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Contexts for column addition and subtraction. (English)
Teach. Child. Math. 17, No. 9, 540-548 (2011).
Summary: In this article, the authors discuss their approach to column addition and subtraction algorithms. Adapting an original idea of Paul Cobb and Erna Yackel’s from "A Contextual Investigation of Three-Digit Addition and Subtraction" related to packing and unpacking candy in a candy factory, the authors provided an analogous context by designing activities concerning the packing and unpacking of cookies in a bakery setting. This context would allow students to construct the algorithms in a way that empowers them to make decisions related to figuring out what to do in particular problem situations as opposed to remembering what ought to be done. This article describes in more detail the context employed; discusses how this context developed into the usual column algorithms for addition and subtraction; and finally, contrasts the approach to other approaches used in teaching place value and the algorithms for column addition and subtraction proposed in the literature. Introducing familiar contexts to elementary school students can be useful in promoting understanding of the standard arithmetic algorithms of primary school education. The context described illustrates how the principle of guided reinvention can be articulated within the framework of Realistic Mathematics Education (RME) to improve students’ understanding‒both at a conceptual level as well as at an operational level‒when implementing the traditional column algorithms for addition and subtraction. By learning the algorithms in this fashion, students are able to uncover a wide collection of abstract questions related to the exchange of units and tens and the use of the algorithms. Even out of context, the cookie bakery imagery, with its implicit operations and actions, somehow remains with the students. (Contains 5 figures.) (ERIC)
Classification: F32 F33 E42 E43 D42 D43