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Paper presented at the 3rd Redesigning Pedagogy International Conference, Singapore, 1 - 3 June 2009
In Singapore, the model method is a problem solving heuristic for arithmetic as well as algebraic word problems. In the former, rectangles are used to represent numbers whilst rectangles represent unknown numbers in the latter. The resulting schematic representation captures the information provided in a problem. Construction of the appropriate model drawing builds on children understanding of parts and whole. The model method can be used to solve one dimension algebraic type word problems involving one or two variables. What makes the model such a powerful tool? One possible explanation for the power of the model method is that is provides an avenue to first describe the problem before the process of calculating for the solution begins. This process of "first-describing-and-then-calculating" (Post, Lesh & Behr, 1988) is one of the key features that make algebra distinct from arithmetic. This paper argues that the introduction of the model method as a tool to solve algebraic word problems helps elementary grade children develop algebraic thinking. How is this development brought about? To answer this question a framework is offered to identify how using the model method may help elementary grade children move from arithmetic to algebraic ways of thinking. The efficacy of this framework was then tested by using it to analyse the work of 151 grade 5 children. The limitations of the model method as a transiting tool from arithmetic to algebraic ways of thinking are also discussed. Strategies to overcome such limitations are discussed with particular reference to the pedagogical practices advocated by teachers. Such strategies include the need to emphasize on the structural nature of algebraic objects.
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