No one would deny the importance of great maths skills in making progress through school and beyond into the world of further study, work and life. But for some children, their struggle with maths is such that specialist interventions are required to help them to flourish in the subject. These children may be experiencing dyscalculia, which affects the ability to develop a grasp of numbers and arithmetical skills. Distinct from acalculia (an inability to do basic arithmetic as a result of a brain injury or disease), dyscalculia is part of three Specific Learning Difficulties alongside dyslexia and dyspraxia
A recent study from Queen’s University in Belfast points to a lack of understanding of, and hence support for, dyscalculia. Usefully, the British Dyslexia Association now has an agreed definition:
“Development dyscalculia is a specific and persistent difficulty in understanding arithmetic and basic number sense. It may also affect retrieval of number facts and key procedures, fluent calculation and interpreting numerical information. It is diverse in character and occurs across all ages and abilities. Dyscalculia is an unexpected difficulty in maths that cannot be explained by external factors.
Maths difficulties are often thought of as a continuum, not a distinct category, with dyscalculia at the extreme end of this continuum. It should be expected that developmental dyscalculia will be distinguishable from general maths difficulties due to the severity of difficulties with symbolic and non-symbolic magnitude, number sense and subitising.
Developmental dyscalculia can often co-occur with other specific learning difficulties, such as dyslexia, dyspraxia and attention deficit hyperactive disorder.”
Tony Attwood, Head of the Dyscalculia Centre, an organisation funded through the sale of its resources to parents and schools which has been offering support for 15 years, explains that children with dyscalculia do not have the ability to deal with concepts that do not exist in isolation. “At the heart of our work are several basic views that have emerged from our own research and those of others across the years,” he explains.
“First, dyscalculic individuals lack certain mental abilities which are natural in most of the population. This can be experienced to some degree by people without dyscalculia, by asking the question “what is six?” Most people will respond by talking about six cars or “one more than five”, but if one insists on understanding six on its own, most people are stumped. What dyscalculic people appear to lack is this ability to deal with a concept that cannot exist in isolation. In this regard it is a bit like colour – colour only exists in relation to the sky, an apple, and so on.
“Second, we can use the example of zero to show that maths is not always the logical process we might think. The Roman Republic and the Roman Empire had a counting system for 1000 years which had no zero. But Arabic maths which we now use had a zero, a non-number that you cannot multiply or divide by. We love to assume maths is logical, but as with this odd non-number zero, often it is not. We might also consider prime numbers which seem to pop up in odd places without any logic as to where they are in the number sequence. Or maybe the way that the area of a circle depends on a constant that has no end.
“Standard maths teaching is based on these assumptions, such as that the abstract notion of “six” can be understood. Dyscalculic people don't see it this way.”
Margaret Malpas, Vice President of the British Dyslexia Association, points to research at Athens University as further background on dyscalculia: “It has been suggested by Giannis Karagiannakis, Prof of Maths at Athens University, that dyscalculia can be seen as 4 quadrants: numerosity, comprehension, working memory and procedural learning. I think this is a particularly helpful way to view it as it enables a teacher to consider quickly where the problems lie and also practical ways to support the pupil.”
Using the 4 quadrants, you might surmise that if a pupil seems to have little concept of number (numerosity), then teachers need to provide plenty of physical practice with objects; if the problems are based in comprehension, then providing support with maths problems helps; working memory issues require the task to be broken up in to bite sized pieces and procedural learning can be helped by providing a crib sheet of the stages of the process along with lots of embedding.
Margaret also believes that viewing strengths through this lens is helpful too. “In my own case,” she explains, “I have good comprehension but am very weak on procedural learning. So I use worked examples always to remind myself of the task. This strength helps me with the other quadrants.”
How can teachers help?
It is a mistake, say experts such as Tony Attwood, to think that children with dyscalculia can be taught maths but at a slower pace than children who do not have the condition. Specialist interventions are required and these may depend on the needs of each child. Tony Attwood explains that schools in England have “an absolute legal duty” to provide suitable maths tuition to dyscalculic pupils and students under the Equalities Act 2010. If you are supporting children with dyscalculia, these ideas may help:
- Early identification of needs in maths, leading to early interventions where necessary.
- The concrete-pictorial-abstract approach to maths teaching, which is known to support children with dyscalculia.
- Tony Attwood recommends making teaching as multi-sensory as possible, so that children can use as many senses as possible each time a number is encountered and manipulated.
- Margaret Malpas suggests using a lot of practical aids such as rods, Unicubes, marbles, Lego bricks – anything that can be physically counted and worked with
- setting up the learning for success, by breaking it down into tiny chunks so that the child is achieving and does not get anxious
- doing lots of recapping and embedding learning throughout.
Find out more
- The British Dyslexia Association has developed a level 5 certificate to enable teachers to become specialists in supporting children with dyscalculia and maths learning difficulties. Find out more about this and the wider work of the British Dyslexia Association here
- There is more about the work of Tony Attwood and the Dyscalculia Centre here