could not see the relationship between the results. This resulted in misalignment between their reasoning and their choice of answers where justification was required. The results also show that limits at infinity were more problematic than those of the form  as where a is a constant. Students’ choice of method used depended mostly on how much efficient the method was in terms of saving time and not really on promoting understanding. The lesson learnt from the study is that when using the adjusted procept theory, the yes or no answers do not qualify to be used in concluding the level of thinking at which students are at. It is recommended that students be asked to show their working and also explain their answers so that the type of understanding that leads to their choices come to fore