Exploring grade 12 learners’ difficulties in solving differential calculus problems at a selected secondary school in Tsumeb, Namibia
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Date
2024
Authors
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Journal ISSN
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Publisher
University of Namibia
Abstract
Differential Calculus is a fundamental topic in Mathematics that deals with the study
of how quantities change over time. Grade 12 learners have difficulties in solving
Differential Calculus questions as per the examiners’ reports year after year. This
study aimed to explore Grade 12 learners’ difficulties in solving Differential Calculus.
One secondary school in Tsumeb was purposely and conveniently selected for this
study. A total population sampling method was used to ensure a representation of all
74 Grade 12 Mathematics AS learners and all 3 grade 12 Mathematics AS teachers.
The research study was based on a mixed methods exploratory approach; i.e., data was
collected from classrooms’ observations, teachers’ questionnaires and learners’
diagnostic test. Only questions involving the learning objectives from Differential
Calculus topic were considered. A pilot study was carried out prior to the main study
in order to test for feasibility and effectiveness of the research design. An analysis was
done in order to determine learners’ common mistakes/misconceptions and errors,
challenges and also the great responses given by the learners.
The results revealed that learners had difficulties in 1) applying the product and
quotient law, 2) differentiating trigonometric functions, 3) applying conceptual and
procedural knowledge to solve Differential Calculus problems (like determining the
nature of stationary points), 4) integrating instead of differentiating and 5) just
applying differential rules in general. These difficulties may be caused by 1) lack of
algebraic knowledge (learners fail to substitute values into functions, solve equations),
2) lack of sufficient time (for both teachers and learners), and 3) teachers’ teaching
approaches. The study recommends that teachers should expose learners to a variety
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of algebraic manipulation problems from an early stage, so that learners begin
differential calculus with solid foundations of algebra; and that teachers should do
diagnostic assessments based on algebraic and functions before teaching Differential
Calculus
Description
A thesis submitted in fulfilment of the requirements for the degree of master of education (mathematics education)
Keywords
Learners’ Difficulties, Misconceptions, Solving Problems, Differential Calculus, Namibia