Learners’ problem-solving processes in calculus at grade 12 level: a case study of selected secondary schools in Lusaka district, Zambia.

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Zulu, Julius
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The University of Zambia
Poor essential workings in Mathematics is an attribute of poor problem solving processes. The study explored learners’ problem solving processes in Calculus at Grade 12 level. Calculus was introduced when the curriculum was revised in 2013 and involves basic differentiation and integration at this level. The study sought to establish Grade 12 learners’ problem solving processes in Calculus, identify the challenges Grade 12 learners’ encounter in solving Calculus problems, and determine strategies teachers and learners would suggest to improve problem solving-skills in Calculus. Twenty learners and two teachers at two secondary schools in the Lusaka district of Lusaka province, Zambia, participated. A qualitative study approach, which followed a descriptive case study design, was used. Data was collected using lesson observations, focus group discussions, and semi-structured interviews. Video and audio recordings were used to capture observations and interviews, respectively, in their totality. Thematic analysis was used to analyse data. The four principles of problem solving by Polya namely, understanding the problem, devising a plan, executing the plan and looking back guided the analysis. Although learners’ read, re-read and wrote Calculus functions before solving, they experienced difficulties in underlining key important words; writing calculus formulas; simplifying Calculus problems; applying appropriate Calculus formulas; and had no reflective skills during and after solving Calculus problems. The challenges included failure to: substitute 𝑓(𝑥+ℎ) and 𝑓(𝑥) when working from first principles, cite Calculus notations, cite the correct formula when working from first principles, and apply appropriate basic Mathematical concepts. Moreover, learners had challenges with understanding the language of Calculus, and teachers’ teaching approaches. In view of these findings, it was recommended that teachers should use problem solving approaches which assist learners in identifying key words in the problem, devising Calculus formulas, monitoring each step during solving and looking back after solving. Applications of basic concepts in earlier grades should also be consolidated and revised on an on-going basis. It was further recommended that teachers should focus on the development of the formulas and introduce Calculus symbols in early grades while learners should practise basic concepts to enhance understanding of Calculus.
Thesis of Masters of Education in Mathematics Education.