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Appreciating mathematical structure for all

Mason, John; Stephens, Max and Watson, Anne (2009). Appreciating mathematical structure for all. Mathematics Education Research Journal, 21(2) pp. 10–32.

URL: http://www.merga.net.au/documents/MERJ_21_2_Mason....
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Abstract

We take mathematical structure to mean the identification of general properties which are instantiated in particular situations as relationships between elements or subsets of elements of a set. Because we take the view that appreciating structure is powerfully productive, attention to structure should be an essential part of mathematical teaching and learning. This is not to be confused with teaching children mathematical structure. We observe that children from quite early ages are able to appreciate structure to a greater extent than some authors have imagined. Initiating students to appreciate structure implies, of course, that their appreciation of it needs to be cultivated in order to deepen and to become more mature. We first consider some recent research that supports this view and then go on to argue that unless students are encouraged to attend to structure and to engage in structural thinking they will be blocked from thinking productively and deeply about mathematics. We provide several illustrative cases in which structural thinking helps to bridge the mythical chasm between conceptual and procedural approaches to teaching and learning mathematics. Finally we place our proposals in the context of how several writers in the past have attempted to explore the importance of structure in mathematics teaching and learning.

Item Type: Journal Article
Copyright Holders: 2009 Merga Inc.
ISSN: 1033-2170
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Interdisciplinary Research Centre: Centre for Research in Education and Educational Technology (CREET)
Item ID: 22701
Depositing User: Sara Griffin
Date Deposited: 07 Sep 2010 11:48
Last Modified: 05 Dec 2012 15:28
URI: http://oro.open.ac.uk/id/eprint/22701
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