Sold a Sum

Sold a Sum 

Right.
Let’s just say the quiet bit out loud.

We were sold a version of maths that doesn’t match how children actually learn.

Not because teachers don’t care.
Not because anyone set out to fail.

But because we were sold a story.

It goes like this:

If children can explain their thinking, they understand.
If they’ve got a strategy, they’re doing fine.
If they look busy — drawing wee boxes, circles and arrows — learning must be happening.

It looks good.
It feels progressive.
It ticks every box on the observation form.

But underneath it, too many children still can’t multiply.
They still rely on finger counting.
They still panic when numbers change even slightly.

And we’ve told ourselves that’s okay.

That’s the scandal.

How we got here

In Scotland, under Curriculum for Excellence, we didn’t lower expectations —
we blurred them.

We softened benchmarks.
We made progression negotiable.
We replaced clarity with flexibility.

We also withdrew from international comparisons like TIMSS and PIRLS in the early 2010s, leaving PISA as our main benchmark. That made it harder to track our progress against systems that still participate fully. Across PISA cycles, Scotland’s relative maths performance has softened compared with consistently high-performing systems (OECD, 2012–2022).

Fluency became optional.
Number facts became secondary to “strategies” and “explanations.”

What the science tells us

This isn’t a philosophical argument.
It’s a cognitive one.

Working memory is limited and easily overloaded. When learners are still calculating basic facts, there is little capacity left for reasoning or problem solving (Sweller et al., 2011; Cowan, 2014).

Jonathan Firth connects this directly to maths classrooms: fluency with number facts reduces cognitive load, freeing up mental space for deeper understanding and flexible thinking (Firth, 2019; 2022).

Fluency is not speed for speed’s sake.
It is what makes thinking possible.

What high-performing systems do

Look at countries that consistently perform well in international studies:
Singapore. Japan. Estonia.

They don’t separate facts from understanding.
They don’t treat recall as optional.

They teach number structure explicitly.
They build fluency deliberately.
They expect automaticity as part of meaning — not instead of it.

What we must do differently

If we are serious about understanding, fluency must be built on purpose:

Start with structure, not tricks.
Protect working memory.
Use fluency-first warm-ups.
Link meaning and recall.
Build fluency into the curriculum, not as an add-on.

These aren’t gimmicks.
They align with how the brain learns — and how high-performing systems teach.

Children with secure recall don’t just perform better.
They feel calmer.
More confident.
More capable.

The line in the sand

We created a generation who could talk about maths —
but too often couldn’t rely on it.

We traded clarity for comfort.
And the bar quietly disappeared.

CfE had good intentions:
Creativity.
Problem-solving.
Understanding.

All brilliant.

But somewhere along the way, we decided:

Facts didn’t matter as much as feelings.
Automatic recall was old-fashioned.
Practice was boring.
If a child couldn’t calculate, they could just explain instead.

That’s not deep understanding.
It’s fragile understanding.

Children can’t reason with numbers they don’t know.

There is no magic strategy that replaces fluency.
There is no diagram that can carry the whole load forever.

Fluency isn’t speed.
It’s freedom.

It’s what lets children stop surviving maths and start using it.

So this is Sold a Sum.

Not to point fingers.
Not to assign blame.

But to ask one honest question:

What if we’ve been doing this the hard way — and calling it good pedagogy?

Children deserve maths that makes sense.
They deserve to feel steady.
Capable.
Confident with number.

Sold a Sum is not a brand.
It’s a line in the sand.

If you’re ready to draw that line with us —
welcome.

Keep the Fluency Conversation Going

If you want to stop surviving maths and start using it — in your classroom, with your pupils, or at home — Not That, But This… is the newsletter for you.

Every month, you’ll get:

• Bite-sized, research-backed ideas that actually work

• Practical fluency routines you can use immediately

• Insights from classrooms and countries getting it right

No fluff. No gimmicks. Just tools that help children feel capable, confident, and fluent with number.

Join the Movement