Love it or loathe it, you just can't get away from the fact that maths matters, yet many people have a ‘difficulty’ with maths – hated it at school, couldn’t see the point – and, like all skills, it is a matter of use it or lose it.
Few adults practise the maths of fractions or algebra after leaving school; indeed, a study found that just under a quarter of 35 year olds had such low numeracy skills that completing everyday tasks successfully would be difficult.
However, dyscalculia is more than just a difficulty with learning maths skills as Dr Steve Chinn explains.
Very little is known about the prevalence of dyscalculia, its causes or treatment. There isn't a single reason why many people fail to master maths, and academic consensus suggests that, despite some shocking levels of numeracy, only three to six per cent of pupils are dyscalculic.
This specific learning difficulty is only just becoming recognised in mainstream education, perhaps as a result of the continuing bad press for GCSE maths.
The DfE website does not currently have any results for dyscalculia, but the American Psychiatric Assocation describes it thus:
Developmental Dyscalculia (DD) is a specific learning disorder that is characterised by impairments in learning basic arithmetic facts, processing numerical magnitude and performing accurate and fluent calculations. These difficulties must be quantifiably below what is expected for an individual’s chronological age, and must not be caused by poor educational or daily activities or by intellectual impairments.
So, dyscalculia could be described as a difficulty in the brain with the whole concept of numbers and how they relate to one another. At its extreme, acalculia, it means an inability even to count.
Early maths is mostly numbers. Later topics such as measure, algebra, data handling and spatial topics appear on the scene, but up to GCSE the major component remains number, especially for the less able in maths. So a weakness in number skills will be the most significant handicap to learning ‘school’ maths.
Maths can be concrete, but fairly quickly moves to the abstract and symbolic (perhaps too quickly?)
Many children experience difficulty because they rely on memory – trying to learn rules and answers by rote rather than investigating and understanding how the numbers are working in relation to each other. Even more fundamentally, maths is a ‘building’ subject, and new information will never make sense unless all the foundation blocks are firmly fixed.
Perhaps in part because some teachers, particularly in primary schools, are not sufficiently skilled to develop this aspect of maths and mathematical thought, foundation blocks often get missed. Gaps in knowledge affect ability in maths in a basic way quite different from, say, history or geography, and if pupils who are slow processors do not grasp every principle before moving on, the whole subject quickly becomes ridden with anxiety and negative attitudes.
An inability with numbers is also a handicap in real life.
Everyday maths include a lot of money, measurement, some time and the occasional percentages.
Paying for a family meal in a restaurant, for instance, requires estimation skills, possibly accurate addition skills, subtraction skills if using cash, and percentage skills for the tip. Not being able to tell if you have been short-changed, or work out how long a train journey is or whether your bank balance is enough to pay the bills puts you at a constant disadvantage.
The demands maths makes on children are varied, sequential and developmental, so gaps in learning can be very damaging and cumulative.
Poor or weak foundations and the whole shakes, even collapses. Basic skills could include good short-term and working memory, vital for mental arithmetic, particularly for those maths thinkers who are very sequential in their thinking processes. And, of course, there is also a need for long-term, mathematical memory.
Spotting problems early on
An early indicator of difficulty in maths is the persistent use of counting in ones rather than developing a recall of basic facts and relationships between numbers.
The first number test on the Butterworth Dyscalculia Screener is for subitising – that is, looking for a sense of what numbers are worth by testing the ability to look at a random cluster of dots and know how many there are without counting.
A later test examines how quickly and accurately children find the answers to basic addition sums such as 4 + 7. If children still count, they are likely to be slow and inaccurate. At a very basic level of skill development they will count all of the 4 + 7, rather than start at 4 (or better still at 7). Relying entirely on counting for addition and subtraction is a severe handicap in terms of speed and accuracy, the more so when trying to use it for bigger numbers and tasks such as multiplication and division.
The writing on the page...
Often a child’s page is covered in endless tally marks, and frequently these are just lined up, with no attempt at grouping. If you show them patterns of dots or groups, say tally groups of 5, they still prefer to see lines of individual markers.
Moving on from one-by-one counting to grouped tallies is just the beginning. Skill in numeracy requires the ability to recognise and use relationships in all numbers, such as seeing 9 as one less than 10; 6 + 5 as 5 + 5 + 1; counting on in twos, tens, fives, especially if the pattern isn’t the basic one of 10, 20, 30 ... but 13, 23, 33, 43...; to see the relationship between the four operations (+ x – and ÷); to see patterns and relationships in numbers and be able to manipulate them.
A dozen dyscalculic indicators
Early indicators of dyscalculia include some or all of:
- A difficulty in recognising ‘how many’ when looking at a small group of objects.
- An over-reliance on counting to arrive at number facts and answers.
- A persistent difficulty in recalling basic facts (addition facts when younger, multiplication facts when older).
- A problem recognising the symbols of maths (in giving them the right name and in knowing what they mean.
- Difficulties with the vocabulary and the language of maths.
- Working at a slow speed.
- A distinctly lower level of achievement than in other subjects and in comparison with their peers.
- An avoidance of maths and lack of confidence with maths tasks.
- Anxieties around anything mathematical.
- Awareness of money values.
- Poor mental arithmetic skills and/or poor written arithmetic skills.
- Persistence of the difficulties despite lots of help.
Things you can do to help
- Never make the problem an ‘issue’.
- Don't say, ‘Never mind, I could never do maths, either.’
- Practise in low-stress ways ... and a little at any one time.
- Make your expectations realistic.
- Have lots of small targets rather than a few big targets.
- Look for improvement, not perfection.
- Don't stick with one target, move around a little, but keep revisiting previous work.
- Negotiate with the school to get better understanding for your child.
What a good school will do to help
Being dyscalculic does not necessarily condemn a child to failure in maths.
- Make learning multi-sensory. Use equipment, apparatus, visual aids etc.
- Make maths practical and where possible related to everyday experiences/the world.
- Link facts and learning, so the child has an anchor fact(s) to return to.
- Get the student to explain how they have come to an answer, whether right or wrong. This helps to understand thought processes, and to identify if, and where, these are breaking down.
- Encourage children to explain to themselves and others how they have done a task.
- Explain concepts carefully. Get the child to develop their understanding by exploring new subject matter and explaining what they think they have been asked to do.
- Emphasise key words, syntax and basic mathematical rules.
- Allow the use of a calculator to progress mathematical thinking, particularly where arithmetical skills are impeding overall progress.
- Create a stimulating environment. Wall displays should be purposeful and well presented.
- Use mnemonics to aid memory.
- Encourage workings which show thought processes rather than just answers.
- Make use of ICT.
- Minimise the need to copy down work from the board. Where unavoidable check it has been copied accurately.
- Ensure exam concessions such as extra time are used.
- Help with and encourage good personal organisation.
The outcome will depend a lot on empathetic and appropriate teaching and, of course, the pupil – the severity of their dyscalculia and their perserverence. ex-pupils of mine have been flagged up as dyscalculic, but have gone on to get A and A* in GCSE maths. Some, however, haven’t!
Steve Chinn has many years experience of teaching children with specific learning difficulties. He has written a number of books on the subject and edited the Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties (2015.