- Rotation – turning, twisting or rolling oneself or objects in the environment
around. Children play circle games, running in circles, and are interested in wind-
mills, wheels and roundabouts. - Going through a boundary– causing oneself or material or an object to go through
a boundary and emerge at the other side. Children in this schema are usually
interested in going through tunnels and under fences. They like to sew, thread
beads and perhaps you might see them go in and out of doorways. - Oblique trajectory– moving in, using or drawing oblique lines. Children might put
the water tap full on to see the angle of the water flow. They make dens using a
table with a sheet that goes at an oblique angle from the table. - Containment– putting materials inside an object which is capable of containing
them. Children put objects in boxes, bags and suitcases and fill up containers in
the sand and water area. - Transformation– transforming oneself by dressing differently or being interested in
changes in state. Children will try on hats in front of the mirror in the role-play
area. Often children are interested in cooking and making things.
This list of frequently observed schemas, recorded by Arnold, may be compared to
those identified in our study within a school setting on pages 46–7.Schemas and mathematics
If we look at the schemas identified by Athey in the Froebel study we can see that
almost all are linked to mathematics (Athey, 1990). Perhaps this is not a surprising
finding because, as most mathematicians would argue, we live in a mathematical
world. Children explore this world and therefore they build on their natural curios-
ity about mathematics.
In her study of 3–5-year-olds in a nursery setting, Nutbrown describes the many
mathematical ideas being investigated by these young children through their
schemas (Nutbrown, 1994). When children are exploring one particular schema,
they can be finding out about different aspects of mathematics through this explo-
ration, for example:The nursery staff have observed John, 4:2, over a period of five weeks.
They have noted he is in an enclosing and containing schema. John often
chooses to go in the play telephone box in the nursery. He goes in the
telephone box with two cars and moves them around the box, on the
floor, up the wall and around the wall. He often plays in the sand, filling up
the containers with small-world toys then sand. He chooses containers
with lids and shuts and opens the lids, taking toys out, rearranging them
and putting them back in.40 Children’s Mathematics8657part 1b.qxd 04/07/2006 18:07 Page 40