Young children’s ‘alternative’ notions of science are well documented but their unorthodox ideas about arithmetic are less well known. For example, studies have shown that young children initially treat numbers as position markers rather than size symbols. Also, children often hold a transformational view of operations; that is, they are reluctant to accept the commutativity of addition and multiplication.
This ‘alternative’ view of operations is often overlooked by teachers, keen to demonstrate the so called ‘laws’ of arithmetic. However, this paper argues that we should not be in any haste to replace these
primitive intuitions; instead, we should show that transformational operations actually reflect how objects behave when acted on in the physical world. The paper draws on earlier research of the writer
in which young children used signs for transformational arithmetic in game scenarios. In particular, it examines the feasibility of ‘sums’ in which the operator is distinguished from the operand. In short, this
paper presents the theory behind an entirely new way of teaching arithmetic, based on children’s ‘alternative’ intuitions about numbers and operations.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:14-qucosa-81151 |
| Date | 22 May 2012 |
| Creators | Womack, David |
| Contributors | HTW Dresden, Informatik, Mathematik |
| Publisher | Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:conferenceObject |
| Format | application/pdf |
| Source | Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 596 - 599 |
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