Children\'s Mathematics

is how this interacts with the learner. Only then will we be in a position to provide

the kind of interaction and provision necessary to promote intellectual and emo-

tional growth. (Matthews, 1999, p. 163)

In recent years several studies have explored the rich variety of ways in which chil-

dren make meaning in ‘multi-modal ways’ through their play and with a variety of

resources and media. Kress argues that such ways form the pre-history of writing for

young children and deserve to be taken seriously by adults (Kress, 1997). Develop-

ing the same argument in her book Transformations: Meaning Making in Nursery Edu-

cation, Pahl uses detailed observations to provide powerful evidence and challenge

our ideas about communication and literacy. These studies make an enormous con-

tribution to teachers’ understanding of the complex ways in which young children

make meaning (Pahl, 1999a).

In the Froebel Block Play Project directed by Tina Bruce, Gura analysed children’s use

of block play at a deep level (Gura, 1992). Through observing children in their block

play, Gura presents ways that they represent their mathematics in three-dimensional

space. Children discover mathematical relationships as they ‘doodle’ in their block play,

which they use in more challenging structures. Gura states that when children engage

in block play that makes sense to them, and in partnerships with adults, they can make

relationships between practical mathematics and the disembedded symbolism of

formal mathematics. When children in the study voluntarily drew their structures they

used a variety of responses from pictographic to iconic. It was noted that children as

young as 3 were moving towards less embedded representations. The Froebel Block Play

Project illustrates many similar pedagogical issues that we found important in support-

ing children’s own mathematical representation. For example, Gura advocates an inter-

actionist approach which includes negotiation, respecting and enabling children and

understanding the variety and diversity of children’s own representations.

In a recent study of play entitled Teaching through Play, Bennett, Wood and Rogers

explore teachers’ thinking and classroom practice, and highlight the teaching of

another member of our Emergent Mathematics Teachers’ group, Petrie Murchison

(‘Jenny’). In their final chapter the authors consider implications for teachers’ pro-

fessional development, advocating that teachers become proactive and ‘use

informed awareness and deliberative thought processes’ (Bennett, Wood and Rogers,

1997). Such a proactive stance is outlined by Manning and Payne (1993) who rec-

ommend a social-constructivist approach which ‘involves the processes of social

interaction with knowledgeable others, scaffolding procedures, the acquisition and

application of knowledge about teaching in general and one’s own teaching in par-

ticular’ (cited in Bennett, Wood and Rogers, 1997, p. 131). In the following section

we outline our enquiry into children’s mathematics as members of the Emergent

Mathematics Teachers’ group where, as proactive teachers, we did just this.

Enquiring into children’s mathematics

Whilst he was visiting England in 1990, Rex Stoessinger, a researcher from New

Zealand, arranged to meet a county mathematics adviser, Mary Wilkinson. Rex was

Who takes notice of children’s own ‘written’ mathematics? 11

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