of these studies explored the relationship with children’s early mathematical marks
and other, multi-modal, ways of representing meaning, or with children’s schemas.
In our own study the stunning range of children’s mathematical graphics and
their ability to make meaning constantly surprises and delights us. Pound empha-
sises ‘children’s truly amazing efforts to make sense of difficult symbolic languages’
and observes that these are ‘intelligent responses which reflect their incomplete
knowledge’ (Pound, 1999, p. 54). Nevertheless, in the nurseries and schools in which
we have taught, we have found that these particular forms of mathematical graph-
ics go largely unnoticed by others. In our interviews (see Chapter 5), less than 24 per
cent of those teachers asked said that they kept some examples of children marks
and used them for children’s records.
Our conclusion is that children’s marks do hold significance for them. Some marks
will be very mathematical but, as Athey observes, ‘without talking with children,
there is little information on whether children are investing their marks with
meaning’ (Athey, 1990, p. 82).Early written numerals
Children refer to their marks as numbers and begin to explore ways of writing numer-
als. Some children use personal symbols that may relate to standard written numerals.
Children’s perception of numerals and letters is of symbols that mean something, first
differentiated in a general sense: ‘this is my writing’, ‘this is a number’.
Young children’s marks gradually develop into something more specific when they
name certain marks as numerals. At this stage their marks are not recognisable as
numerals but may have number-like qualities. This development is similar to the
beginning of young children’s early writing (Clay, 1975). Children also mix letters and
numerals when they are writing. They appear to see all their marks as symbols for com-
munication and at this early stage their marks for letters may be undifferentiated from
their marks for numerals.Often teachers refer to a young child as ‘not knowing his numbers’. Alex, 4:11, has
written his own symbols for numerals (see Figure 6.3b).This was self-initiated and
did not appear to relate to any items that he counted: he used elements of
standard letters (for example his ‘2’, ‘5’, ‘6’ and ‘7’) and numerals (his ‘3’ and ‘4’) that
he knew. He was consistent when repeating ‘5’. It is clear from this that Alex does
know his numbers – it is adults’ numbers that he does not yet know.Molly, 3:11 (Figure 6.3a) has made separate marks which are a development from
Matt’s linear scribbles which he named as a string of numbers (see Figure 2.1 in
Chapter 2). Molly’s marks are what Clay identified as letter-like and written from
left to right (Clay, 1975).We would add that they are also number-like. Molly
referred to her marks as numbers ‘seven, six and number eight’.96 Children’s Mathematics8657part 1b.qxd 04/07/2006 18:14 Page 96