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

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What came out of the study?

Strategies used
There was variation in the types of strategies that pupils used for solving problems involving different numerical types and between context and bare problems. The study showed that when the problem was shown in context, rather than as a bare number, pupils were more likely to be successful at finding the correct answer.

The informal strategy of ‘High Level Chunking’ was the most effective method in both tests, with mental methods being the second most efficient. Despite this, the standard algorithm was the most frequently used method throughout.

Low level chunking led to long, inefficient working out, successful in only 1 in 4 cases. Working with separate digits and partitioning into hundreds, tens and units were rarely successful in either test.

Test scores
The analysis of pupils’ test scores at the beginning and end of the five month period showed that:

52% of pupils showed an improvement from the first to the second test;
19% answered the same number of questions correctly; and
29% answered fewer questions correctly.

What strategies did pupils use?
The researchers identified nine broad strategies that pupils used for attempting division problems:

Long calculations with no attempt to gain efficiency (such as repeated addition);
Breaking down the numbers using place value;
Low level chunking including some halving and doubling;
High level chunking using efficient subtotals and short procedures;
The standard algorithm;
Mental calculations showing an answer but no working out;
A wrong operation;
Unclear strategy; and
No attempt or missing data.

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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 came out of the study? Strategies used There was variation in the types of strategies that pupils used for solving problems involving different numerical types and between context and bare problems. The study showed that when the problem was shown in context, rather than as a bare number, pupils were more likely to be successful at finding the correct answer. The informal strategy of ‘High Level Chunking’ was the most effective method in both tests, with mental methods being the second most efficient. Despite this, the standard algorithm was the most frequently used method throughout. Low level chunking led to long, inefficient working out, successful in only 1 in 4 cases. Working with separate digits and partitioning into hundreds, tens and units were rarely successful in either test. Test scores The analysis of pupils’ test scores at the beginning and end of the five month period showed that: 52% of pupils showed an improvement from the first to the second test; 19% answered the same number of questions correctly; and 29% answered fewer questions correctly. What strategies did pupils use? The researchers identified nine broad strategies that pupils used for attempting division problems: Long calculations with no attempt to gain efficiency (such as repeated addition); Breaking down the numbers using place value; Low level chunking including some halving and doubling; High level chunking using efficient subtotals and short procedures; The standard algorithm; Mental calculations showing an answer but no working out; A wrong operation; Unclear strategy; and No attempt or missing data.