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Relating Flexibility in Concept Image and Understanding of Limits and Derivatives

Reaburn, R ORCID: 0000-0002-4235-7732, Oates, G ORCID: 0000-0001-7132-3198, Dharmadasa, K ORCID: 0000-0003-2869-799X and Brideson, M ORCID: 0000-0001-7547-5084 2018 , 'Relating Flexibility in Concept Image and Understanding of Limits and Derivatives', in F-J Hsieh (ed.), Proceedings of the 8th ICMI-East Asia Regional Conference on Mathematics Education , National Taiwan Normal University, Taiwan, pp. 239-247 .

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Abstract

Mathematics educators accept that if students demonstrate procedural knowledge - how toget to an answer in mathematics - it does not necessarily imply that these studentsunderstand why the procedure works (e.g. Tall, 1992; Rittle-Johnson & Alibali, 1999;Hiebert, 2013). In contrast, if students have conceptual knowledge, we consider they dounderstand these principles. Conceptual knowledge can be described as "Explicit or implicitunderstanding of the principles that govern a domain and of the interrelations betweenpieces of knowledge in a domain" (Rittle-Johnson & Alibali, 1999, p. 175). One of the waysthat students demonstrate conceptual knowledge is by procedural flexibility, where students have "knowledge of multiple ways to solve problems and when to solve them"Rittle-Johnson & Star, 2007). Tall and Vinner (1981) defined conceptual understanding of;the necessary procedures as the concept image, the "total cognitive structure that isassociated with the concept" including ''all the mental pictures and associated properties and processes" that are "built up over the years through experiences of all kinds, changing as the individual meets new stimuli and matures" (p. 152).

Item Type: Conference Publication
Authors/Creators:Reaburn, R and Oates, G and Dharmadasa, K and Brideson, M
Keywords: student limit derivative
Journal or Publication Title: Proceedings of the 8th ICMI-East Asia Regional Conference on Mathematics Education
Publisher: National Taiwan Normal University
Copyright Information:

Copyright 2018 the authors

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