Children\'s Mathematics

Figure 5.1 Scott’s addition

Understanding symbols

Semiotics

Any serious discussion concerning the development of symbols concerns semiotic

activity which, concerning children’s representations, Oers defines as: ‘the activity of

relating a sign and its meaning, including use of signs, the activity of investigating the

relationship (changes of) signs and (changes of) meaning, as well as improving the

existing relationship between sign (or sign system) and meaning (and meaning

system)’ (Oers, 1997, p. 239). This is what White termed the symbolic initiative (1949).

Gardner views our complex use of symbols as ‘our final building block’. He argues that

‘the disciplines of our world, reconstructed on the basis of symbols; and our capacity

to master them, and to invent new systems, also presupposes the symbolic fluency that

is launched in the years after infancy’ (Gardner, 1997, p. 21).

From a Vygotskian perspective, symbols or graphic representations bridge the gap

between ‘enactive, perception-bound thinking and abstract, symbolical thinking’

(Oers, 1997, p. 237).

Understanding abstract mathematical symbols begins long before children enter

school, with a ‘pre-history’ that Vygotsky believed originates in both gesture and alter-

native meanings that children assign to objects within their play. An example of this is

Melanie’s ladybird (Figure 6.1) in Chapter 6. DeLoache observed that children as young

as 18 months old can pretend that ‘a block of wood is a car, or that a banana is a tele-

phone’: in doing this they demonstrate that they are able to represent something in two

different ways (DeLoache, 1991, p. 749). This flexibility of meaning and object allows

children later to understand that marks – or written symbols on a page – stand for

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