Learners’ problem-solving processes in calculus at grade 12 level: a case study of selected secondary schools in Lusaka district, Zambia.
Date
2019
Authors
Zulu, Julius
Journal Title
Journal ISSN
Volume Title
Publisher
University of Zambia
Abstract
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 !(# + ℎ) and !(#) 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.
Key words: Calculus, Problem solving processes, Integration, Derivative
Description
Thesis
Keywords
Mathermatics--Study and Teaching , Mathematics Education