Grade 12 Students’ Misconceptions when Modelling their Calculus Ideas into their Learning of an Optimisation: A Real-Life Problem

Calculus remains a major topic embedded in South African’s Curriculum Assessment Policy Statement (CAPS), with about 40% coverage of its subtopics, as stipulated by the Department of Basic Education (DBE) document for upper grade students. It was mentioned as a major topic area that must be covered by Grade 12 students taking mathematics in South Africa. Calculus-related subtopics were incorporated into their mathematics curriculum to increase students’ mental reasoning and capacity when modelling calculus into the learning of some engineering-related courses in higher institutions. Despite the efforts of the government to increase the understanding of the students in applying and modelling some vital areas in calculus into their learning of real-life mathematics concepts, some Grade 12 students still find it difficult to recognise, interpret, and apply the appropriate conceptual aspects, symbols, and style into the learning of optimisation in calculus. For this reason, this paper deems it to investigate the misconceptions of some Grade 12 students when modelling some aspects of calculus into their learning of optimisation. In achieving this, a qualitative approach was adopted to probe the misconceptions of the Grade 12 students when modelling their calculus idea into their learning of optimisation in a real-life situation A sample question was used to select five students with the best understanding of optimisation as a subtopic learned in calculus out of 35 Grade 12 students. After data collection and analysis, the result of the study confirms that the limited understanding of optimisation, which appears to be based on the concepts of maximum and minimum turning points, has resulted in the misconception among students when modelling some mathematical knowledge in optimisation. As a result, we discovered that the forms of misconceptions among Grade 12 students when learning optimisation can be classified into conceptual errors, generalisation errors, language errors and other hidden errors.