Social science students’ concept images and concept definitions of anti-derivatives

Abstract

Calculus is an important branch of mathematics in a number of social and natural science disciplines. In the social sciences anti-derivatives are required in tackling problems in marginal analysis and optimisation problems. In the natural sciences students need to understand antiderivatives to deal with rates of change for concepts such as velocity, acceleration and rate of flow. However, students fail to understand some of the basic concepts of calculus (Brijlall & Ndlazi, 2019; Maharaj, 2014; Metaxas, 2007; Grundmeier, Hansen & Sousa, 2006). For example, students have problems in relating fundamental concepts and their definitions with associated procedures. This disconnect suggests that students have difficulties understanding functional and operational relationships between the mathematical notations and the calculus concepts they represent. What is desirable is that mathematical procedures be understood conceptually, but this is not necessarily the case since many students continue to learn mathematical procedures by rote application of an algorithm (Moru & Qhobela, 2013). A general anti-derivative, which is sometimes referred to as an indefinite integral, is an essential concept in calculus because it serves as a basis for many reallife problems and when students continue further into calculus courses, they frequently encounter anti-derivatives more than derivatives (Jones, 2013).