Children\'s Mathematics

• From these examples we can see that Catherine understands that various marks
  and ways of representing are used for different conventions.


• She decided to use a drawing that can be used to stand for her sister and a letter
  ‘C’ for her own name.


• She knows the conventional number symbols that on paper stand for the ages
  ‘two’ and ‘four’.


• Her approximation of a ‘half’ is an ingenious solution and shows considerable
  insight: she has defined ‘a half’ by representing only (approximately) a half of the
  preceding numeral.

Learning theories

It is valuable to look at learning theories past and present and reflect on the many

views of learning, to determine the extent to which we have developed in our think-

ing of mathematical learning and teaching. For many people including many teachers

and Early Years practitioners, mathematics teaching is synonymous with traditional

teaching, based on the behaviourist theory: mathematics has a reputation for being

that kind of subject. Ernest (1991) has challenged such a view of mathematics, opening

mathematics up to the fallibilistic viewpoint that this subject can be challenged. Math-

ematics teaching does not need to be a straitjacket for teachers or children.

Table 2.1 gives an account of the development of some theories of learning and

teaching mathematics throughout the last century to the time of writing. Although

this book centres on the current theory of socio-culturalism, one can safely assume

that it is not a well-known theory among teachers. Even those theories which we

espouse to often lie in our heads for some time, fermenting before we actually put

them into practice in our Early Years settings.

Behaviourism

The theory of behaviourism has had considerable influence on the teaching of math-

ematics and beliefs about young learners. Each child was believed to learn best at their

her sister’s age. Catherine then added the symbol next to the picture that looks

like either a ‘C’ underlined or a reversed numeral ‘2’ and Catherine read it out

loud as ‘two’. At this point I wondered if she was using the initial letter of her

name now to stand for ‘two’. Smiling, I remarked, ‘Oh! I thought your sister was

two and a half!’ Catherine turned to reach for a pen and added the ‘C’ symbol to

the right.Was this her way of representing, approximately, a half of a numeral 2?

The following day Catherine confidently walked over to the writing area and

soon brought some more marks to me saying, ‘I’m 4½ years old’. She had written a

numeral ‘4’ followed by the vertical and horizontal bars of another numeral 4 but

had omitted the short vertical line at the bottom.

20 Children’s Mathematics

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