The effect of different representations on Years 3 to 5 students' ability to generalise

Cooper, Thomas J. & Warren, Elizabeth (2008) The effect of different representations on Years 3 to 5 students' ability to generalise. ZDM The International Journal on Mathematics Education, 40(1), pp. 23-37.

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Over the past 3 years, in our Early Algebra Thinking project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus in Advanced Mathematical Thinking. Kluwer, Dordtrecht, pp. 25–41, 1991, and Duval in Proceedings of the 21st conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 1, pp. 3–26, 1999). The studies have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This presentation will use a variety of studies to explore the interrelation between verbal and visual comprehension of context and generalisation. The studies showed in a variety of contexts the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations.

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ID Code: 20422
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: Early algebra, Generalisation, Equivalence and equations, Years 3 to 5, Primary mathematics
DOI: 10.1007/s11858-007-0066-8
ISSN: 1863-9704
Subjects: Australian and New Zealand Standard Research Classification > EDUCATION (130000) > CURRICULUM AND PEDAGOGY (130200) > Mathematics and Numeracy Curriculum and Pedagogy (130208)
Divisions: Current > Research Centres > Office of Education Research
Current > Schools > School of Teacher Education & Leadership
Current > QUT Faculties and Divisions > Faculty of Education
Copyright Owner: Copyright 2008 Springer
Deposited On: 06 Dec 2009 22:22
Last Modified: 25 Mar 2013 08:09

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