Development of division strategies for Year 5 pupils in ten English schools (Updated)

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What does the study help us to understand about the teaching and learning of division?

Children first encounter the concept of division as “sharing”, or partitive division, e.g. ‘How can six sweets be shared amongst three children’. Later they learn that division also relates to the number of equal groups in a given total, or quotitive division e.g. ‘How many groups of two are there in six?’. In some ways this relates better to multiplication than sharing. The formal mathematical representation of both of these contexts is 6 ÷ 3 = ?.

Research suggests that in the early stages of a child’s mathematical development, division is undertaken by repeated addition or subtraction of numbers, for example to find how many 2s in 6, and that many children do not progress beyond such inefficient methods in primary school. In Year 5 pupils are introduced to a standard written method for division in order to direct and organise the calculation. So we see that the children’s approach to problem solving comes before recording.

What did the researchers set out to learn?
The author’s intention was to analyse the strategies that pupils used to solve division problems before and then after they had been taught to do division in Year 5. During the intervening time classroom activities would have involved the direct teaching of division.
The researchers wanted to look at pupils’ written recording of their work in order to:

identify pupils’ informal and intuitive approaches to division;
look at individual approaches to using standard ‘taught’ methods; and
assess any changes in strategies that children use after teaching.

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Research Home Themes \| Find digests \| About the digests resources glossary researchers contact TRIPS Introduction What did the researchers set out to learn? What came out of the study? Which pupils were involved and what were they involved in? What were the effects on pupil performance? What does the study help us to understand about the teaching and learning of division? What does the study mean for teaching? The way forwards? Definitions of technical terms Implications Where can I find out more? Send us your feedback Collated digests To view/remove/add notes and save your collated digests click here Get Word Reader Development of division strategies for Year 5 pupils in ten English schools (Updated) This digest found in Thinking skills Mathematics Send to a friend Word doc 70KB Printer friendly Collate for later What does the study help us to understand about the teaching and learning of division? Children first encounter the concept of division as “sharing”, or partitive division, e.g. ‘How can six sweets be shared amongst three children’. Later they learn that division also relates to the number of equal groups in a given total, or quotitive division e.g. ‘How many groups of two are there in six?’. In some ways this relates better to multiplication than sharing. The formal mathematical representation of both of these contexts is 6 ÷ 3 = ?. Research suggests that in the early stages of a child’s mathematical development, division is undertaken by repeated addition or subtraction of numbers, for example to find how many 2s in 6, and that many children do not progress beyond such inefficient methods in primary school. In Year 5 pupils are introduced to a standard written method for division in order to direct and organise the calculation. So we see that the children’s approach to problem solving comes before recording. What did the researchers set out to learn? The author’s intention was to analyse the strategies that pupils used to solve division problems before and then after they had been taught to do division in Year 5. During the intervening time classroom activities would have involved the direct teaching of division. The researchers wanted to look at pupils’ written recording of their work in order to: identify pupils’ informal and intuitive approaches to division; look at individual approaches to using standard ‘taught’ methods; and assess any changes in strategies that children use after teaching.