Children\'s Mathematics

From our research we found that children’s personal explorations indicate that by the

time they are tackling calculations and simple problems (for example, see Chapters 7

and 9, this volume), children are already achieving many of the criteria for this strand

of the curriculum. There are also suggestions that in some of the examples in this book

children achieve at levels expected for older children in using and applying mathematics.

Further support for children’s own mathematical graphical representations can be

seen in the English Curriculum Guidance for the Foundation Stage(QCA, 2000) for

teachers of children from 3 to 5 years of age. Teachers are recommended to promote

confidence in children when they begin to record their mathematics: ‘asking chil-

dren to “put something on paper” about what they have done or have found out will

allow them to choose how to record or whether to, for example, use a picture, some

kind of tally or write a number’ (QCA, 2000, pp. 71–2).

However, whilst curriculum innovations have been introduced the fact remains

that translating guidance into practice does not always result in intended

outcomes. In a recent study in England, researchers analysed the effect that the

introduction of the Foundation stage curriculum (a play-based approach) had had

on the quality of teaching and on children’s experiences. Their findings suggest

that mathematics teaching is often misunderstood and the authors of the study

recommend that teachers ‘re-examine the values and priorities of their approaches

to literacy and numeracy teaching ... to consider whether their current emphasis

on the smallest and most basic mechanical units of literacy and numeracy learning

is altogether appropriate’ (Adams et al., 2004, p. 27: 3.13). In a major recent study

of the effectiveness of pre-school provision researchers found that ‘sustained shared

thinking’ was of key importance (Siraj-Blatchford and Sylva, 2004). However, in

their study of reception classes, the researchers emphasise their ‘most worrying

finding: the limited opportunities for sustained, shared, purposeful talk; for

complex, imaginative play and for authentic, engaging, first-hand experiences

(Adams et al., 2004, p. 27).

A recent inspection report also raises concerns about teaching mathematics in the

Foundation stage where in many lessons pupils failed to build on the knowledge and

understanding they brought with them to school (HMI, 2005, p. 6). ). From our research

with teachers recently (Carruthers and Worthington, 2005b) it was evident that

many teachers were unclear about how they might do this, and were confused about

the official guidance on teaching the beginnings of written mathematics. This

appears to be one of the most challenging aspects of teaching in the Foundation

stage. It seems clear to us that guidance on all aspects of children’s early mark-

making including the development of mathematical graphics should be a priority.

Our findings – teachers’ questionnaire

We wanted to find out the extent to which recommendations in the National

Numeracy Strategy had influenced classroom practice, in terms of children’s own

marks and written methods.

Who takes notice of children’s own ‘written’ mathematics? 7

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