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RESEARCH PAPER
Undergraduate students’ abstractions of kinematics in differential calculus
1
Walter Sisulu University, Mthatha, SOUTH AFRICA
Online publication date: 2024-08-19
Publication date: 2024-09-01
EURASIA J. Math., Sci Tech. Ed 2024;20(9):em2497
KEYWORDS
ABSTRACT
When undergraduate students learn the application of differentiation, they are expected to
comprehend the concept of differentiation first, make connections between particular constructs
within differentiation and strengthen the coherence of these connections. Undergraduate
students struggle to comprehend kinematics as a rate of change in their efforts to solve contextual
problems. This study sought to explore undergraduate students’ construction of connections and
the underlying structures of these relationships as they learn calculus of motion. The action
process-object-schema and Triad theories were used to explore undergraduate students’
construction of connections in differentiation and the underlying structures of these relationships
as they learn the calculus of motion. This study was qualitative which involved a case study of 202
undergraduate mathematics students registered for a Bachelor of Education degree. Data were
collected through an individual written test by the whole class and semi-structured interviews with
ten students purposively selected from the class. The interviews were meant to clarify some of the
responses raised in test. The findings revealed that students’ challenges in differentiating the
given function were insignificant, but they need help to make connections of differentiation to its
application to kinematics. Furthermore, students’ coherence of the connection among
displacement, velocity and acceleration was weak, coupled by their failure to consider the point
when the object was momentarily at rest (which is central in optimization). The results of this study
have some implications for instructors. The teaching of calculus and other 456 mathematical
concepts should connect to the real-life application of those concepts so that 457 students can
make meaningful interrelationships thereof. Kinematics for differentiation paves way for
kinematics under the application of integration hence students’ optimal conceptualization is of
utmost importance.
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