How are pupils’ working memory skills linked to their mathematical abilities?

Introduction

Authors

Holmes, Joni and Adams, John W. University of Durham

Publisher

Educational Psychology, 26 (3), 2006, 339-366
[Original Title: Working memory and children’s mathematical skills: implications for mathematical development and mathematics curricula]

Several studies have identified a general link between pupils’ working memory skills and their mathematical ability. The researchers defined working memory as the system within the brain that is responsible for manipulating and storing information for brief periods of time.
This study aimed to find out how specific aspects of working memory contributed to pupils’ mathematical skills at Key Stage 2.

The study involved 148 pupils from three primary schools in the North East of England who participated in two testing sessions. Their working memory skills were assessed in the first session and their mathematical abilities were assessed in the second.

The researchers found that the pupils’ working memory skills predicted over a quarter of the differences in children’s scores on a mathematics test, and that pupils’ mathematical abilities, independent of their age, were related to their ability to
• process information; and
• store and manipulate visual information.

The researchers also found that:
• pupils in Year 3 were more reliant on their ability to manipulate and store visual information to solve mathematical problems; and
• pupils in Year 5 were beginning to rely on their ability to manipulate and store verbal information to solve simple mathematical problems.

Keywords: England; Key Stage 2; Primary schools; Pupils; Mathematics; Thinking skills; Cognitive development; Problem solving.

What did the study find?

The researchers found that the pupils’ working memory skills predicted over a quarter of the differences in their scores on a mathematics test. The researchers found that pupils’ mathematical abilities, independent of their age, were related to their ability to

to process information; and
to store and manipulate visual information.

The researchers suggested that their findings indicated that the working memory processes that pupils use to support their work in maths change with age.

This study found that pupils in Year 3 were more reliant on their ability to manipulate and store visual information than on their ability to manipulate and store verbal information when solving mathematical problems. The researchers suggested that these pupils were using their visual memory as a mental blackboard to represent abstract problems in a concrete form, for example representing numbers along a mental number line.

Pupils in Year 5 were beginning to use verbal aspects of their working memory when solving simple mathematical problems. But when they encountered more complex problems they reverted to using visual aspects of their working memory. The researchers suggested that this happened when pupils could not rely on direct retrieval of a solution from long term memory, e.g. drawing on remembered number bonds (simple combinations of numbers that add up to the same value, number bonds to 10 include 3+7, 4+6, 8+2).

The researchers suggested that Year 5 pupils may have used their ability to manipulate verbal information to solve simple mathematical problems because they are able to use mature solution strategies, which include the direct retrieval of an answer from long term memory. Pupils in Year 5 continued to rely on their ability to manipulate and store visual information to solve more difficult questions, and researchers suggested that this occurred when direct retrieval strategies could not be applied.

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How did the researchers define working memory and how was it tested?

The researchers defined working memory as the system within the brain that is responsible for manipulating and storing information over brief periods of time. This study used a model of working memory that had three core components. Each of these was assessed using measures from the Working Memory Test Battery for Children (Pickering and Gathercole, 2001).

Component of working memory Suggested link to mathematical ability Test

The first component is responsible for storing and manipulating verbal information. Researchers suggest that this was important for the acquisition of number facts in early childhood. Pupils listened to nonsense words and were asked to recall the sequence of words in the same order they had heard them.

The second component is responsible for storing and manipulating visual and spatial information. Researchers have suggested that this is used as a ‘mental blackboard’ upon which material is encoded, retained and manipulated during mathematical calculations. Pupils were presented with two dimensional mazes for three seconds with a route in red travelling from the middle to the outside. Pupils traced the route with their finger and immediately after they had traced it they were asked to recall it by drawing it on a blank copy of the maze.

The third component is a central unit which co-ordinates the functions of the first two components. Its other functions include planning, switching attention between items, and processing information. Researchers suggest that this plays a role in children’s arithmetical reasoning and that it supports the retrieval of arithmetic facts from long term memory. Pupils listened to short sentences (between one and two seconds long) some of which were false. Immediately after a sentence was presented pupils had to judge whether it was true or false. Once all the sentences within a trial had been presented the pupils were asked to recall the final word of each sentence in the exact order that they heard them.

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How were pupils' mathematical skills tested?

The mathematics skills assessments were age appropriate and tested all four skill areas of the National Curriculum:

Number and algebra (written test) – pupils were required to show understanding of the four number operations, recognise number patterns and sequences, deal with fractions and decimals, and use mathematical vocabulary to solve problems.
e.g. Sarah goes to the shop. She has £2.00. She spends £1.20 on a book. How much money has she got left from the £2.00?
Shape, space and measure (written test) – pupils were asked to show their understanding of standard units of measurement and properties of shape, position and movement.
e.g. Find the area of the rectangle.
Handling data (written test) – pupils were required to interpret and draw tables and graphs, and understand measures of spread.
e.g. Read the table below:

a) How much does it cost to hire a rowing boat for one hour?

Rowing boat

Motor boat

£2 for 1 hour

£1.50 for 10 minutes

b) Which boat is more expensive to hire?

Mental arithmetic (oral test) – the pupils were asked a question and given 5, 10 or 15 seconds to respond depending on how difficult the question was.
e.g. What is 88 take away 42?

Examples of simple and difficult mathematics questions used in the assessments with pupils in Year 5.

Simple Question Write in the missing numbers:
35 + = 100

Difficult Question Calculate:
152 ÷ 8 =

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How was the study designed?

This study aimed to find out how different aspects of working memory contributed to pupils’ mathematical skills at Key Stage 2. The study involved 148 pupils from three primary schools in the north east of England:

78 Year 3 pupils, 46 boys and 32 girls, with a mean age of 8 years and 1 month; and
70 Year 5 pupils, 33 boys and 37 girls, with a mean age 9 years 10 months.

The percentage of children achieving level 4 attainment and above was higher than the national average, for maths, English and science, in two of the schools and lower than the national average in the third school.

The pupils participated in two testing sessions:

the first session involved three working memory tasks; and
the second involved age appropriate maths assessments focusing on all four areas of the curriculum, number and algebra, shape, space and measures, handling data and mental arithmetic.

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What are the implications?

For leaders:

The researchers found that the pupils’ working memory skills were linked to their mathematical ability. Could teachers within your school work together to identify effective strategies to support the development of pupils’ working memory skills within the lessons they teach? How might teachers increase the number of opportunities they offer pupils to develop these skills? Would it help pupils to know why these skills are useful?

For practitioners:

This study found that pupils were better at manipulating and storing verbal information but that their ability to manipulate and store visual and spatial information accounted for 3% of the differences in their maths scores. Could you work with a colleague to identify activities that would help your pupils to develop the visual component of working memory?
This study found that pupils in Year 3 were more reliant on the visual component of their short term memory, but in Year 5 they were beginning to use the verbal component of their short term memory. Could you identify activities which are just outside pupils’ comfort zones in order to help make this transition? Would encouraging your pupils to make their learning processes explicit help you to do this?

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Where can I find out more?

Centre for Working Memory and Learning, web pages containing information for teachers and parents: http://www.york.ac.uk/res/wml/indexxteacher.htm

Adams, J. W., & Hitch, G. J. (1997) Working memory and children’s mental addition in Journal of Experimental Child Psychology, 67, 21-38.

Gathercole, S.E., Brown, L., & Pickering, S.J. (2003).Working memory assessments at school entry as longitudinal predictors of National Curriculum attainment levels. Educational Psychology, 70, 177-194.

Rasmussen, C. & Bisanz, J. (2005). Representation and working memory in early arithmetic. Journal of Experimental Psychology, 91, 137-157.

Swanson, H.L., & Beebe-Frankenberger, M. (2004). The relationship between working memory and mathematical problem solving in children at risk and not at risk for math disabilities. Journal of Educational Psychology, 96, 471-491.

Web pages for teachers and parents provided by the Centre for Working Memory and Learning can be found at: http://www.york.ac.uk/res/wml/indexteachers.htm

A TRIPS digest on how psychological theory can help to improve students' achievement in school can be found at: http://www.standards.dfes.gov.uk/ research/ themes/ thinkingskills/ WedJan140948552004/

Other TRIPS digests on the topic of numeracy can be found at:
http://www.standards.dfes.gov.uk/research/themes/numeracy/?digest=all

For a more detailed summary of research into effective teaching of numeracy with related teacher case study examples go to: http://www.gtce.org.uk/research/romtopics/rom_curriculum/numeracy1/

For a more detailed summary of research into leading staff development in primary mathematics with related teacher case study examples go to: http://www.gtce.org.uk/research/romtopics/rom_managementoflearning/

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Component of working memory	Suggested link to mathematical ability	Test
The first component is responsible for storing and manipulating verbal information.	Researchers suggest that this was important for the acquisition of number facts in early childhood.	Pupils listened to nonsense words and were asked to recall the sequence of words in the same order they had heard them.
The second component is responsible for storing and manipulating visual and spatial information.	Researchers have suggested that this is used as a ‘mental blackboard’ upon which material is encoded, retained and manipulated during mathematical calculations.	Pupils were presented with two dimensional mazes for three seconds with a route in red travelling from the middle to the outside. Pupils traced the route with their finger and immediately after they had traced it they were asked to recall it by drawing it on a blank copy of the maze.
The third component is a central unit which co-ordinates the functions of the first two components. Its other functions include planning, switching attention between items, and processing information.	Researchers suggest that this plays a role in children’s arithmetical reasoning and that it supports the retrieval of arithmetic facts from long term memory.	Pupils listened to short sentences (between one and two seconds long) some of which were false. Immediately after a sentence was presented pupils had to judge whether it was true or false. Once all the sentences within a trial had been presented the pupils were asked to recall the final word of each sentence in the exact order that they heard them.

Rowing boat	Motor boat
£2 for 1 hour	£1.50 for 10 minutes