Technolandy

SOL Summer of Learning 2026 – how the brain deals with numbers… mathing different(iated)

What does your brain do when you see 7?

Let’s start pulling another thread (assuming you saw yesterdays blog on reading different(iated)

There is good neuroscience behind the brain thinking about numbers in different ways.

But we don’t do a good job differentiating brain processes in reading (see yesterday) so why would we do a good job thinking around maths…

The same mathematical symbol can trigger profoundly different internal experiences. So why would we assume there is one best way to teach someone what that symbol means?

Dyscalculia tends to get incorrectly applied as ‘math dyslexia’ and remains more of an umbrella term… like ‘chronic pain’…

Numerical cognition isn’t one single process nor one “math centre.”

Quantity/magnitude processing is strongly associated with the intraparietal sulcus (a groove on the outer surface of the brain), while calculation recruits broader networks involving language, memory, attention, visual-spatial processing and executive functions. Developmental math difficulties also appear to involve a distributed network rather than one universal neurological deficit. As I shared on reading… language, memory, attention, visualization etc does not work the same way in every brain…

And again, I want to emphasize: avoid simply making dyscalculia the “dyslexia equivalent.” The research is much more interesting than that.

The popular “number sense deficit” explanation is influential, but researchers have challenged the idea that there is one discrete number-sense mechanism that explains mathematical ability. Despite what the textbooks would prefer…

Symbolic numbers, quantities, calculation and mathematical reasoning can involve partly distinct systems.

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So: What Does Your Brain Do When You See 7?

7

What did your brain just do?

For one learner:

7 → seven → 7 objects

Another:

7 → •••••••

Another:

7 → 5 + 2

Another:

7 → 10 − 3

Another:

7 → a position on a number line

Another:

7 → “prime number”

Another:

7 → July

Another:

7 → jersey number

Another might experience almost nothing beyond recognizing the symbol (a reason I am wary about flash cards… I’d prefer 5×3 creating a mindset of five trees each with three apples than just a symbol of “1 and 5” on the back… but my brain likes working in visuals… not every brain does… wow, I wish I knew then what I know now!

Someone with significant mathematical learning difficulties may have to work considerably harder to establish the relationship between the symbol and its quantity. This is not just ‘memorize better’.

How many of our math strategies assume that another person’s internal experience works like ours?

I’m finding this a very uncomfortable question.

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2. The Number 8 Is Not the Number 8

Consider

8

SOME of the representations:

8

eight

●●●●●●●●

5 + 3

4 × 2

10 − 2

2⁳

VIII

0.8 × 10

8/1

position 8 on a number line

eight dollars

8°C

8:00

8 km

an octagon

The mathematical symbol is just one doorway into a network of meanings.

So,

When we say a student “knows 8,” what exactly are we claiming they know?

Because “knowing a number” isn’t necessarily one thing.

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3. The Math Equivalent of Reading Regression

My reading post has a particularly interesting idea around rereading: the learner sees the text, but meaning doesn’t immediately “stick.” There is a numerical analogue:

Calculation regression

7 × 8

→ 56?

→ wait…

→ 48?

→ 56.

→ wait, what was I doing?

Or:

37 + 28

A learner may understand the operation but lose track of:

place value

the carried quantity

which column they are in

the intermediate answer

the question itself

That opens the door to working memory.

And math cognition relies heavily on working memory, spatial skills and language.

So perhaps:

What if some students aren’t “bad at math” but are trying to hold too many pieces of the mathematical process in working memory at once?

That’s a very different instructional conversation.

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4. What Does Your Brain Do With 23 + 19?

This might be my favourite pedagogical one.

23 + 19

I love asking people to silently solve it. (I’m a fan of @Howie_Hua ’s Mental Math Monday…)

Cuz… so many options…

Brain A

23 + 20 = 43

43 − 1 = 42

Brain B

20 + 10 = 30

3 + 9 = 12

30 + 12 = 42

Brain C

23 + 19

9 + 3 = 12

carry 1

2 + 1 + 1 = 4

42

Brain D

Visualizes two quantities combining.

Brain E

Recalls the answer from somewhere.

Brain F

Starts counting.

Brain G

Sees 23 + 20 − 1 almost automatically.

Then:

Which one is “doing math correctly”?

All of them. ALL. OF. THEM.

And then the more interesting question:

Which one does our assessment system reward?

Now we’re back in the ‘game of school’ territory.

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5. When Numbers Become Pictures

This is the numerical equivalent of your visualization/aphantasia section.

Some learners seem to have particularly strong visual-spatial approaches to mathematics.

Think:

number lines

arrays

ten frames

dot patterns

manipulatives

geometric relationships

spatial arrangements

graphs

visual estimation

But be careful here because “visual learner” is not a scientifically useful catch-all. I’m not saying visual ‘learning style’…

The more interesting question is:

What representations does a particular learner spontaneously construct when thinking mathematically?

5b.

When Numbers Have Colours — Or Live Somewhere. grapheme-colour synesthesia,

For some people, numbers don’t just represent quantities.

They may have colour.

This is grapheme-colour synesthesia, where letters or numbers consistently evoke particular colours.

So:

7

might not simply be seven.

It might be yellow 7.

And 8 might always be blue.

Not because someone learned them that way. That’s simply part of their experience of the symbol.

But it gets even more interesting with number-form synesthesia.

Where is 7?

For many of us, that’s metaphorical.

For someone with number-form synesthesia, it might not be.

Numbers may occupy specific locations in an internally experienced spatial arrangement:

1 → 2 → 3 → 4 → 5

then perhaps 6–10 rise upward.

Maybe 20 turns a corner.

Maybe 100 is far away.

The particular arrangement isn’t universal. That’s the point.

Which makes me wonder:

When I draw a number line for a learner, am I showing them a useful mathematical representation — or asking them to replace one they already have?

How is this making students feel? That there is ‘a’ way to do maths, and if they can’t do it in the same way as the majority… well: work harder, not smarter??

5c.

Spatial-sequence synesthesia is probably the biggest synesthesia. Ordered sequences—numbers, months, days of the week—can have persistent spatial locations. July itself might occupy a location in someone’s mental space separate from ‘the 7th month’.

5d:

Ordinal linguistic personification is wonderfully weird too. Numbers, letters, days, or months can have personalities, genders, ages, or interpersonal relationships. Someone might experience 7 as arrogant, 4 as friendly, or 8 as maternal. It sounds whimsical until you remember your thesis: the internal experience triggered by a mathematical symbol is not necessarily the same from brain to brain.

And there’s an especially fun connection to your 23 + 19 section. For a grapheme-colour synesthete, that problem potentially isn’t visually neutral:

23 + 19

Each digit can carry an involuntary colour association. The resulting 42 has another combination. That doesn’t mean synesthesia necessarily makes arithmetic easier or harder; rather, it’s another striking demonstration that two students looking at exactly the same worksheet may literally not be having the same perceptual/cognitive experience.

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6. Subitizing: Your Brain Counts Before You Count

● ● ●

Most people don’t consciously count them.

Now:

● ● ● ● ● ● ● ● ●

Something changes.

The brain can rapidly apprehend small quantities, while larger or more complex quantities require different processes. This connects to the approximate number system and subitizing.

What happens when the thing we expect children to “just know” isn’t actually automatic for them?

Thisleads naturally into dyscalculia without making dyscalculia the whole story.

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7. Dyscalculia Isn’t Just “Dyslexia With Numbers”

This could be important.

We have become much better at recognizing dyslexia.

We’re increasingly talking about dyscalculia.

But what if we’re making the same mistake in reverse?

What if “dyscalculia” is sometimes being used to describe a collection of very different neurologies?

There is evidence for multiple possible cognitive contributors, including:

magnitude processing,

symbolic number processing,

working memory,

attention and

other domain-general processes.

There isn’t one single neurological explanation that accounts for every learner with mathematical difficulty. Even though it would be convenient if there were one text that would work with every student at the same time they reach a certain age…

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8. The Student Who Hates Math May Not Hate Math 🔥.

I love the hate on the social medias around: math anxiety.

Math anxiety isn’t simply “I don’t like math.” It can interact with working memory and attentional resources, potentially making mathematical performance worse precisely when the learner is being evaluated.

So:

What does your brain do when you see a math test?

Student A:

Numbers → curiosity → puzzle

Student B:

Numbers → retrieve strategies

Student C:

Numbers → “I’m going to get this wrong” → anxiety → working-memory resources consumed → harder to solve

Now suddenly the assessment itself has become part of the neurological story.

And that’s very aligned with my broader thinking about feedback, anxiety and personalized assessment.

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9. The Number Line Isn’t Actually a Line

This could be a fun one.

Ask:

Where is 7?

Most people immediately imagine something like:

1 2 3 4 5 6 7 8 9 10

But numerical magnitude isn’t always represented that neatly.

You could explore:

magnitude

estimation

spatial representation

logarithmic vs linear representations

fractions

decimals

negative numbers

very large numbers

Then hit them with:

Where is 0.7?

Where is ⅔?

Where is −3?

Where is 7,000,000?

Suddenly the “simple” number line becomes a cognitive landscape.

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10. Math Has a Reading Problem

Words and letters – and imaginary letters that act as numbers…

When I shared the other day about reading, I highlighted that “we talk about reading as though reading is one neurological act.” Then I started thinking that…

We talk about mathematics as though mathematics is one cognitive act.

But mathematical cognition involves a whole ecosystem:

quantity → symbols → language → spatial representation → working memory → retrieval → calculation → reasoning → abstraction → executive function → emotion

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A Deep Dive Option – a rabbit hole to explore…

We actually know quite a lot about the “math brain”

Numerical cognition has been studied seriously for decades. There are established models such as Dehaene’s Triple Code Model, distinguishing roughly between quantity/magnitude, verbal number representations, and visual Arabic-number representations. More recent work makes the picture considerably more networked and complicated. A major 2025 review describes calculation as involving different mental strategies and kinds of arithmetic knowledge that can actually be dissociated neurologically.

It means, I used to… “Here are six strategies for addition.”

It has evolved to: “Here are six possible cognitive routes to addition — and an individual may favour some routes over others.”

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In Summary

What happens inside your head when you see 7?

One person:

7 → yellow

Another:

7 → a particular spatial location

Another:

7 → seven dots

Another:

7 → 5 + 2

Another:

7 → word “seven”

Another:

7 → an auditory/verbal representation

Another:

7 → quantity

Another:

7 → memorized symbol with surprisingly weak magnitude attached

Another:

7 → anxiety

And presumably many people:

7 → several of those things simultaneously. <—— this is me!

Research has studied many of those components individually. What we don’t yet have is anything approaching a neat educational taxonomy saying:

Here are the different ways human beings experience mathematical thought, determine which your learner uses, and teach accordingly.

It certainly doesn’t fit nicely into any one textbook…

TikTok Script

What happens inside your brain when I say…

SEVEN?

Do you see:

the number 7?

The word seven?

Seven dots?

5 + 2?

Do you hear the word?

Is seven a colour?

Does seven exist somewhere in space?

Does it trigger a memory?

Or — like me — do several of those things happen at once, creating a kind of mathematical mosaic?

Because here’s what I’m wondering:

We talk about dyscalculia a lot like it’s dyslexia… but with numbers.

Maybe dyscalculia shouldn’t be the beginning of our conversation about how differently brains do mathematics.

Maybe it’s evidence that we need a much bigger conversation.

Because brains are different.

And there is no single universal way that every brain experiences and synthesizes numbers.

So…

how does YOUR brain math?