Bridging abstract formulas and real-world applications: Developing grade 10 learners’ conceptual understanding of cylinders in South African mathematics classroom
DOI:
https://doi.org/10.30862/jhm.v9i2.1311Keywords:
Digital simulations, Eastern cape mathematics, Geometry education, Real-world applicationsAbstract
Understanding geometric formulas conceptually remains a persistent challenge for secondary school learners, particularly when mathematical representations are disconnected from familiar real-world contexts. This study investigated the extent to which real-world applications could enhance Grade 10 learners’ conceptual understanding of the total surface area of a cylinder in the Eastern Cape, South Africa. Guided by Kolb’s experiential learning theory, the study employed a mixed-method case study design involving 39 mathematics learners. Quantitative data were obtained through pre-test and post-test measures administered before and after a three-step learning intervention incorporating digital simulations and hands-on construction of cylindrical models. Qualitative data were generated through classroom observations and semi-structured interviews with nine purposively selected learners. Quantitative analysis using a paired-samples t-test indicated a statistically significant improvement in learners’ performance following the intervention, t(38) = 6.30, p < 0.001, with a 35.1% increase in the mean score and a large effect size (Cohen’s d = 1.01). Qualitative analysis identified four interrelated themes: enhanced conceptual understanding, increased motivation through contextualised learning, development of transferable problem-solving skills, and the value of collaborative and visual learning approaches. Collectively, the findings indicate that connecting abstract geometric formulas with tangible cylindrical objects can support learners in developing more meaningful conceptual understandings and reduce misconceptions associated with formula-based reasoning. The study provides empirical evidence that experiential, application-oriented mathematics instruction can strengthen conceptual learning and learner agency, particularly in under-resourced educational contexts in South Africa.
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