European Research in Mathematics Education I - Fakultät für ...

European Research in Mathematics Education I: Group 4 373
Secondly, the situation may act as a scaffold to allow children to achieve in ways
that a more abstract setting would not. Ian was seen to be able to conserve number in the
context of children on the bus though he had previously been unable to do so with
concrete materials in full view. He later needed to revert to counting when working in
the small group, perhaps because at this stage he did not realise that the situation was
the same and the bus and children pictures had been left behind. He needed both the
social situation and the bus picture to give him a confident understanding of
conservation. Whereas the standard Piagetian conservation of number task appears to
confuse the child who cannot see whether to concentrate on the discrete or continuous
nature of the line of counters, is it the discrete nature of children and the clear boundary
of the bus that aid Ian’s thinking?
Thirdly, situating the mathematics in a social setting appears to allow the children to
reflect on other social settings with respect to mathematics. Jacob’s story about Martin
was not related to the social context of the bus in any way we could recognise, yet gives
us insight into the links he is making in his mind. We do not see here the construction of
mathematical concepts in the abstract, for the child is making links to other experiences
of life which number words and concepts bring to mind. Perhaps it is the maintenance
of such links that will allow children to use and apply their mathematics more
effectively in the future.
The mathematics pupils in the classroom are not just ‘doing maths’. They are trying
to make sense of the world, making links between their present experience and those of
the past. For these young children it is not just about mathematics it is about life. An
understanding of the social world of children is essential to our understanding of how
children learn mathematics.
Acknowledgement
With thanks to ‘Beth’ and the children in her class for allowing me to observe,
interview and write about them, and to Barbara Jaworski for finding time to comment
on an early draft of this paper on the eve of a visit to Pakistan.
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