A multi-sensory approach to teaching mental arithmetic

last updated:April 2009

We chose this case study because it shows how multi-sensory teaching activities developed mental arithmetic capability in children from nursery through KS1. It illustrates nicely an approach to numeracy teaching that combines number and space, an approach the research suggests is more effective than drill learning in developing neural pathways.

The study took place in an infant school on the south coast of England, serving a mixed catchment area with one in three pupils on the special needs register. In each class in Key Stage 1, six children were chosen. To give a balance of age and gender, in each group of six, there were three boys and three girls who were autumn, spring and summer born, otherwise the children were randomly chosen resulting in a spread of ability.

The focus was to construct multi-sensory teaching activities to develop mental arithmetic capability in children from Nursery through KS1. The teacher-researchers wanted children to develop an understanding of number that relates numbers to each other, relational understanding, which could be generalised to solve new problems.

Teaching and learning with the programme of activities
All classrooms and the nursery created a visually rich mathematics environment giving number a high profile so that children could see number being used. For example, drawers were numbered as well as labelled, storage pots were marked to show how many pencils they should contain. Teachers were encouraged to take opportunities to use clocks and calendars and to show numbers in daily use in data handling sessions.

Visual structured apparatus was used throughout the school in a daily mathematics lesson. The activities were predominantly practical and multi-sensory because they involved the children seeing and feeling the structured images, whilst they were hearing and saying connected mathematical language. The tendency to move into formal symbols was resisted.

Teachers were encouraged to make connections between classroom teaching activity using the structured apparatus and the 'real world.' For example, if the children were working on addition, they would be invited to make up their own addition story to apply the number bonds they had learnt.

The programme of activities was carefully designed to scaffold children's learning so they were not expected to take on too many new ideas at a time. Each activity built on and extended previous learning. The activities were very simple, for example, to practise addition children might throw a number die and then feel in a 'feely bag' for two shapes that made that number.

How successful was the programme?
The Year Two children's scores in the National Tests at the end of KS2 showed dramatic improvement over previous cohorts' scores. They had developed a range of strategies to solve arithmetic problems, seeing numbers as related 'wholes' and generally did not solve arithmetic problems by counting. Many were able to apply their arithmetic to solve problems.

With very few exceptions children had developed confident and positive attitudes to maths. Children were drawn to the images and enjoyed working with them. Children benefited from frequent opportunities to count ever larger sets of objects. This gave them experience of higher numbers and understanding of the structure of the number system.

Frequent reminders to use mental imagery – phrases such as 'let your fingers be your eyes' if they were feeling for shapes in a feely bag and 'try to see the shapes in your mind's eye' when they were doing mental arithmetic – were found to be helpful.

Children were able to write arithmetic quickly and accurately and were only asked to record arithmetic when they had understood arithmetic symbols and knew addition and subtraction facts to ten in practical activities. It was found that it was also important that children developed pencil control before recording their number work so the writing process was not laborious for them. The early work on the multi-sensory approach to teaching mental arithmetic has been further developed and is now known as Numicon.

Reference:
Tacon, R., & Wing, A. (2004) A multi-sensory approach to teaching mental arithmetic. London: DFES