This observation was 25 minutes long. During this session Naomi explored going
round a boundaryor perimeter and other mathematical concepts. These included
length, comparison, lining up end-to-end (also related to measuring length), ascend-
ing order and ordinality, and thick/thin and transformation(from cylinder to sphere
and back again).
Observations of schemas in this study with children 4 to 6 years of age appeared
to share a number of features highlighting the fact that:- the children’s involvement at the time was often very intense
- children exploring a schema often concentrated for extended periods of time.
These qualities were certainly clear in the observation of Naomi exploring going round a
boundarywith clay. Such high levels of involvement resonate with the work of Ferre
Laevers on ‘intrinsically motivated involvement’ (1993), and the ‘child-involvement
scale’ of the Effective Early Learning (EEL) Project (Pascal and Bertram, 1997).Exploring spiral schemas in one classroom
The following section is based on a one–year study of schemas, in the same class of 4–6
year olds in which one of us taught.A boy nearby shouts loudly to another child but Naomi appears untroubled
and continues to roll the clay with regular movements. Next she places her long
cylinder above those she made earlier, so that they are arranged in order of
length.The shortest is nearest to her on the table, ascending to the longest
cylinder furthest away. Naomi lifts the cylinders one at a time and joins each to
the end of the previous one.The nursery nurse asks if Naomi is going to join
them all: Naomi smiles but does not answer and looks down at her long ‘rope’ of
clay on the table.
Now she stands up for a moment and begins to roll more clay with increasing
vigour. She has a sufficient length of clay to stretch along one side of the square
table where the children are seated. Naomi begins to add more clay cylinders
around the perimeter of the table.The other children silently co-operate by
taking care not to remove her clay: they move out of the way as she walks round
or reaches across the table.
Naomi has used all the clay she had but a gap remains along of one side of the
table. She walks away from the table, looking around at various objects in the
room. After a few minutes Naomi returns to the table with some wax crayons,
bottles of paint and paint brushes – all are cylindrical.Thomas reaches to take
some things from her, occasionally instructing ‘move this one up’ and ‘one more’.
Together the two children fill the gaps to complete the perimeter enclosing the
table (Worthington, 1996b).46 Children’s Mathematics8657part 1b.qxd 04/07/2006 18:07 Page 46