Daniel
Daniel’s sums may be an extreme example of a child’s mathematical experience but
it does highlight some important points. If we take a closer look at the above
examples, we see that Daniel has no complex calculating to do. He does not need to
make any adjustments because the calculations could be done as single number
addition within ten. What I really believe Daniel knows from these particular
examples is how to mechanically add, with the use of some counting bricks, two
numbers. He has performed a trick. Hughes’s (1986) study highlighted the fact that
school-age children as old as nine who used conventional signs every day in school,
were reluctant to represent addition and subtraction with the standard signs when
given a situation other than a page of sums. Their ability, it seems, to understand
these symbols and transfer and use them in different contexts was lacking. Given this
evidence, think how much more difficult it must have been for Daniel, aged 4, to
make sense of these sums he was asked to do. He may have desperately struggled to
put these into some context of what he knows about the real world. Children are
powerful meaning-makers (Wells, 1986). After some confusion Daniel may have fitted
the sums idea only into the context of that nursery. He may have thought, ‘these are
the tricks we perform at nursery’. This is not Daniel’s mathematics: this is adult’s
mathematics put on a child. If we give children, at an early age, the message that
mathematics is not connected to the real world, to any sort of context or to their
growing knowledge, then children’s understanding of conventional symbols and
mathematical algorithms will not go beyond the contexts in which they are taught.
There is much confusion about how to teach mathematics in nursery settings.
Munn, Gifford and Barber (1997) cite research that shows that in nurseries there is a
very poor diet of mathematical content. Teachers often provide activities in which
they say that children are learning mathematics but children seem more interested in
the social aspects of the play or the materials that are provided. Nursery teachers
appear less confident in their knowledge of mathematics learning than of literacy
learning. Many teachers often show less interest in developing numeracy than literacy
(Gifford, 1997; Munn and Schaffer, 1993). Studies of nursery staff indicate thatI was teaching a class in their first term of school. All of the children were 4 but
would be 5 years old in that term. Daniel’s mother gave me his arithmetic book
from the pre-school he had been attending. Above are typed copies of the
calculations that Daniel did in his book.The teacher had written out the
calculation in this vertical format and Daniel had put in the answers. His mother
said he used some sort of apparatus to work out these sums.
From these examples I do not really know what Daniel knows about numbers. I
know he seems to know how to write numerals well, as his written numbers were
easy to read. He seems to have made remarkable progression in the space of two
months: he counted in ones through tens and hundreds and then into the thousands!70 Children’s Mathematics8657part 1b.qxd 04/07/2006 18:10 Page 70