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Title: Developing procedural fluency in algebraic structures : Case study of a mathematics classroom in Singapore
Authors: Berinderjeet Kaur
Issue Date: Mar-2008
Citation: Paper presented at the annual meeting of the American Educational Research Association, New York, 2008
Abstract: This paper focuses on how a mathematics teacher in a Singapore school mathematics classroom engaged her grade eight students in developing procedural fluency in algebraic structures. Procedural fluency entails skill in carrying out procedures flexibly, accurately, efficiently, and appropriately (Kilpatrick, Swafford & Findell, 2001). The four conceptions of school algebra as outlined by Usiskin (1988) are:
generalized arithmetic; a study for solving certain kinds of problems; the study of relationships among quantities; the study of structures.
These four conceptions form the basis of algebra in Singapore’s school mathematics curriculum. Students are first introduced to the formal idea of using algebra as generalized arithmetic in grade six. In the following grades from seven to ten, the study of algebra revolves around all of the four conceptions. In grade eight, a significant component of the school mathematics curriculum is Algebra and the topics, in particular, expansion and factorization of algebraic expressions, solving quadratic equations by factorization, algebraic manipulation and formulae, and simultaneous equations lay the foundation for subsequent study of more advanced topics such as functions and problem solving and modelling in mathematics.
From the corpus of data collected in Singapore, in accordance with the protocol set out in the Learner’s Perspective Study (Clarke, 2006), the video records and lesson tables of one teacher were the main source of data analysed. In particular the first lesson was studied to document teacher actions that aided the development of procedural fluency in factorisation, namely by difference of squares. The instructional pattern, nature of classroom discourse, nature of learning and practice tasks, and the expectation of test items constitute the focus of this paper.
The paper concludes with some discussion of what constitutes procedural fluency and the role of learning tasks that unfold the development of connected bits of knowledge and practice tasks that aid the development of necessary skills. The pedagogy of the teacher, used to develop procedural fluency, is examined in relation to the theory of variation developed independently by Marton and Booth (1997) and Gu et al. (2004).
Project number: CRP 3/04 BK
Appears in Collections:CRPP - Conference Papers

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