How have five years of the National Numeracy Strategy affected Year 5 pupils’ written division calculations?

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What did the researcher conclude from the study?

Schools varied in their teaching strategies for division
The variety of strategies pupils in different schools used in tackling the division problems suggested that teaching practice also varied from school to school. This apparent variety led the researcher to ask why five years of the NNS had not led to greater similarity in teaching practice. She suggested that teachers need time and a clear understanding of what to do and why to make changes to their classroom practice. She suggested that teachers in the study might not have reached a clear understanding of what they were being asked to do or, just as importantly, the reasons underlying the proposed changes.

Some schools did not teach the new chunking algorithm
In some schools, pupils made extensive use of the new chunking algorithm, but in other schools, no pupils used it. The researcher suggested that although the chunking method, based on repeated subtraction, would seem to fit well with children’s intuitive understanding of division, it would have been new to many English teachers. It was introduced in the NNS as an ‘informal written method’ and this, as well as its unfamiliarity, may have deterred some teachers from using it. Most schools continued to teach the traditional standard written method. However, it is difficult to progress logically from chunking, which works with whole numbers, to the traditional method, which works with separate digits.

Did teaching the chunking algorithm help Dutch pupils?
In the Netherlands, in contrast, the chunking algorithm is the standard method used for division and Dutch teachers rarely use the standard algorithm traditionally used in England. The author noted that Dutch pupils did much better on the original tests than either group of English pupils. She suggested that the standardised use of the chunking algorithm allowed Dutch teachers to build on pupils’ intuitive understanding of division more effectively and helped them to progressively develop pupils’ informal approaches into a structured, written record.

Supporting pupils to use structured written records
Another issue that emerged was that, although the NNS proposed that structured written methods should be introduced in Year 4, it was clear that not all schools in the study had done so before the end of Year 5. Pupils in these schools used neither the chunking algorithm nor the traditional English short division algorithm but relied solely on unstructured written records. These strategies could be correct and show understanding but were cumbersome and subject to error, especially when large numbers were involved. Pupils who relied on them scored less well than pupils who could use a written strategy in the tests. In contrast, pupils in the two best performing schools made extensive use of more structured written methods.

The researcher concluded that it was important to support pupils to develop a structured written record in a timely fashion, rather than leaving them to use informal recording for too long. Such teaching should build on pupils’ informal approaches and their established ideas of division. She particularly highlighted the need to move from the idea of division as sharing to division as repeated subtraction.

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Research Home Themes \| Find digests \| About the digests resources glossary researchers contact TRIPS Introduction How did pupils differ in their division methods and success rates? What strategies did pupils use in more and less successful schools? Did boys and girls perform differently? What did the researcher conclude from the study? What were the aims of the study and how was it designed? What are the implications of the study? Where can I find out more? Definitions Send us your feedback Collated digests To find out more about collated digests click here Get Word Reader How have five years of the National Numeracy Strategy affected Year 5 pupils’ written division calculations? This digest found in Mathematics Send to a friend Word doc 60KB Printer friendly Collate for later What did the researcher conclude from the study? Schools varied in their teaching strategies for division The variety of strategies pupils in different schools used in tackling the division problems suggested that teaching practice also varied from school to school. This apparent variety led the researcher to ask why five years of the NNS had not led to greater similarity in teaching practice. She suggested that teachers need time and a clear understanding of what to do and why to make changes to their classroom practice. She suggested that teachers in the study might not have reached a clear understanding of what they were being asked to do or, just as importantly, the reasons underlying the proposed changes. Some schools did not teach the new chunking algorithm In some schools, pupils made extensive use of the new chunking algorithm, but in other schools, no pupils used it. The researcher suggested that although the chunking method, based on repeated subtraction, would seem to fit well with children’s intuitive understanding of division, it would have been new to many English teachers. It was introduced in the NNS as an ‘informal written method’ and this, as well as its unfamiliarity, may have deterred some teachers from using it. Most schools continued to teach the traditional standard written method. However, it is difficult to progress logically from chunking, which works with whole numbers, to the traditional method, which works with separate digits. Did teaching the chunking algorithm help Dutch pupils? In the Netherlands, in contrast, the chunking algorithm is the standard method used for division and Dutch teachers rarely use the standard algorithm traditionally used in England. The author noted that Dutch pupils did much better on the original tests than either group of English pupils. She suggested that the standardised use of the chunking algorithm allowed Dutch teachers to build on pupils’ intuitive understanding of division more effectively and helped them to progressively develop pupils’ informal approaches into a structured, written record. Supporting pupils to use structured written records Another issue that emerged was that, although the NNS proposed that structured written methods should be introduced in Year 4, it was clear that not all schools in the study had done so before the end of Year 5. Pupils in these schools used neither the chunking algorithm nor the traditional English short division algorithm but relied solely on unstructured written records. These strategies could be correct and show understanding but were cumbersome and subject to error, especially when large numbers were involved. Pupils who relied on them scored less well than pupils who could use a written strategy in the tests. In contrast, pupils in the two best performing schools made extensive use of more structured written methods. The researcher concluded that it was important to support pupils to develop a structured written record in a timely fashion, rather than leaving them to use informal recording for too long. Such teaching should build on pupils’ informal approaches and their established ideas of division. She particularly highlighted the need to move from the idea of division as sharing to division as repeated subtraction.