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

This digest found in

What were the effects on pupil performance?

Some findings were identified which may help teachers to relate to their pupils understanding of division:

Over the course of the duration of the research, 48% of pupils made no improvement in their achievement;
Many errors were attributed to errors with the more formal algorithm;
Children who used low level chunking in the first test were not very successful but when they changed to the use of the standard algorithm or mental methods their overall performance in the second test did not improve; and
When the algorithm was inappropriate children did not seem to be able to change to the use of a more appropriate informal strategy to calculate 64 ÷ 16.

Where the context was given there was evidence in the children’s working that it influenced how they selected procedures e.g. some children had done drawings of shopping baskets in a problem that involved sharing apples.

Similarly, in the second test, where the problems were reversed so that bare problems became context problems and vice versa it was notable that the percentage of correct answers increased for the problems that became context problems and decreased for the problems that became bare problems. This suggests that where the child could not model a given context, he or she was more likely to use a procedural approach to doing the problem.

Pupils appeared to be strongly influenced to use the standard algorithm with the ‘bare’ problems. The use of the standard algorithm rose from 38% of all questions in Test 1, to 49% in Test 2. However, half of these attempts led to an incorrect solution. Where the increases in use of the algorithm were largest, there were decreases in the number of correct answers suggesting that it replaced a more successful informal strategy.

In both tests, informal strategies were most often low-level and inefficient for the large numbers involved. The results suggests that more efficiency must be gained without losing the children's intuitive understanding. One way of doing this is to develop the idea of repeated subtraction but introducing progressively larger chunks to subtract.

Gender issues
Girls had a better initial success rate and made greater overall improvement in their test performance, despite a tendency to use lower level strategies more than boys. They were also more likely to use written methods of computation.

Boys used more higher-level strategies than girls, including mental methods of computation, but were more likely to resort to guesswork or omit answers.

Your path: Home > Welcome to The Research Informed Practice Site (TRIPS) > Themes > Thinking skills > Development of division strategies for Year 5 pupils in ten English schools (Updated) > What were the effects on pupil performance?
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 were the effects on pupil performance? Some findings were identified which may help teachers to relate to their pupils understanding of division: Over the course of the duration of the research, 48% of pupils made no improvement in their achievement; Many errors were attributed to errors with the more formal algorithm; Children who used low level chunking in the first test were not very successful but when they changed to the use of the standard algorithm or mental methods their overall performance in the second test did not improve; and When the algorithm was inappropriate children did not seem to be able to change to the use of a more appropriate informal strategy to calculate 64 ÷ 16. Where the context was given there was evidence in the children’s working that it influenced how they selected procedures e.g. some children had done drawings of shopping baskets in a problem that involved sharing apples. Similarly, in the second test, where the problems were reversed so that bare problems became context problems and vice versa it was notable that the percentage of correct answers increased for the problems that became context problems and decreased for the problems that became bare problems. This suggests that where the child could not model a given context, he or she was more likely to use a procedural approach to doing the problem. Pupils appeared to be strongly influenced to use the standard algorithm with the ‘bare’ problems. The use of the standard algorithm rose from 38% of all questions in Test 1, to 49% in Test 2. However, half of these attempts led to an incorrect solution. Where the increases in use of the algorithm were largest, there were decreases in the number of correct answers suggesting that it replaced a more successful informal strategy. In both tests, informal strategies were most often low-level and inefficient for the large numbers involved. The results suggests that more efficiency must be gained without losing the children's intuitive understanding. One way of doing this is to develop the idea of repeated subtraction but introducing progressively larger chunks to subtract. Gender issues Girls had a better initial success rate and made greater overall improvement in their test performance, despite a tendency to use lower level strategies more than boys. They were also more likely to use written methods of computation. Boys used more higher-level strategies than girls, including mental methods of computation, but were more likely to resort to guesswork or omit answers.