Numerical Magnitude Processing – What Is It? | Dyscalculia

Which is bigger: 8 or 6?

Is 48 closer to 50 or 100?

If something costs £9, is £10 roughly enough?

Most of us make judgements like these almost automatically. We don't need to count from one or work through a calculation because we have an understanding of the size of the numbers involved.

This ability is linked to something called numerical magnitude processing.

It's a term that many parents (and even many teachers) may never have come across.

However, it is particularly important when we are trying to understand persistent maths difficulties and developmental dyscalculia.

Close-up view of a child comparing two groups of dots on paper

1. What is numerical magnitude processing?

Put simply, numerical magnitude processing is about understanding how much or how many a number represents, and how numbers relate to one another.

For example, when we see 3 and 8, most of us immediately know that 8 is larger. We don't need to count through the numbers to work it out.

As mathematical understanding develops, this helps us to:

• compare numbers and quantities;

• put numbers in order;

• estimate;

• understand place value;

• understand where numbers sit in relation to one another;

• judge whether a mathematical answer seems reasonable.

It's therefore about much more than being able to recognise numbers or remember number facts. It is about developing an underlying understanding of quantity and numerical relationships.

2. Numbers and quantities

There are different ways in which we can think about magnitude.

If I ask:

Which is bigger... 7 or 9?

you are comparing written number symbols.

If I show you two groups of dots and ask which group contains more, you are comparing quantities without written numbers.

As children develop mathematically, they learn to connect the number symbol they see (such as 8) with an understanding of the quantity that 8 represents.

For most people, these connections become increasingly automatic. For some, they remain much less secure.

3. What might difficulties with numerical magnitude processing look like?

A child or adult with difficulties in this area might find it unexpectedly hard to:

• decide which of two numbers is larger;

• put numbers in order;

• estimate quantities;

• understand place value;

• judge where a number belongs on a number line;

• understand the relative size of numbers;

• recognise whether the answer to a calculation is sensible;

• move away from counting towards more efficient ways of working with number.

For example, someone might learn a procedure for completing a calculation successfully, but have much less intuitive understanding of whether the answer they have reached makes sense.

They may therefore appear to be able to 'do' the maths, while the underlying understanding of number is much less secure.

4. Why does numerical magnitude processing matter for maths?

Consider the calculation:

8 + 9 = 17

A child can learn this as a number fact.

But an understanding of magnitude tells us much more.

We know that 8 and 9 are fairly similar in size. We know that adding them together should give us an answer somewhere below 20. And we know that an answer such as 70 couldn't possibly be right.

That underlying feel for the quantities involved helps mathematics to make sense.

When numerical magnitude processing is less secure, maths can remain much more dependent upon counting, remembered facts and taught procedures. This can make mathematical work slower, more effortful and more vulnerable to error.

5. Does difficulty with numerical magnitude processing mean dyscalculia?

Finding one aspect of number difficult does not mean that someone has dyscalculia.

However, current guidance from the SpLD Assessment Standards Committee (SASC) identifies a pronounced and persistent difficulty with numerical magnitude processing and understanding as the cognitive impairment most commonly observed in developmental dyscalculia.

This is an important part of understanding what dyscalculia actually is.

Dyscalculia isn't simply another word for being bad at maths.

A diagnostic assessment looks for a persistent pattern of difficulty and considers this alongside mathematical attainment, other areas of cognitive processing, educational history and the individual's experiences of learning maths.

6. Is dyscalculia the only Specific Learning Difficulty that affects maths?

No, and this is something that is not widely understood.

Current SASC guidance recognises a broader diagnosis of Specific Learning Difficulty (SpLD) in Mathematics.

Developmental dyscalculia sits within this broader category.

Dyscalculia is a type of SpLD in Mathematics, but not every SpLD in Mathematics is dyscalculia.

This distinction is important.

Someone can experience persistent and substantial difficulties with mathematics without showing the particular difficulties with numerical magnitude processing and understanding that are most commonly associated with dyscalculia.

Instead, their mathematical learning may be affected by difficulties in other areas of processing, including language, working memory, executive functioning or visual-spatial processing.

The difficulties can still have a considerable impact on learning and everyday life. The underlying profile is simply different.

High angle view of educational materials including number cards and counting blocks

7. Is numerical magnitude processing the same as 'number sense'?

You may have heard the term 'number sense', particularly in schools.

The ideas are related, but they aren't quite the same thing.

'Number sense' is a broad term that has been used to describe many aspects of understanding and working with numbers.

Numerical magnitude processing is more specific. It focuses particularly on understanding numerical quantities, their relative size and the relationships between them.

This more precise terminology is now important when considering and assessing developmental dyscalculia.

8. How is numerical magnitude processing assessed?

There isn't one single 'dyscalculia test'.

During a specialist assessment of mathematical difficulties, an assessor explores a range of mathematical and cognitive skills to understand the individual's particular profile.

Numerical magnitude processing may be explored through activities involving areas such as:

quantity • comparison • ordering • estimation • place value

Some activities will be formally standardised, while others may provide useful qualitative information about how someone approaches a mathematical task.

The assessor will also consider the individual's wider mathematical attainment, other areas of cognitive processing, educational history and experiences of learning maths.

Importantly, no single score should be interpreted in isolation.

The aim is to understand the pattern across the whole assessment.

9. Can someone be good at some areas of maths and still have a Specific Learning Difficulty?

Absolutely.

Mathematics isn't one single skill.

Someone may have excellent mathematical reasoning but find recalling basic number facts unusually difficult.

Another person may have become very good at following mathematical procedures while continuing to struggle with the underlying relationships between numbers.

Older children and adults may also have spent years developing strategies that help them work around their difficulties.

Equally, struggling with maths does not automatically mean that someone has dyscalculia or another SpLD.

There are many reasons why mathematical learning can become difficult.

10. Understanding the 'why'

    
    

This is why an assessment of maths difficulties needs to look beyond a simple question such as:

'How good is this person at maths?'

A much more useful question is:

'Why is maths difficult for this individual?'

For some people, pronounced and persistent difficulties with numerical magnitude processing and understanding will form an important part of the picture and may support an identification of developmental dyscalculia.

For others, numerical magnitude processing may be relatively secure, but difficulties in areas such as working memory, language or visual-spatial processing may be affecting mathematical learning. Their profile may therefore be better understood as an SpLD in Mathematics.

And for others, their difficulties may have a different explanation altogether.

A comprehensive assessment brings together the individual's strengths, difficulties, cognitive processing, mathematical attainment, history and experiences to build a much fuller picture.

Because understanding why maths is difficult is an important first step towards identifying the support that may help.

If you want to learn more or explore assessment options, visit Clarity Assessment for expert guidance and support tailored to your needs. Clarity assessment provides accredited dyslexia and dyscalculia diagnostic assessments and screeners for children and adults, carried out by an experienced Specialist Assessor holding a PG Level 7 Dip SpLD and SpLD Assessment Practising Certificate (APC).

Assessments are available in Caversham, Reading, and in schools and workplaces across Berkshire and Oxfordshire.