Children\'s Mathematics

with young children, Brizuela has also focused on certain aspects of their mathe-

matical ‘notations’, recognising that young children invent their own ways of rep-

resenting (Brizuela, 2004).

We suggest that ‘now we have to jump from the idea of “human sense” to observ-

ing children’s learning in terms of “child sense”. Allowing the child to lead, gives a

deeper indication of their natural development, indicating ways to support their

growing knowledge’ (Carruthers, 1997a, p. 13). When we observe children’s own

mathematical marks on paper, then it is this ‘child sense’ that we see and that is vital

to the child’s thinking about mathematics. Their own marks make meaning to them

and through these, children can further their mathematical thinking. At the same

time, the teacher gains insights into the child’s current and developing understanding.

Different literacies: mathematical literacy

Marks on paper (and other media) can be used to represent languages and meaning,

and can be shaped to form specific symbols of that language. The Centre for

Literacy of Quebec (1999) defines literacy in the following way: ‘literacy

encompasses a set of abilities to understand and use the dominant symbol systems

of a culture for personal and community development. In a technological society,

the concept of literacy is expanding to include the media and electronic text, in

addition to alphabetic and number systems’. To this definition we would add play

with objects, model-making, art, music and science. This broader perspective is in

tune with Malaguzzi’s ‘hundred languages’, the theme of a poem that refers to the

diverse ways children can express themselves and that recognises children’s

amazing potential in making sense of their experiences and abstract symbol

systems (Malaguzzi, 1996, p. 3).

Barratt-Pugh and Rohl (2000, p. 25) argue that ‘literacy is a complex and multi-

faceted process which is continually evolving’. For young learners, representing

mathematics on paper through the use of their own marks, approximations of

symbols, numbers and other graphics is also ‘literacy’. This definition of literacy pro-

vides a much broader perspective for supporting early mathematics than seeing

writing, art, mathematics, music and science as having distinctive and unrelated

systems of symbols and visual representation.

In this book we use the term ‘literacy’ to include mathematics: we see the terms

‘mathematical literacy’, ‘emergent mathematics’ and ‘mathematical graphics’ as

sharing the same meaning.

Children represent their mathematical actions and

understanding on paper

The following examples are a selection of children’s mathematical marks on paper:

they are from children in our families and Early Years settings in which we have

worked.

14 Children’s Mathematics

8657part 1b.qxd 04/07/2006 18:05 Page 14