Journal of Research in Science, Mathematics and Technology Education

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

M.F Machaba 1,
G Jameson 1,
Vojo George Fasinu 1 *
1 University of South Africa* Corresponding Author
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Journal of Research in Science, Mathematics and Technology Education, Online-First Articles, pp. 61-89
OPEN ACCESS VIEWS: 99 DOWNLOADS: 141 Publication date: 15 Jun 2025
ABSTRACT
Optimisation is a key topic in calculus and an essential component of the Grade 12 mathematics curriculum in South Africa. However, many students struggle with the modelling of the calculus concepts correctly when solving real-world optimisation problems. The reason behind this is not far from some misconceptions exhibit by some students when calculus. It is on this note that this study investigates the misconceptions that Grade 12 students exhibit when applying calculus to optimisation problems. A qualitative research approach was used, involving a test and follow-up interviews with five students selected from a class of 35 based on their responses. Data collected and analysed by the researchers revealed that students commonly confuse the derivative with the function itself, struggle with interpreting the concept of rate of change, and misapply algebraic techniques when solving optimisation problems. These misconceptions were therefore classified into conceptual errors, generalisation errors, language errors, and other hidden errors. The findings suggest that these misconceptions stem from a combination of inadequate conceptual understanding, procedural reliance, and language barriers. The study recommends and targets the instructional interventions focusing on deep conceptual understanding, explicit connections between calculus and real-world applications, and the refinement of mathematical language use to improve students’ modelling abilities in optimisation.
KEYWORDS
calculus, misconception, Grade 12, modelling, optimisation
CITATION (APA)
Machaba, M., Jameson, G., & Fasinu, V. G. (2025). Grade 12 Students’ Misconceptions when Modelling their Calculus Ideas into their Learning of an Optimisation: A Real-Life Problem. Journal of Research in Science, Mathematics and Technology Education. https://doi.org/10.31756/jrsmte.824
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