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Mathematics Education Research Journal 2009, Vol. 21, No. 2, 33-49
Recent educational research has turned increasing attention to the structural development of young students' mathematical fllinking. Early algebra, multiplicative reasoning, and spatial structuring are fllree areas central to fllis research. There is increasing evidence that an awareness of mathematical structure is crucial to mathematical competence among young children. The purpose of fllis paper is to propose a new construct, Awareness of Mathematical Pattern and Structure (AMPS), which generalises across mathematical concepts, can be reliably measured, and is correlated with general mathematical understanding. We provide supporting evidence drawn from a study of 103 Grade I students.
Virtually all mathematics is based on pattern and structure. As Warren (2005) asserts, "The power of mathematics lies in relations and transformations which give rise to patterns and generalisations. Abstracting patterns is the basis of structural knowledge, the goal of mathematics learning" (p. 305).
There are many indications that an understanding of pattern and structure is important in early mathematics learning. For example, one of our earlier studies examined the structural characteristics of the representations of various numerical situations made by students from Grades 2-5 (Mulligan, Mitchelmore, Outhred, & Russell, 1997). Low achievers consistently produced poorly organised pictorial and iconic representations lacking in structure whereas high achievers used abstract notations with well-developed structures from the outset (Mulligan, 2002).
Other mathematics education research provides further evidence. Studies focused on imagery and arithmetic have indicated that students who recognise the structure of mathematical processes and representations acquire deep conceptual understanding (Pitta-Pantazzi, Gray & Christou, 2004; Gray, Pitta, & Tall, 2000; Thomas & Mulligan, 1995). Students with lower numerical achievement reported descriptive and idiosyncratic images; they focused on non-mathematical aspects and surface characteristics of visual cues. Visualisation skills, which frequently involve recognition of pattern and structure, are positively correlated with mathematical achievement (Arcavi, 2003; Booth & Thomas, 2000) and analogical reasoning (English, 2004). And psychological research has repeatedly shown that scores on mathematics achievement tests correlate moderately highly with scores on intelligence tests~-which invariably include pattern recognition tasks.
Awareness of Pattern and Structure in Early Mathematical Development
Joanne Mulligan & Michael Mitchelmore Macquarie University, Sydney
34 Mulligan & Mitchelmore
Despite all this evidence, there have been remarkably few studies that have attempted to...