Children\'s Mathematics

schemas. Compare a less stimulating mathematical curriculum where the teacher has

a script to ‘teach’ shapes. The teacher in this situation shows a triangle (usually equi-

lateral) and says ‘this is a triangle’, she repeats this for the four basic shapes. Very often

the geometry of the given curriculum never goes beyond the naming of the shapes. If

we give children experience and opportunities to explore their schematic concerns

then we will see that children will be engaging with the properties of shape that define

this mathematical area. They will have gone beyond the narrow curriculum and will

be investigating concepts such as perimeter, angle, circumference, height, position and

area. This is a much more useful and cognitively challenging curriculum, on an intel-

lectual level, that befits young children’s capabilities.

Key points about schemas

• Schemas can be described as a child’s repeated pattern of behaviour.


• Schemas cannot be taught, they come from the child’s own self-interest.


• When children are involved in a schema the level of involvement can be very
  intense.


• Some of this schematic thinking is represented in their drawings.


• These schemas whether graphic or actions, form ‘footstools’ for more complex
  structures and mathematical ideas.


• The schematic marks, like other mathematical mark-making, help bridge the gap
  between informal and formal mathematics.


• Supporting children’s schemas feeds their natural curiosity which, in turn, extends
  their thinking.

In the following chapter we focus on children’s early writing, showing some links

with their schemas. We look at the relationship between early writing development

• Early writing and early mathematical marks

Further Reading

Schemas

• Arnold, C. (1997) Child Development and Learning 2–5 Years: Georgia’s Story.
  London: Hodder and Stoughton.


• Arnold, C. (2003) Observing Harry: Child Development and Learning 2–5.Bucking-
  ham: Open University Press.


• Athey, C. (1990)Extending Thought in Young Children: A Parent–Teacher Partnership.
  London: Paul Chapman Publishing.


• Bruce, T. (1997) ‘Schemas’: chapter 5 in Early Childhood Education. London: Hodder
  & Stoughton.
  Nutbrown, C. (1994) Threads of Thinking: Young Children Learning and the Role of
  Early Education.London: Paul Chapman.

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