Early Awareness of Mathematical Pattern and Structure
This chapter provides an overview of the Australian Pattern and Structure Project, which aims to provide new insights into how young students can abstract and generalize mathematical ideas much earlier, and in more complex ways, than previously considered
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Introduction One of the most fundamental challenges for mathematics education today is to inspire young students to develop “mathematical minds” and pursue mathematics learning in earnest. Current research shows that young students are developing complex mathematical knowledge and abstract reasoning much earlier than previously considered. A range of studies in prior to school and early school settings indicate that young students do possess cognitive capacities which, with appropriately designed and implemented learning experiences, can enable forms of reasoning not typically seen in the early years (e.g., Clarke et al. 2006; Clements et al. 2011; English 2012; Papic et al. 2011; Perry and Dockett 2008; Thomas et al. 2002; van den Heuvel-Panhuizen and van den Boogaard 2008; van Nes and de Lange 2007). Our research aims to provide new insights into how young students can abstract and generalize mathematical ideas much earlier, and in more complex ways, than previously considered. Although there is a large and coherent body of research on individual content domains such as counting and arithmetic, there have been remarkably few studies that have attempted to describe general characteristics of structural development in young students’ mathematics. The Australian Pattern and Structure Project, initiated in 2001, aims to develop a different approach to understanding mathematics learning, beginning with very young students, that reaches beyond basic numeracy to one that cultivates mathematical patterns and relationships. Over the past decade, a suite of studies with 4- to 8-year old students has found that an awareness of mathematical pattern and structure is both critical and salient to mathematical development among young students (Mulligan and Mitchelmore 2009). Our J.T. Mulligan (B) · M.C. Mitchelmore Macquarie University, Sydney, Australia e-mail: [email protected] M.C. Mitchelmore e-mail: [email protected] L.D. English, J.T. Mulligan (eds.), Reconceptualizing Early Mathematics Learning, Advances in Mathematics Education, DOI 10.1007/978-94-007-6440-8_3, © Springer Science+Business Media Dordrecht 2013
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J.T. Mulligan and M.C. Mitchelmore
research aims to find reliable and consistent methods for describing the growth of students’ awareness of mathematical structures and relationships over time. Utilizing this knowledge to develop quantitative reasoning at an optimum age, when they are eager to learn, is central to this project. One purpose of this chapter is to describe the construct, Awareness of Mathematical Pattern and Structure (AMPS), which our research has shown generalizes across early mathematical concepts, can be reliably measured, and is correlated with mathematical understanding. It is our belief that a focus on AMPS could bring more coherence to our understanding of mathematical development and the development of effective pedagogical approaches. We refer to a range of studies with diverse samples in order to describe as explicitly as possible the bases for our identification
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