numerals daily in meaningful contexts. She counted with her mum, dad and sister. She
knew the function of numbers in many contexts, e.g. time, measurement and money.
She liked to count out apples into a bag when she went shopping with her mum. She
also enjoyed sharing things, like sweets between people. She has a sense of fairness. If
there were any left over she suggested that everybody have a half each. She was there-
fore coming to understand fractions through natural problem-solving. She liked to play
a game with ages: for example, she said ‘when I am seven Daddy will be forty-three’.
She enjoyed finding out about larger numbers and counting up to 100 and beyond.
Her mother told me that one of their last conversations together before Susie started
school was about infinity. Susie had posed the question, ‘What is the lastnumber?’Figure 10.1Susie’s worksheetSusie’s home mathematics is in sharp contrast to the worksheet she had to complete
at school. The worksheet told us little about Susie’s number knowledge. Perhaps the
teacher could have asked Susie’s group an open question for initial assessment. We
argue that if Susie had been given the opportunity to make her own marks she would
have made more sense of them. It is vital to ask parents and carers about the math-
ematics children do at home. There is an increasing number of studies that shows
there is great discrepancy between the mathematics of school and home. Many
young children come to school with a sense of mathematics which is never truly
uncovered by their first teacher (Aubrey, 1994b; MacNamara, 1992).
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