Three concepts or one? Students' understanding of basic limit concepts

Fernández-Plaza, J.A.; Simpson, A.

doi:10.1007/s10649-016-9707-6

Three concepts or one? Students' understanding of basic limit concepts

Fernández-Plaza, J.A.; Simpson, A.

Authors

J.A. Fernández-Plaza

Professor Adrian Simpson adrian.simpson@durham.ac.uk
Principal

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