Teaching Maths to Children with Dyscalculia
See also: What is Learning?Dyscalculia, like dyslexia, is one of a family of conditions known as specific learning difficulties. All these conditions can cause issues with learning, including with mathematics, but in slightly different ways. Dyscalculia is defined as a persistent difficulty in understanding numbers, or grasping the concept of quantity.
Children (and older learners) with dyscalculia therefore have major difficulties learning maths. These difficulties often start to show at an extremely early stage of schooling. Unfortunately, maths is what is known as a hierarchical subject: that is, topics are constantly revisited at higher and higher levels. This means that if basic concepts are not understood, learners will continue to struggle. This page explains what maths teachers can do to help children with dyscalculia.
More common than you might think!
You may think that dyscalculia is a rare problem, and that you have never seen a child who has it.
However, research suggests that around 5% of children have dyscalculia.
This means one in 20 children are affected.
In other words, statistically speaking, there is likely to be one child with dyscalculia in every class of 20 or more.
Put like that, it is clearly a lot more common than most people think.
Recognising Dyscalculia
One of the first areas where maths teachers can help is recognising the potential presence of dyscalculia.
Unfortunately, this is not easy. First, teachers are not routinely taught about specific learning difficulties, including dyscalculia. Second, the issues can manifest in different ways. Our page on Understanding Dyscalculia sets out some of the signs that may help to distinguish dyscalculia from other specific learning difficulties like dyslexia. They include:
Age-inappropriate problems with maths (that is, other children of the same age do not have the same issues);
Problems with arithmetic, but not necessarily apparently more complex issues such as algebra or geometry;
No trouble with subjects that do not involve numbers (although dyscalculia can co-occur with other problems such as dyslexia);
Trouble understanding number bonds and relationships between numbers; and
Trouble understanding simple mathematical concepts (for example, that multiplication is repeated addition).
The importance of attitude
Parents of children with specific learning difficulties often report that teachers assume that their children are just not trying hard enough. More, they say that this is the ‘go to’ assumption.
Perhaps the biggest difference that any teacher can make is to accept that a child is trying, and that something else is the problem.
Problems with Dyscalculia
It should be clear from the list of signs of dyscalculia that this condition is likely to cause fundamental problems with learning maths—and probably from the very first day.
Children with dyscalculia will find it hard to understand basic mathematical concepts such as adding and subtracting, or number bonds, or grasp the meaning of mathematical symbols. However, if they are taught well, they will be able to understand and use these concepts.
The real problems arise if children are taught procedurally, and never get to grips with the concepts.
The British Dyslexia Association suggests that if the basics are in place, children with dyscalculia can learn to do maths. It also suggests what those basics might be (see box).
The basics of maths teaching
“In early learning, children should not just be taught the digit symbol and the name but also form an internal visual representation of that number, in other words ‘see’ the number as a dice pattern or numicon tile. This helps establish a good understanding of the relationship between the name of the number, the symbol and its magnitude or size. Children then need to develop flexibility of number and know how numbers are made up, for example, 6 can be 4 + 2, double 3, 5 + 1, 7 – 1. This is equivalent to being able to match letters to sounds in learning to read.
“Thereafter all concepts need to be modelled using concrete materials such as Cuisenaire rods, dice patterns, Dienes apparatus and similar.”
“We also need to be careful to use maths language correctly and ensure that its meaning is understood.”
The British Dyslexia Association, on dyscalculia.
Tips for Teaching Maths to Children with Dyscalculia
As with teaching maths to children with dyslexia, there are some useful broad principles that will help when teaching maths to children with dyscalculia. These include:
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Use physical objects
Encourage children to use physical objects, such as blocks, dice or coins, to understand mathematical concepts.
This can help them by enabling them to see physically how 2 + 2 is the same as 2 × 2, for example. This approach makes maths less abstract, and much more comprehensible, as well as building the basic understanding described by the British Dyslexia Association. Once children have fully understood the concept using concrete examples, you can make it more abstract again.
Dice and dominoes are particularly helpful because they enable children to start to recognise ‘spot patterns’. These are important for being able to recognise quantities without having to count each item individually (a concept known as subitising).
The next step is to encourage children to use these physical objects to build a mental picture of each number. This will enable them to solve problems without the physical object in front of them.
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Break problems down into smaller steps
Many children struggle with multi-step problems.
They become overwhelmed by having to keep track of several processes, and cannot follow through. This is particularly true of children with dyslexia, but others may also find it difficult, including children with dyscalculia.
Breaking problems down into smaller steps can help children to see how this is done, and enable them to apply the same approach to other problems.
It is also a good idea to verbalise your thinking process, and encourage your students to do the same, to avoid any misunderstandings.
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Provide visual aids
It is often helpful to use visual aids such as diagrams, graphs and charts.
Like using physical objects, this helps children with dyscalculia to understand problems and concepts more clearly. It is just another way of thinking about it.
Children with dyscalculia also often have problems with memory. It is therefore helpful to give written multiplication tables and lists of number bonds, so they are not struggling to remember them.
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Use real-world examples
Another way to make maths problems less abstract is to relate them to real-world experiences.
It is often easier to understand about adding things together if you are baking, and need 100g of one product, and 50g of another. It also makes maths seem much more relevant and important, and therefore more engaging.
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Allow children to use physical aids and tools
One of the easiest ways to support children with dyscalculia is to allow them to use tools designed to help, such as calculators or computer maths programmes.
There have sometimes been tendencies in schools, especially primary schools, not to use these aids until children have understood ‘the basics’, and particularly can do simple mental arithmetic. However, mental arithmetic is likely to be near-impossible to a child with dyscalculia. It is far better to show them how to use the tools available, and empower them.
You would never insist that a child should draw a straight line without a ruler, so why would you stop them using a calculator when they need one?
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Provide extra time in lessons as well as exams
Like dyslexia, dyscalculia slows children down.
Teachers can give them back some of that time by removing time pressure, and allowing plenty of time to solve problems and understand concepts. Surveys on numeracy show repeatedly that many people are fundamentally innumerate when they leave school. Taking time to explain the basic principles and concepts is crucial to overcoming this—meaning that all your students will benefit.
It is also essential to give children with dyscalculia extra time to process questions and instructions.
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Take a ‘little and often’ approach
All of us learn better when information is repeated.
Children with dyscalculia (like children with dyslexia) may also have trouble with memory and retaining information. A ‘little and often’ approach that repeats and revises learning at the start of each lesson is likely to be essential to support their learning. However, it is also likely to help everyone else as well.
Similarly, repeated practice—revisiting concepts through practical exercises—will also build everyone’s learning, but is crucial for children with dyscalculia.
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Use mathematical language—but explain it
It is a good idea to use mathematical language, but also to explain it clearly.
Children need to understand the terms used for different operations in maths, and the meaning of symbols. They also need to be able to recognise symbols and know what to do with them. These are not precisely the same thing (just as knowing the name of a number does not mean that you have a concept of how many it means). Teachers need to ensure that their students understand these concepts and can use the language of maths correctly.
Top tip! Use synonyms
It is particularly important that children understand that there is not just one single word for each mathematical concept. For example, ‘subtract’ is the same as ‘minus’ or ‘take away’.
Introducing synonyms early can help children to appreciate this.
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Help children to develop basic strategies, and then encourage their extension
Children with dyscalculia often have trouble memorising facts, functions and formulae. This can also mean that they struggle to remember different strategies for solving problems.
One recommended approach is therefore to teach them just a few widely applicable strategies, and make sure that they really understand these.
You can then encourage them to extend these strategies to new problems when necessary.
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Always reward and praise effort
Specific learning difficulties like dyscalculia often lead children to be more anxious about their schoolwork, and to have lower self-confidence.
Praising effort rather than achievement is crucial to build back self-confidence.
It is also a crucial part of helping children to develop a growth mindset, the idea that they can learn and improve by applying themselves to a problem. People with a growth mindset are also more tolerant of failure, seeing it as a way to learn. It is important for teachers to model this as behaviour in maths as well as elsewhere.
A Final Thought
These methods will specifically help children with dyscalculia. However, they should also help other children to understand mathematical concepts more clearly.
Given the widely reported problems with poor numeracy, this can only be a good thing.