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Durham Research Online
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Three concepts or one? Students' understanding of basic limit concepts.

Fernández-Plaza, J.A. and Simpson, A. (2016) 'Three concepts or one? Students' understanding of basic limit concepts.', Educational studies in mathematics., 93 (3). pp. 315-332.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s10649-016-9707-6
Publisher statement:The final publication is available at Springer via https://doi.org/10.1007/s10649-016-9707-6
Date accepted:21 April 2016
Date deposited:04 May 2016
Date of first online publication:19 July 2016
Date first made open access:19 July 2017

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