J.A. Fernández-Plaza
Three concepts or one? Students' understanding of basic limit concepts
Fernández-Plaza, J.A.; Simpson, A.
Abstract
In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these notions are made explicitly and few papers in the large literature on student understanding of limit connect them. This paper examines the nature of connections made by students exposed to this fragmented curriculum. The study adopted a phenomenographic approach and used card sorting and comparison tasks to expose students to symbols representing these different types of limit. The findings suggest that, while some students treat limit cases as separate, some can draw connections, but often do so in ways which are at odds with the formal mathematics. In particular, while there are occasional, implicit uses of neighbourhood notions, no student in the study appeared to possess a unifying organisational framework for all three basic uses of limit.
Citation
Fernández-Plaza, J., & Simpson, A. (2016). Three concepts or one? Students' understanding of basic limit concepts. Educational Studies in Mathematics, 93(3), 315-332. https://doi.org/10.1007/s10649-016-9707-6
Journal Article Type | Article |
---|---|
Acceptance Date | Apr 21, 2016 |
Online Publication Date | Jul 19, 2016 |
Publication Date | Nov 1, 2016 |
Deposit Date | May 4, 2016 |
Publicly Available Date | Jul 19, 2017 |
Journal | Educational Studies in Mathematics |
Print ISSN | 0013-1954 |
Electronic ISSN | 1573-0816 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 93 |
Issue | 3 |
Pages | 315-332 |
DOI | https://doi.org/10.1007/s10649-016-9707-6 |
Public URL | https://durham-repository.worktribe.com/output/1405692 |
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Copyright Statement
The final publication is available at Springer via https://doi.org/10.1007/s10649-016-9707-6
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