How children learn maths and theories of number development

A predominant focus of mathematics in early years’ contexts is the development of an understanding of number. The literature identifies two theories of number development (e.g. Gelman & Gallistel, 1978). The first of these stresses the role of counting. This theory is grounded on the idea of preconsciousness of counting principles. In this theory, young students’ focus on an item in the pre-verbal stage is upon gauging its magnitude; that is, how many objects there are. Thus the acquisition of the first few number words is achieved by mapping the word onto the magnitudes they have already registered before they can talk. Things are quantified by counting. The second theory relies upon the recognition of difference using perceptual or spatiotemporal cues—cues that are not numerical (Beniot, Lehalle & Jouen, 2004). Fundamental to this theory is the notion of subitising, the ability to quantify something without really counting (either internally or externally). Things are quantified by looking.

Subitising is the ability to rapidly and accurately apprehend the numerosity of a small collection of objects without counting the objects. The ability to subitise is not based on pre-verbal counting (or even fast counting), and is commonly limited to no more than four objects (Balakrishnan & Ashby, 1992). For numbers beyond four, Balakrishnan & Ashby (1992) suggest that students tend to break the number into components less than four and add the numbers (e.g. 10  is 4 + 4 + 2, or 10 is 3 + 4 + 3). Historically there has been much debate about the relationship between the ability to subitise and count. Some researchers have suggested the ability to count does not necessarily imply an understanding of number, whereas the ability to subitise does (e.g. Douglass, 1925). Some have claimed that subitising is a more basic skill than counting and a necessary precursor to counting (e.g. Klahr & Wallace, 1976). Others believed subitising develops later as a shortcut to counting (e.g. Beckwith & Restle, 1966). More recently, Benoit, Lehalle & Jouen (2004) claim that subitising may be regarded as a necessary developmental pathway for understanding the significance of the first few number words. They also found that young students were more competent at naming familiar configurations of objects, such as dice patterns, than they were at naming unfamiliar configurations.” (47)

Clements and Sarama (2007) believe it would be an error to restrict quantitative development to number competence. Yet many mathematics educators see counting as the first step towards more advanced mathematical thinking (Young-Loveridge, 2002).” (47)

Ref: Elizabeth Warren, Antoinette Cole, Eva deVries (2009) ‘Closing the gap: Myths and truths behind subitisation’ Australasian Journal of Early Childhood34(4)Dec: 46-53

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About backyardbooks

This blog is a kind of electronic storage locker for ideas and quotes that inform my research... literary research into fiction for young adults (with a special focus on New Zealand fiction). Kiwis are producing amazing literature for younger readers, but it isn't getting the academic appreciation it deserves. I hope readers of this blog can make use of the material I gather and share by way of promoting our fiction. Cheers!
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