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

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The way forwards?

The author argues that “applying a correct procedure in a ‘mechanical’ way can be highly effective.” However, in all but the simplest cases, the division algorithm involves approximations and checks that are not automatic, even with good mastery of associated multiplication facts. This implies that, for children who need to think carefully about the intermediate steps in this algorithm, the complexity of the whole procedure frequently appears to cause confusion.

The report concludes:

If children are to retain confidence in their invented strategies and see mathematical problem-solving as a progression in procedures, it is necessary that any more procedural algorithm is deferred until they have their own reliable and efficient intuitive approaches. Unless the algorithm complements pupils’ informal working and builds on the understanding they display through more intuitive approaches to division, it is likely to inhibit performance and have a negative effect on the development of mathematical thinking.

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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 The way forwards? The author argues that “applying a correct procedure in a ‘mechanical’ way can be highly effective.” However, in all but the simplest cases, the division algorithm involves approximations and checks that are not automatic, even with good mastery of associated multiplication facts. This implies that, for children who need to think carefully about the intermediate steps in this algorithm, the complexity of the whole procedure frequently appears to cause confusion. The report concludes: If children are to retain confidence in their invented strategies and see mathematical problem-solving as a progression in procedures, it is necessary that any more procedural algorithm is deferred until they have their own reliable and efficient intuitive approaches. Unless the algorithm complements pupils’ informal working and builds on the understanding they display through more intuitive approaches to division, it is likely to inhibit performance and have a negative effect on the development of mathematical thinking.