Making Associativity Operational |
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| Authors: | Amir H Asghari Leyla G Khosroshahi |
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| Institution: | 1.School of Education,Liverpool John Moores University,Liverpool,UK;2.Mathematics Department,Shahid Beheshti University,Tehran,Iran |
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| Abstract: | The purpose of this paper is to propose an operational idea for developing algebraic thinking in the absence of alphanumeric symbols. The paper reports on a design experiment encouraging preschool children to use the associative property algebraically. We describe the theoretical basis of the design, the tasks used, and examples of algebraic thinking in 5–6-year-old children. Theoretically, the paper makes a critical distinction between operational and structural meanings of the notion of equality. We argue that mathematical thinking involving equality among young learners can comprise both an operational and a structural conception and that the operational conception has a side that is productively linked to the structural conception. Using carefully designed hands-on tasks, the crux of the paper is the realization of algebraic thinking (in verbal mathematics) as operationally experienced in the ability to transform one number structure, with a quantity that is subject to change, into another through equality-preserving transformations. |
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