We have also explored the relationship between art and mathematical graphics
and argue that children’s mathematical graphics appear to support deep levels of
thinking in ways that are similar to the role of drawing for adult artists and mathe-
maticians (Worthington and Carruthers, 2005c).Idiosyncratic or meaningful?
We have found the categories that Hughes developed to be a helpful starting point.
Hughes’s study helped many teachers recognise that children could use their own
marks to represent numerals that they could then read. For teachers who
understand and support early ‘emergent’ writing, this has resonance. However, after
careful consideration, we decided not to use Hughes’s ‘idiosyncratic’ category.
The term idiosyncratic was used by Hughes when the researchers ‘were unable to
discover in the children’s representations any regularities which we could relate to
the number of objects present’. Many of the idiosyncratic marks in Hughes’s study,
in which the children’s response was to ‘cover the paper with scribble’, could
perhaps have related directly to the number of bricks the children counted (see
Hughes, 1986, p. 57). However, it appears that the children had not been asked to
explain their marks. In the clinical method of interviewing young children there is
a flaw, in that young children may not wish to respond to a stranger. They might
have responded more openly to a teacher or some other key adult in their life.
We argue that these idiosyncratic responses are significant and need to be under-
stood by Early Years teachers in order that they can support children’s written math-
ematical communication. It is easy to disregard scribbles and what appears to be
idiosyncratic responses, if we are unable to readily understand their meaning. As
experienced Early Years teachers we expect children’s early marks and symbols to
carry meaning for the child. Whilst we can only conjecture about the possible mean-
ings of some marks, we do believe that young children’s marks carry meaning.
Ewers-Rogers studied children’s early forms of representation (for example, in
party invitations and notes for the milkman). The most noteworthy finding from
her study was that a highly significant proportion of graphical responses were those
she also termed ‘idiosyncratic’ (Ewers-Rogers and Cowan, 1996). Like Saint-Exupéry
as a child in Le Petit Prince, the marks the children make often fail to be understood
by adults (Saint-Exupéry, 1958).
The five graphical forms discussed in this section (listed on pp. 87–8), encompass the
full range of marks we found. Whilst this is not a rigidly hierarchical list, children do
appear to move from their earlier forms of dynamic marks and scribbles towards later stan-
dard symbolic forms of calculations with small numbers. These five categories refer
directly to the type of marks that children choose to make. But whilst they are significant,
the formsalone do not represent the development of children’s own written methods.
We have often found that children use a combination of two forms of graphical
marks, for example iconic and symbolic, when they are in a transitional period. It
appears that when they do this they are moving from their familiar marks towards
new ones although they are not yet ready to dispense with non-essential elements.90 Children’s Mathematics8657part 1b.qxd 04/07/2006 18:12 Page 90