tively by simply being taught them as an abstract procedure’ (Whitebread, 1995, p. 35).
Whitebread contends that within this (emergent) approach ‘it is clearly important ...
that children are encouraged to be reflective about their own processing and to adopt
strategies in ways which put them in control’ (Whitebread, 1995, p. 26).
In 1997 Gifford discussed the theory underpinning emergent mathematics
approaches and compared what she termed the ‘British’ and ‘Australian’ models,
concluding ‘the Australian model of emergent mathematics (therefore) provides a
clearer image of the teacher’s role in terms of activities and support for children’s
learning’ (Gifford, 1997, p. 79). What Gifford did not know, however, was that the
‘Australian model’ was not quite so far away: Stoessinger and Wilkinson (1991) had
written an article on emergent mathematics.. Stoessinger was a researcher visiting
England from the Centre for Advanced Teaching Studies in Tasmania, and Wilkin-
son was one of the founder members of the Emergent Mathematics Teachers’ group
based in Devon, to which we belonged (see pp. 11 and 12).
Gifford argues that one benefit of encouraging children to represent their own
mathematics is the way in which the teacher ‘makes links between different aspects
of an operation. She does this by showing children that the same words and signs
relate to a variety of contexts, thus preventing children giving limited meanings to
signs’ (Gifford, 1997, p. 85). Gifford reasons that the ‘advantage of an emergent
approach in encouraging children’s own representations, is that it allows children to
make sense of ideas by representing them in their own way’ (Gifford, 1997, p. 86).
In the same year that Gifford wrote of the ‘importance of making links’, the
authors of theEffective Teachers of Numeracyreport recognised the value of a ‘con-
nectionist orientation’, characterised by teachers who believe that being numerate
involves being efficient, effective and ‘having the ability to choose an appropriate
method’ (Askew et al., 1995, p. 27). Askew et al.’s study documents some of the most
significant features of a connectionist orientation of teaching.
In the Netherlands Bert van Oers has worked extensively on children’s ‘schema-
tising’ within a Vygotskian perspective: he argues that in a sense the history of math-
ematics can be characterised as a struggle for adequate symbols (notations) for the
expression and communication of (new) mathematical ideas: ‘mathematics itself
depends on the use of symbols’ (Oers, 1996, p. 96).
Discovering Athey’s (1990) inspirational study of children’s schemas, Extending
Thought in Young Children, we found we gained huge insights into children’s cognitive
behaviour or schemas. By closely observing, assessing and supporting children’s
schemas we added considerably to what we knew about their mathematical concerns.
One means of understanding children’s mathematical graphics is to view them
from joint perspectives – from the mathematics and from the wider subject of all
their marks, including writing and drawing. In his recent and important study of the
evolution of children’s art The Art of Childhood and Adolescence: The Construction of
Meaning, Matthews traces the development of children’s early marks. He writes:
...the subject domain is important only insofar as it contains instruments, processes
and experiences which will promote human development and learning (Blenkin &
Kelly, 1996).What needs to be added to our understanding of the subject discipline,10 Children’s Mathematics8657part 1b.qxd 04/07/2006 18:05 Page 10