Children\'s Mathematics

‘The beginning is everything’ – (Plato)

Early marks

Young children’s first marks – sometimes referred to as scribbles – are a major devel-

opment in a child’s step towards multi-dimensional representations of her world.

Malchiodi recognises that a child’s first scribbles symbolise a ‘developmental land-

mark’, since they now can make connections with their actions on paper to the

world around them (Malchiodi, 1998). Gardner (1980) found that the naming of

scribbles occurs often in some children and not at all in other children. In the

samples we analysed of children in this graphic stage, we found that many of them

had actually attributed numbers to their marks (see, for example, Figure 2.1, ‘Matt’s

numbers’; Figure 6.3a, ‘Molly’s numbers’; and Figure 9.2, ‘the number line’, Jessie).

We believe that when children do this, they have understood that numbers can be

written down and communicated to another person.

Malchiodi suggests that if children are giving meaning to their scribbles then they

may be moving forward in their development of representational images. Before the

advent of speech many infants ‘form in visual media a powerful expressive and com-

municative language’ which is not recognised by many as being significant

(Matthews, 1999, p. 29). Indeed, many of the studies on early drawings refer to scrib-

bles in an almost scientific way (for example, Burt, cited in Selleck, 1997; Kellog,

1969). They address the scribbles as something that is useful for later drawing. Fein

(1997) elaborated what she calls the ‘visual vocabulary’ to describe children’s early

marks, whilst Engel (1995) focuses on descriptions that stress meaning.

In his seminal study of the development of children’s art, Matthews observes that in

almost all studies of children’s drawings, a wide range of different marks is labelled

‘scribbling’. These ‘scribbles’ are, he proposes, ‘products of a systematic investigation,

rather than haphazard actions, of the expressive and representational potential of

visual media’ (Matthews, 1999, p. 19). Scribbles are not careless accidents without

worth but have significance for the child. ‘At every phase in the development of the

symbolic systems used by the child are legitimate, powerful systems capable of cap-

turing the kinds of information the child feels is essential’ (Matthews, 1999, p. 32).

After visiting the nurseries of Emilia Reggio, Selleck argued that ‘scribbles’ is a

derogatory term for young children’s art (Selleck, 1997). Children’s first marks on

paper therefore cannot be dismissed as a generic ‘scribbles’ stage, because children

are expressing in form and content the identities, structures, symbols, events, objects

and meanings of their worlds.

Studies of mathematical marks

In Chapter 5 we referred to Hughes’s categories of young children’s early writing of

numbers. In their separate studies Munn and Sinclair also identified and categorised a

small range of marks (Munn, 1994; Sinclair, 1988). Atkinson, whilst not directly

addressing the development of children’s mathematical graphics, provides a range of

teachers’ accounts from classes of children from 3 to 11 years (Atkinson, 1992). None

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