Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning
Cooper, Thomas J. & Warren, Elizabeth (2011) Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning. In Cai, J. & Knuth, E. (Eds.) Early Algebraization. Springer-Verlag, Berlin Heidelberg, pp. 187-214.
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Over the last three 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 models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results 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 chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.
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|Item Type:||Book Chapter|
|Keywords:||Early algebra, Generalisation, Models, Representations|
|Subjects:||Australian and New Zealand Standard Research Classification > EDUCATION (130000) > CURRICULUM AND PEDAGOGY (130200) > Curriculum and Pedagogy Theory and Development (130202)|
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 Curriculum
Current > QUT Faculties and Divisions > Faculty of Education
|Copyright Owner:||Copyright 2011 Springer-Verlag Berlin Heidelberg|
|Deposited On:||10 Jan 2011 10:20|
|Last Modified:||25 Mar 2013 18:11|
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