Tony Harries

CHILDREN'S RESPONSES TO CONTRASTING 'REALISTIC' MATHEMATICS PROBLEMS: JUST HOW REALISTIC ARE CHILDREN READY TO BE?

In recent years there has been an increasing emphasis within the world of mathematics education on realistic problem solving. At the same time research has shown that children typically remain apparently unwilling or unable to introduce realistic considerations when solving supposedly realistic word problems, though research has also shown that childrens behaviour in this domain does vary as a function of the nature of the item, its context and the childs social background. This paper analyses 11–12 year-old English childrens responses to two ‘realistic’ problems. The first is taken from English national tests; the second is a revised version of this item which has been rewritten to encourage a more realistic pattern of responses. Through a comparison of responses to the two items it is suggested that, given suitable ‘realistic’ problems, many children may be more willing and able to introduce realistic responses in a testing context than earlier research might lead us to expect.

Making sense of realistic word problems: portraying working class ‘failure’ on a division with remainder problem

Children of 10–11 years of age were interviewed while undertaking a range of mathematic problems, most of which embedded mathematical operations in textually represented realistic settings. One problem, concerning a lift moving people in the morning rush, comprised a division‐with‐remainder problem in which children are required, conventionally, to introduce a particular realistic consideration in order to produce the ‘correct’ answer. Another problem was an extended version of this, requiring children to comment on four competing answers produced by other children. Analysis of responses to the first of these two problems demonstrated that it was working class children who were especially likely to fail to produce the conventionally required answer. Having shown this, the paper concentrates on portraying the ways in which ‘failing’ working class children interpret and respond to the two problems. Our purpose here is to contribute to understanding the difficulties working class children appear to have in negotiating the demands of contextualized problems.

Working through complexity: an experience of developing mathematical thinking through the use of Logo with low attaining puils

In this article Tony Harries focuses on the work of a group of low attaining pupils as they undertake tasks within the Logo environment. The tasks were designed to encourage the pupils both to move beyond single step procedural ways of working, and to explore ideas of generalisation. The results of the study suggest that while there is a tendency for these pupils to work in small steps and with instant feedback on each step, they can be enabled to move beyond this way of working and that this can be a means of empowering their mathematical development.

A representational approach to developing primary ITT students' confidence in their mathematics

Representations of mathematical concepts play an important role in understanding: both in helping learners understand the to-be-learned material and in facilitating teachers’ understanding of pedagogical processes which, in turn, are involved in developing learners’ understanding. In this paper, we report on work with a cohort of pre-service primary teachers, with the aim of developing their understanding of mathematics, their confidence in their subject knowledge and their confidence in teaching mathematics. This was attempted through the introduction and use of a ‘representational approach’ to the teaching of the mathematical concepts required of teachers training to teach in primary schools in the UK. We present the results of attitude measures and a follow-up qualitative questionnaire in identifying whether and how the use of this representational approach supported pre-service teachers’ understanding and their confidence in teaching mathematics. The results suggest that the representational approach used had a positively significant impact on the attitudes towards studying and teaching mathematics.