id: 06646830
dt: j
an: 2016f.00756
au: Siyepu, Sibawu Witness
ti: Analysis of errors in derivatives of trigonometric functions.
so: Int. J. STEM Educ. 2, No. 1, Paper No. 16, 16 p., electronic only (2015).
py: 2015
pu: Springer (SpringerOpen), Berlin/Heidelberg
la: EN
cc: D70 I40
ut: APOS theory; derivatives; errors; trigonometric functions
ci:
li: doi:10.1186/s40594-015-0029-5
ab: Summary: Background: This article reports on an analysis of errors that
were displayed by students who studied mathematics in Chemical
Engineering in derivatives of mostly trigonometric functions. The poor
performance of these students triggered this study. The researcher
(lecturer) works in a mathematics support programme to enhance
students’ understanding of mathematics. The purpose of this study was
to identify errors and their origins when students did calculations in
derivatives of trigonometric functions. The participants of this study
were a group of thirty students who were registered for Mathematics in
a university of technology in Western Cape, South Africa. The
researcher used a qualitative case study approach and collected data
from students’ written work. This study used Dubinsky’s APOS Theory
(Actions, Processes, Objects, and Schemas) to classify errors into
categories and analyse the data collected. Results: Errors displayed by
students were conceptual and procedural; there were also errors of
interpretation and linear extrapolation. Conceptual errors showed a
failure to grasp the concepts in a problem and a failure to appreciate
the relationships in a problem. Procedural errors occurred when
students failed to carry out manipulations or algorithms, even if
concepts were understood. Interpretation errors occurred when students
wrongly interpreted a concept due to over-generalisation of the
existing schema. Linear extrapolation errors occurred when students
over-generalised the property $f(a+b)=f(a)+f(b)$, which applies only
when $f$ is a linear function, to the form $f(a*b)=f(a)*f(b)$, where
$f$ is any function and $*$ any operation. The findings revealed that
the participants were not familiar with basic operational signs such as
addition, subtraction, multiplication and division of trigonometric
functions. The participants demonstrated poor ability to simplify once
they had completed differentiation. Conclusions: This study recommends
the strategy of focusing on elimination of errors to develop
students’ understanding of derivatives of trigonometric functions.
This can be done through learning activities that lead to
identification and analyses of students’ errors in classroom
discussions.
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