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RESEARCH PAPER
Mathematics Education Students’ Understanding of Binomial Series Expansion Based on the APOS Theory
1
Walter Sisulu University, SOUTH AFRICA
Publication date: 2021-10-21
EURASIA J. Math., Sci Tech. Ed 2021;17(12):em2035
KEYWORDS
ABSTRACT
Undergraduate students study the topic of binomial series expansion as part of their Calculus
course. The purpose of this study was to explore the mental constructions of binomial series
expansion of a class of 159 students. Data were collected through a written assessment task by
each member of the class. A convenient sample of eleven students from the class was selected to
undertake semi-structured interviews. The Action-Process-Object-Schema theory which was used
depicts development of understanding of mathematics concepts through the hierarchical growth
of mental constructions. Students in the study coped well with questions requiring action-level
engagements but grappled with those calling for higher-level mental constructions, namely,
processes and objects. Developing an object conception for a mathematical concept is the
pinnacle for all teaching but also the most difficult to develop. Thus, this study underlines the
significance of helping students construct object conceptions in binomial series expansion.
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