Someone can be a brilliant storyteller and struggle to spell.

We understand that.

But can someone struggle profoundly with numbers and still have a mind that is unusually good at abstraction, logic, patterns, systems or conceptual mathematical thinking?

The answer is surprisingly unclear.

And that matters, because bad at math is not merely a description. In education, it can become a direction. It can influence what someone studies, what teachers encourage, what opportunities become available and, eventually, what that person believes they are capable of.

So perhaps we need to ask more precise questions:

• What if someone is extremely weak in one kind of mathematical processing and exceptionally strong in another?
• Are we sure we know what mathematical talent looks like?
• So what does being “bad at math” actually tell us — and what doesn't it tell us?

And there is another possibility worth considering.

What if some highly analytical or conceptually strong people effectively disqualify themselves from mathematics — and perhaps later from science and technology — because school has already taught them that they are “bad at math”?

They may not know that they have unusual strengths. Their teachers and parents may not know either.

Particularly in a twice-exceptional profile, high ability and a learning difficulty can obscure each other. The learner may simply experience something confusing: some things seem to come remarkably easily, while something that apparently should be easy seems almost impossible.

So they may avoid math. Drop it when they can. Choose another direction.

And perhaps nobody ever discovers what else might have been there.

Does dyslexia make someone bad at language?

Dyslexia gives us a useful comparison.

Someone with dyslexia might struggle to:

• connect letters with their sounds;
• decode unfamiliar words;
• read fluently;
• spell accurately;
• keep letters or parts of words in the right order;
• or, for some readers, deal with words or letters that seem to blur, shift or become difficult to track.[1]

Different people can experience very different difficulties.

And yes, a person with some of these difficulties may well look bad at language in school.

But that tells us remarkably little about how they might use language elsewhere.

Someone can struggle with spelling and be an extraordinary speaker. A storyteller. A salesperson. A comedian. A negotiator. A poet. Someone with an exceptional vocabulary or an instinctive feel for how words affect other people.

A brilliant storyteller can struggle profoundly with the mechanics of getting a story onto the page.

Language is more than spelling.

Difficulty with one part of language does not tell us everything about someone's ability with language.

So should difficulty with one part of mathematics tell us everything about someone's ability with mathematics?

What does “bad at math” actually mean?

Dyscalculia is much less familiar than dyslexia.

Someone with dyscalculia will often simply be described — or describe themselves — as “bad at math.”

But what does that actually mean?

Dyscalculia can look very different from one person to another. Difficulties can include:

• understanding or estimating quantities and numerical magnitude;
• retrieving basic arithmetic facts that other people seem to remember automatically;
• performing calculations accurately or fluently;
• understanding or manipulating mathematical symbols;
• keeping track of numerical information;
• judging time, reading clocks or working with money;
• and, in some profiles, difficulties involving direction or spatial orientation.

The core features concern numbers, arithmetic and numerical processing. Some of the other difficulties above are associated experiences rather than defining features of dyscalculia.[2]

Already, bad at math starts to look like a remarkably imprecise description.

Because mathematics is also more than calculation.

It can involve calculation and number sense, certainly. But also logic, abstraction, pattern recognition, spatial reasoning, conceptual understanding and the ability to recognize relationships between ideas.

So what if someone struggles profoundly with some of the first abilities while being unusually strong in some of the others?

What if someone who appears bad at math is also:

• highly analytical;
• strongly conceptual;
• interested in underlying principles;
• quick to identify contradictions or connections;
• inclined to question assumptions;
• constantly asking not merely how, but why?

The question is whether the two can coexist.

Can this person be good at science, technology, engineering or mathematics (STEM)?[3]

And if they can coexist:

Would we ever find out?

Are we sure we know what mathematical talent looks like?

Perhaps the problem begins with the phrase mathematical ability itself.

Mathematics can draw on:

• calculation and arithmetic;
• number sense and symbolic processing;
• spatial reasoning;
• pattern recognition and logic;
• abstraction;
• conceptual understanding.

These abilities overlap. They cannot simply be separated into neat boxes, and being strong in one does not necessarily compensate for serious difficulty in another.

But they are not identical either.

So can someone be extremely weak in one and exceptionally strong in another?

Could someone understand a mathematical idea they struggle to calculate?

Could they recognize a relationship without being the best person to express it in formal notation?

Could one person formulate the question and another prove it?

Could technology perform some of the processing that currently blocks access to the idea?

There will be contexts in which the answer is no. Some mathematical abilities are indispensable for particular tasks.

But which ones?

What exactly are we measuring when we decide that someone has — or does not have — mathematical talent?

We already know we don't measure everything

There is at least one good reason to take that question seriously.

Long-running research following highly able young people into adulthood found that spatial ability predicted later STEM outcomes beyond mathematical and verbal ability.

In one cohort followed for more than 30 years, mathematical and verbal ability together accounted for 10.8% of variation in later patents and scientific publications. Adding spatial ability accounted for another 7.6%.[4]

Larger longitudinal research has similarly found spatial ability independently associated with later STEM degrees and occupations.[5]

Yet spatial ability was historically underused in traditional talent identification.[6]

That does not mean mathematical and verbal measures were wrong.

It means they did not capture everything that mattered.

A good predictor is not necessarily a complete description of potential.

And that leaves an obvious question:

What aren't we measuring?

What if the strength and the weakness hide each other?

This is where twice-exceptionality — or 2e[7] — becomes particularly important.

A twice-exceptional person combines high ability or giftedness with a disability or learning difference.

But that doesn't necessarily produce a person who obviously looks gifted and learning disabled.

Sometimes it produces someone who looks surprisingly ordinary.

The strength may compensate for the weakness enough to prevent the difficulty from becoming obvious. At the same time, the weakness may suppress performance enough to prevent the high ability from becoming obvious.

The strength may help to hide the weakness, while the weakness helps to hide the strength.[8]

A learner who reasons unusually well, makes unexpected connections or continually questions underlying principles may not have those abilities recognized as giftedness at all — particularly if their school performance in another area is weak.

They may simply seem inconsistent.

Capable but careless.

Bright but not achieving.

Good at some strange things, inexplicably poor at others.

Or simply average.

So what happens when the learning difficulty involves mathematics?

How would we know what we're missing?

This is where the evidence becomes much thinner.

Dyscalculia has historically received much less research attention than dyslexia.[9] We know that it is heterogeneous: different people can show different patterns of difficulty involving calculation, arithmetic facts, numerical magnitude and symbolic number processing.[10]

What we cannot currently say is that people with dyscalculia generally have preserved — let alone exceptional — higher-order mathematical reasoning.

The limited direct research does not establish that. Some research with children has found broader mathematical reasoning difficulties.[11]

So we should not replace one stereotype with another:

Bad at calculation? Perhaps you're secretly a mathematical genius.

There is no evidence for that.

But there is another problem.

Advanced mathematical and abstract reasoning in dyscalculic adults appears to be remarkably under-researched. And giftedness combined specifically with dyscalculia has received much less attention than giftedness combined with dyslexia.[12]

Perhaps a profile combining profound numerical difficulty with exceptional abstract or conceptual reasoning is extremely rare.

Perhaps it isn't.

How would we know?

If someone struggles badly enough with basic mathematics, when do they ever get far enough into mathematics for us to discover what else they might be capable of?

When “bad at math” is only half the story

For me, this is not an entirely abstract question.

I have significant difficulty with numerical processing, calculation and spatial reasoning. At the same time, abstract, conceptual and analytical thinking are areas that come naturally to me — and conceptual mathematical ideas can interest me immensely.

That combination does not make me evidence for a theory about dyscalculia.

But it does make the question difficult for me to ignore.

Like many people who struggle with mathematics at school, I learned what I could not do.

What I was rarely given access to was mathematical thinking without calculation and notation first functioning as the prerequisite.

Much later, I encountered mathematical ideas through logic and concepts rather than calculation. Gödel's incompleteness theorem was one example. Explained through ideas and structure rather than equations, it made me want to understand it, argue with it and keep going.

That doesn't mean I would have been a mathematician.

Perhaps I wouldn't.

But I never got far enough to find out what kind of mathematical thinking I might have been good at.

And that is a very different statement from I was bad at math.

Are we sure we know what STEM talent looks like?

This becomes particularly consequential in STEM because mathematics is such an important gateway.[13]

And mathematics genuinely matters.

Engineering, physics, mathematics, computer science and many other STEM fields require mathematical knowledge and ability, although what they require — and how much — differs considerably.

The argument here is not that mathematical requirements should simply disappear in the name of inclusion.

There is, however, an important difference between saying:

this ability matters

and saying:

this ability tells us everything important about your potential.

A prerequisite can be legitimate and still be an imperfect instrument for identifying talent.

And STEM does not need only people who can calculate.

It needs people who can analyse problems, recognize patterns, challenge assumptions, develop models, understand systems, formulate questions, create technologies, design experiments and make connections that other people have missed.

Many of those activities require mathematics.

But does success in school mathematics always identify the people who might eventually be good at them?

And what happens to someone who is highly analytical or conceptually strong but has already concluded:

STEM? No. I'm bad at math.

They may never choose the subjects that would allow anyone to discover otherwise.

What does this mean for inclusion?

This question becomes especially relevant when institutions are trying to broaden participation in STEM.

Women and girls are one obvious example.

A great deal of attention is rightly given to encouragement, role models, confidence, belonging, stereotypes, recruitment and creating more inclusive STEM environments.

But all of those interventions happen somewhere along an educational pathway.

What about the people who changed direction earlier?

This is not an argument that dyscalculia explains women's underrepresentation in STEM. There is no evidence for that.

And if the mechanism proposed here exists, there is no reason to assume it would affect only women. Men may be affected too — potentially in different ways, given gendered expectations around mathematical ability.

The broader question is more interesting:

Could some people with potentially valuable STEM abilities have stopped considering themselves candidates because an early difficulty with mathematics came to define what they believed they could do?

If so, attracting them later may be difficult.

They may already have chosen different subjects.

They may already have built an identity around being not a math person.

They may never appear in the pool of people a STEM initiative is trying to attract.

That means inclusion may require more than asking how to persuade more people to enter through the existing gate.

It may also require asking:

• What does the gate actually measure?
• Which abilities are genuinely indispensable?
• Which abilities are we failing to see?
• Where can support, technology or collaboration change what someone is able to contribute?
• And at what point might an unusual learner disappear from the pathway before anyone recognizes their potential?

Who never gets far enough to find out?

The question underneath this article is larger than dyscalculia.

And it is larger than STEM.

It is about potential — and what happens whenever a visible difficulty becomes a complete description of someone's ability.

Bad at spelling.

But perhaps brilliant with language.

Bad at math.

But perhaps highly analytical, conceptual or capable of seeing patterns and relationships that others miss.

Those things are not equivalent to mathematical talent. Nor do they guarantee STEM potential.

But neither should we assume that difficulty with one part of a domain tells us everything about someone's capacity within it.

We already know that talent identification has underused abilities that later proved relevant to STEM outcomes.

We know that twice-exceptional profiles can conceal both disability and giftedness.

We know that dyscalculia is heterogeneous.

And we know remarkably little about dyscalculia combined with giftedness or advanced conceptual mathematical reasoning.

The consequences may also extend far beyond school.

If lifelong learning is something we genuinely value, then what people believe they are capable of learning matters. Someone who leaves school having learned I am bad at math may not simply avoid the next mathematics course. They may stop exploring entire areas of knowledge that appear to belong behind that door.

And that makes this more than a question about assessment.

It is a question about lost potential.

Education inevitably creates prerequisites. Some are necessary. But we should at least be curious about what happens when difficulty with the prerequisite prevents us — and the learner — from ever discovering the ability that might lie beyond it.

So perhaps bad at math should sometimes be the beginning of a question rather than the end of one.

What if “bad at math” is only half the story?

And how many people never get far enough to discover the other half?