cannot see it?’ This links with babies’ fascination with the ‘peek-a-boo’ game. In his
observations Piaget saw that early schemas of 2- and 3-year-olds included children
grouping and sorting. This was unfortunately translated into the ‘pre-number’
theory of the 1960s and 1970s. It was believed that children needed to sort and do
sets before they were ready for number. Five-year-olds, who had long passed this
concept when they were 3, were made to sort objects such as green and blue frogs.
The published mathematical schemes of this time had workbook pages, so that chil-
dren could colour in sets of green frogs and blue frogs or suchlike: then the children
had to partition the sets. Very little mathematics went on; the main time was taking
up with colouring in.
Athey took Piagetian research further and, more importantly, observed children’s
actions from a positive stand, looking for what children know, not what they do not
know. For example, from a Piagetian perspective the acquisition of one-to-one cor-
respondence is seen as the watershed of the child’s knowledge about number. From
this perspective the child had little knowledge of number before she understood this
concept. Athey’s research, right from the start, threw out the deficit model and
therefore brought out many enlightening details about children’s knowledge. It is
vital to note this because it gives us as teachers an important observational strategy.
The studying of schemas is a useful observational tool. As Athey has documented, it
is a wonderful way to share children’s experiences with parents and for parents to
share experiences of their children with teachers. Done in an open, honest, way it
forms a true partnership (see for example the letter from Chloë’s mother, Figure 3.1).Figure 3.2 Imogen constantly lines things up38 Children’s Mathematics8657part 1b.qxd 04/07/2006 18:07 Page 38