Overcoming obstacles for learners with dyscalculia

Dyscalculia is a specific learning difficulty in maths — particularly in arithmetic. The word dyscalculia has both Greek and Latin roots, literally meaning: counting badly. Essentially, it’s a specific difficulty in maths, caused by structural differences in the areas of a learner’s brain responsible for numerical calculation.

Learners with dyscalculia generally function well in other areas, but show a complete lack of number sense and intuition for number. The effects of their difficulties in maths can be far-reaching and can significantly impair daily living.

So how can you support a learner with dyscalculia? You can identify dyscalculia in your learners in a few ways. Once you’ve identified a learner with dyscalculia, here are some of the main obstacles to look out for, and tips for helping learners move past them.

Obstacle 1: Inability to subitise

Subitising means you can immediately recognise the number of items in a set without actually having to count them. Most people can subitise up to six or seven items. A learner with dyscalculia will not be able to do this, and may have trouble subitising just three items.

The teaching strategy: Ten frames

Visual imagery from five frames and ten frames can help children develop instant recognition of numbers up to 10 by using patterns for arranging counters or cubes.

Obstacle 2: Poor number sense

Number sense is the ability to understand numbers and how they relate to each other. A learner with good number sense knows what they can and can’t do with numbers and is able to manipulate numbers and use them flexibly.

Learners with good number sense have a strong intuition about numbers and their relationships. Theorist Hilde Howden talks about how visualising numbers in different contexts and relating them in ways that go beyond traditional methods helps develop good number sense.

So it makes sense that children with poor number sense find it hard to develop meaning for numbers and operations. They don’t look for relationships and connections among numbers and operations and they don’t have any flexibility in the way that they use numbers.

The teaching strategy: Emphasise number sense

You can help children develop number sense by looking at number bonds to all numbers (not just bonds to 10). This helps children to develop an understanding of how numbers are made and how they can be decomposed.

By encouraging learners in your class to explore and play with numbers, you’ll help them discover the connections and relationships between numbers and number concepts.

Obstacle 3: Inability to estimate

Most children are reluctant to estimate an answer before they calculate it, but a learner with dyscalculia has no concept of whether the answer they have calculated is reasonable or not.

The teaching strategy: Look for the ‘reasonableness’ of an answer

Emphasise estimation and questioning on whether an answer is reasonable or not. This helps children question whether their approach and answer makes sense and puts them in a good position to spot mistakes.

Obstacle 4: Persisting with immature strategies

Learners with dyscalculia tend to cling to procedures they feel the most secure with: for example, counting all instead of counting on when adding two numbers. They don’t have the confidence to play with the numbers or to try out new more efficient methods.

This way of working things out means that they often end up doing a harder more laborious form of maths. They apply long-winded and inefficient procedures instead of finding a quicker, more elegant route to the answer.

The teaching strategy: Journaling

There are a million reasons why your learners should be journaling, (well, at least four).

Journals give children the space to record their ideas. Learners can show their thinking and present multiple methods which they can then evaluate and comment on. This helps them to move on from immature strategies and explore more efficient, sophisticated, and often easier solutions to maths problems.

Obstacle 5: Inability to notice patterns

Learners with dyscalculia find it difficult to spot the patterns in maths. Being able to see patterns makes it much easier to generalise and to predict solutions.

The teaching strategy: CPA and pattern spotting

The pictorial stage of the CPA approach is designed to reveal the underlying structures and patterns in maths so that children can not only recognise patterns, but can actively start seeking out patterns and connections.

Obstacle 6: Inability to generalise

Generalising is all about transferring acquired knowledge to a novel situation. This helps learners make sense of maths and helps them understand the connections and patterns.

Learners with dyscalculia struggle with generalisation of ideas and concepts and find it hard to transfer information from one area of maths to another. For these learners, maths is a multitude of individual pieces of information that have to be stored and remembered or calculated from first principles every time.

The teaching strategy: Generalisation as a core competency

Generalisation is one of the five core competencies in Maths — No Problem! Children are encouraged to use what they know to find out what they don’t know.

Look for ways to extend what learners know to help them realise that being secure in just a few simple facts can help them solve new problems. Two examples of this are:

Given that 3 + 4 = 7, can I now work out 700 – 400?
I know that 5 × 7 = 35 and 2 × 7 = 14, can I use this to help me work out 7 × 7?

Being on the lookout for connections and relationships helps develop depth of understanding and reduces the load on working memory.

Obstacle 7: Decomposing numbers

Children with dyscalculia find it very hard to break numbers up into smaller parts, like recognizing that 10 is made up of 4 and 6, 7 and 3, or 8 and 2.

Mahesh Sharma compares this to phonemic awareness. Breaking words into meaningful chunks and blending those chunks fluently back together are predictors of early reading performance.

In a similar way, the ability to decompose and recompose number is a precursor to numerical development. Learners without this sense of how numbers are constructed will struggle to develop fluency in mathematical thinking.

The teaching strategy: Number bonds and visualisation

Encourage children to visualise number by using number bond diagrams, ten frames, and the use of two-coloured counters. This lets children see how numbers are built up, how they can be broken up, and when to choose a particular way of breaking up a number.

Using a maths mastery programme and the CPA approach can make a huge difference to learners with dyscalculia. By supporting them to overcome their challenges, your classroom can be an inclusive learning environment where everyone succeeds.

References

Howden, H. (1989). Teaching Number Sense. The Arithmetic Teacher, vol. 36(6) pp. 6–11. Available from: www.jstor.org/stable/41194455

Sharma, M (2015). Numbersense: A window into dyscalculia and other mathematical difficulties. In: S. Chinn, ed. The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties. Abingdon, Oxon; New York, NY: Routledge.