tic references made to children’s informal understandings, these are not central to
curriculum design’ (Zevenbergen, 2002, p. 4).
In 1999, England introduced the National Numeracy Strategy which is a framework
of objectives for teaching mathematics for 5–11-year-olds (QCA, 1999). Like the Dutch
model, this document also has a heavy emphasis on mental calculation but introduces
standard and expanded written forms of mathematics much earlier. England, unlike
other countries we have mentioned, has recognised the importance of young chil-
dren’s own mathematical marks and their own choice of written methods have been
highlighted in official documentation. Guidance for teachers emphasises: ‘children
will need to have plenty of experience of using their own individual ways of recording
addition and subtraction activities before they begin to record more formally’ (QCA,
1999 p. 19). The documents also advise that ‘at first, children’s recordings may not be
easy for someone else to interpret, but they form an important stage in developing
fluency’ (QCA, 1999, p. 12). However, although the Numeracy Strategy supports chil-
dren’s own mark making and refers to children drawing pictures and making tallies
this is not clearly explained, with the outcome that teachers are often confused as to
how they might support children’s mathematical marks and when to start teaching
standard written methods. This has resulted in teachers in the early years either intro-
ducing formal standard methods too soon or completely ignoring any written mathe-
matics whether they are children’s own representations or the standard methods.
There has been no guidance in nursery mathematics except the much criticised Math-
ematical Activities for the Foundation Stage(DfES, 2002b). Gifford reviewed these materi-
als and concluded that they gave teachers mixed messages and were not founded on
research and the general ethos of the Foundation Stage (Gifford, 2003b). Therefore
teachers of under fives are even more in the dark, and as one nursery teacher explained
to us, ‘between the ages of three and seven there is a no man’s land in the teaching of
written mathematics’. This dilemma is confirmed by the outcomes of two studies we
made with other teachers (see pp. 7–9 and 81–2, and p. 34).Using and applying mathematics
The ‘using and applying’ strand is at the heart of mathematics in the English National
Curriculum (NCC, 1992) and concerns the processes involved in mathematics through
a problem-solving approach. This strand of the curriculum has been regarded as ‘perhaps
the most significant challenge for teaching mathematics’ (NCC, 1989, para. D.1.5).
We believe that young children are amazingly talented and that they need challeng-
ing opportunities to develop their thinking at deep levels. It is significant that ‘using
and applying mathematics’ emphasises symbol use and representing mathematics.
For children from five to seven years of age, they are expected to be able to:- Select the mathematics they use, begin to represent their work using symbols and
simple diagrams and discuss and explain their work using mathematical language. - Try different approaches, find ways of overcoming difficulties that arise, begin to organ-
ise work and check results. They should also use and interpret mathematical symbols
and diagrams, discuss what they have done and begin to explain their thinking.
Based on the level descriptions for Attainment 1: using and applying mathematics (DfEE, 1999a).
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