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

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What strategies did pupils use in more and less successful schools?

Pupils in both of the two best performing schools made extensive use of structured written methods but each school used a different approach. In one which performed especially well, (school 7, average score 6.1), pupils used both the chunking and traditional algorithms extensively. In another top-scoring school (school 5, average score 6.5), the pupils used the traditional short division algorithm for over 75% of the items and no-one used the chunking algorithm. This was a surprising finding in the light of the earlier research in which pupils found it hard to use the traditional algorithm successfully.

The 1999 NNS introduced a structured way of recording division calculations based on repeated subtraction of multiples of the divisor (high level chunking). This offered a new algorithm for division that could build on pupils’ informal understanding of division by repeated subtraction of the divisor itself (low level chunking). The study found that not all schools were teaching this new algorithm, as pupils from some schools made no attempt to use it.

Pupils from some schools, (for instance, schools 3, 6 and 8; average scores 4.42, 4.25 and 4.07), made very limited use of any structured written method. They used mainly informal methods to approach the problems. These schools were clustered at the lower end of the range of scores. It seemed that the biggest difference between schools whose pupils scored well on the test of division and those who did less well was that pupils from the former made much use of structured written methods and those from the latter relied heavily on less efficient, informal methods.

Unusually large numbers of individual pupils in the high-scoring school 7 used more than one approach – 86% of pupils at this school used the chunking algorithm for at least one question. Elsewhere, the number of different strategies pupils used varied, but no relationship was found between the number of different strategies that pupils used and their score on the test.

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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 strategies did pupils use in more and less successful schools? Pupils in both of the two best performing schools made extensive use of structured written methods but each school used a different approach. In one which performed especially well, (school 7, average score 6.1), pupils used both the chunking and traditional algorithms extensively. In another top-scoring school (school 5, average score 6.5), the pupils used the traditional short division algorithm for over 75% of the items and no-one used the chunking algorithm. This was a surprising finding in the light of the earlier research in which pupils found it hard to use the traditional algorithm successfully. The 1999 NNS introduced a structured way of recording division calculations based on repeated subtraction of multiples of the divisor (high level chunking). This offered a new algorithm for division that could build on pupils’ informal understanding of division by repeated subtraction of the divisor itself (low level chunking). The study found that not all schools were teaching this new algorithm, as pupils from some schools made no attempt to use it. Pupils from some schools, (for instance, schools 3, 6 and 8; average scores 4.42, 4.25 and 4.07), made very limited use of any structured written method. They used mainly informal methods to approach the problems. These schools were clustered at the lower end of the range of scores. It seemed that the biggest difference between schools whose pupils scored well on the test of division and those who did less well was that pupils from the former made much use of structured written methods and those from the latter relied heavily on less efficient, informal methods. Unusually large numbers of individual pupils in the high-scoring school 7 used more than one approach – 86% of pupils at this school used the chunking algorithm for at least one question. Elsewhere, the number of different strategies pupils used varied, but no relationship was found between the number of different strategies that pupils used and their score on the test.