3 A collaborative ‘parents’ mathematics group’ during which we explored mathe-
matical schemas together. Some parents in this group kept diaries of their 4–6-
year-old children’s mathematical schemas.
4 A ‘holiday study’ that involved parents of a class of 7–8-year-olds keeping diaries
of their children’s mathematical interests outside school.
These four pieces of research provided evidence of children’s mathematical interests,
family mathematical ‘events’ and parents’ perceptions about children’s mathematics
(Barton, 1994).The home as a rich learning environment
Before the child enters her first Early Years setting, her home has provided a mean-
ingful environment where mathematics is used in real contexts. Children have seen
the purpose of mathematics bound up with the day’s events. They know the impor-
tance adults attach to mathematical areas such as time. ‘I am going to be late, it is
nearly seven o’clock and I am not ready yet.’ In each home there may be different
cultural considerations about the areas of mathematics that are used. In Chapter 2
we discussed some examples of these cultural differences. Children will see mathe-
matics written down for different purposes. This written mathematics is not usually
the formal abstract symbolism of traditional school approaches but there will be ele-
ments of this. Resnick states that ‘school cultivates symbolic thinking whereas
mental activity outside school engages directly with objects and situations’ (Resnick,
1987, p. 16). For example, symbols will be used in shopping lists, for example ‘2
cartons of juice’ and on addresses such as ‘105, Brewland Street’.
One of the central themes of this book is that there is a gap between home infor-
mal mathematics that children bring to school and the school mathematics that
seems detached from the outside world. The most difficult concepts children face are
when they have to read or write the formal standard symbolisation of mathematics
at school. We argue that the gap can be bridged by encouraging children to continue
the informal home mathematics that they understand, as they gradually assimilate
the standard symbolisation of mathematics into their own methods. In Chapters 6
and 7 we have shown how children’s early numbers and calculations develop from
their informal marks.
Tizard and Hughes in their study concluded that the home provides a ‘very pow-
erful learning environment’ (Tizard and Hughes, 1984, p. 249). Their research
included families from varied socio-economic backgrounds. It revealed that there
were no vast differences in learning opportunities whatever the background of the
child. The differences appeared in content and values: all mothers in the study were
keen to give their children literacy and numeracy experiences. ‘But the most fre-
quent learning context was that of everyday living. Simply by being around their
mothers, talking, arguing and endlessly asking questions, the children were being
provided with large amounts of information relevant to growing up in our culture’
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