Children\'s Mathematics

Conclusion

We have tried to show something of the level of challenge and thinking that chil-

dren experience when working in more open ways and when selecting their own

written methods. This is, we have argued, ‘provocative maths, that is to say it

inspires, motivates and challenges children’s minds’ (Worthington and Carruthers,

1998, p. 15).

In this chapter we have concentrated on children’s methods of representing addi-

tion and subtraction. We have also found that young children do represent division

and multiplication in their own ways (see Chapter 9). We believe that the links

between the operations can be seen in children’s own thinking through their

representations. Further studies of young children’s own representations of division

and multiplication are needed to inform us how to continue supporting children’s

mathematics.

Development

As children develop mathematically beyond what we have described here, continu-

ing support for their own methods is vital, otherwise their confidence and cognitive

integrity are sacrificed. This ‘focus on the pupil’s own thinking has the benefit of

encouraging autonomy in tackling problems but if personal confidence is to be

maintained, there needs to be a progressive process of negotiation as more formal

calculations methods are introduced’ (Anghileri, 2001, p. 18). There is no point

where there is a definite separation of intuitive and standard methods. Children will

adapt from the models they have been given and use what makes sense to them, if

they are encouraged to do so. Anghileri (2000) and Thompson (1997) both give

examples of older children’s own methods of calculation. In many ways they have

had some similar insights into how children use their own methods and how this is

helpful to their understanding of mathematics.

Children’s understanding of the abstract symbols of mathematics and their role in

algorithms is not immediate. Claxton has identified time as a vital element in

problem solving. He suggests that it is not really a question of quantitiesof time, but

rather of taking one’s time. He writes:

the slow ways of knowing will not deliver their delicate produce when the mind is

in a hurry. In a state of continual urgency and harassment the brain-mind’s activity

is condemned to follow its familiar channels. Only when it is meandering can it

spread and puddle, gently finding out such fissures and runnels as may exist.

(Claxton, cited in Pound, 1999, p. 49)

In the following chapter we focus on practical aspects that teachers may wish to con-

sider developing in their Early Years settings, in order to support young children’s

mathematical literacy.

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