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Years 2 to 6 Students’ Ability to Generalise: Models, Representations and Theory for Teaching and Learning

  • Tom J. Cooper
  • Elizabeth Warren
Part of the Advances in Mathematics Education book series (AME)

Abstract

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 results for a theory that describes a growth in integration of models and representations that leads to generalisation.

Keywords

Number Line Abstract Representation Balance Principle Algebraic Thinking Early Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Queensland University of TechnologyBrisbaneAustralia
  2. 2.Australian Catholic UniversityBrisbaneAustralia

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