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

Abstract

Citation for published item:pern¡ ndezElzD tFeF nd impsonD eF @PHITA 9hree onepts or onec tudents9 understnding of si limit oneptsF9D idutionl studies in mthemtisFD WQ @QAF ppF QISEQQPF Further information on publisher's website:The nal publication is available at Springer via https://doi.org/10.1007/s10649-016-9707-6Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. 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.

Implementation of Digital Technologies into Pre-Service Mathematics Teacher Preparation

“…Pinto and Scheiner [23] investigated how mathematics university students understood the limit concept of a sequence. Fernández-Plaza and Simpson [24] explored how students linked different basic limit concepts. As the literature review on this stage of research shows, there are minimal steps forward in finding the best way of how to work with a limit concept properly and avoid PMTs misconception.…”

Four conceptions of infinity

“…On the other hand, Fernández-Plaza and Simpson (2016) in their research in the understanding of three basic uses of the notion of limit (the limit of a sequence, the limit of a function at a point, and the limit of a function at infinity) point to a group of undergraduate students who have a static conception of infinity. Similarly, analogous to Sierpinska (1994) or Ely (2010), this 'appears to contradict the assumption that understanding of limit of function at a point necessarily involves thinking about sequences or using dynamic imagery' (Fernández-Plaza & Simpson, 2016, p. 317).…”

Examining Course-Level Conceptual Connections Using a Card Sort Task: A Case Study in a First-Year, Interdisciplinary, Earth Science Laboratory Course

“…Across disciplines, the majority of studies have looked at some combination of undergraduate students as novices and graduate students or faculty as the experts. Many disciplines have multiple studies with varying participants and timelines: in physics, where the applicability of the card sort tool was introduced looking at undergraduate students compared to graduate students (Chi, Feltovich, and Glaser 1981); in math, comparing first-and second-year undergraduate students (Fernandez-Plaza and Simpson 2016); in biology, studies have looked at biology faculty against non-biology majors (Smith et al 2013), non-majors, early and advanced majors, graduate students and faculty to look at the transition over a career (Bissonnette et al 2017), and tracking changes in undergraduates over a single semester (Hoskinson et al 2017); similarly in chemistry, studies have looked at chemistry undergraduates against faculty (Krieter et al 2016), as well as a comparison of students with no chemistry background, high school students, general chemistry undergraduates, upper-level chemistry undergraduates, graduate students, and faculty (Irby et al 2016), and tracking changes in undergraduates over a single-semester, (Lapierre and Flynn 2020) and two-semester organic chemistry course (Galloway, Leung, and Flynn 2019). In general, these studies find that the card sorting activity is a suitable tool for investigating whether a participant displays more novice-like or expert-like thinking in their respective field.…”