Small Steps are not Atomisation

A lethal mutation

Jan 19, 2026

0:00

-4:59

Podcast is AI generated, and will make mistakes. Interactive transcript available in the podcast post.

I wrote this back in May last year.

I felt a little annoyed at the time, so held back on publishing it. I felt annoyed not because atomisation was being criticised, but because it wasn’t atomisation that was being criticised.

Atomisation - something that has already transformed the experiences of so many teachers and students - was being misrepresented.

Other things got in the way, and I didn’t publish it until now, as we begin our series deep-dive into atomisation. We’re starting here with what it is not - the common misconception that teachers trying to promote atomisation in their schools keep running into.

Next week we’ll look at the kinds of teacher experience it promises to transform. From there we’ll start digging deeper into what atomisation really is, over a dozen benefits it offers, and how it realises its promise.

Rather embarrassingly I think the AI podcast did an almost better job than me in places of making the point, so that one’s probably worth listening to as well.

When Craig Barton , Lee Wheeler , and I had this conversation, Craig asked me if I ever encountered the opposition that ‘we shouldn’t break maths down into small steps like this.’

I said I hadn’t.

I think I haven’t because atomisation isn’t really about breaking processes down into small steps. So that objection wouldn’t make sense; it would never come up.

Small steps are not atomisation.

Since that conversation I’ve now seen this objection crop up in a few places.

One excellent case in point is here, in an article from the renowned Colin Foster.

The problem is that what Colin describes as ‘atomisation’ is not atomisation.

I don’t believe it’s a straw man. I expect that what Colin describes here is what teachers really are doing when they say they are ‘doing atomisation.’ But it’s not atomisation. What we have here is a new lethal mutation.

So what’s the difference?

Small steps:

breaking a process down into small steps
—> doesn’t reveal mathematical structure, relationships, or concepts

Atomisation:

breaking a cognitive routine into its constituent atoms
each atom is a concept, fact, or another cognitive routine (so atomise again, if needed)
for any new concepts, communicate them through initial instruction, testing and expansion sequences
these sequences should be constructed according to the five principles of instruction
—> as a result, enormous depth of mathematical structure and inter-relationships are revealed, as concepts are explored in great detail

Small steps are not atomisation.

What I just described was routine atomisation. It can also be applied to facts, revealing the concepts that are connected by the fact.

It can also be applied to topic strands, revealing concepts that usually go unexplored because they’re not examined, for example:

Did you know that the distance from a parabola’s axis of symmetry to its roots will always be this:

\(\frac{\sqrt{b^2 - 4ac}}{2a}\)

Did you know the reason the sine rule works is because each ratio describes the diameter of the triangles circumcircle? It’s Atom 28 in our conceptual atomisation of the sine and cosine rules.

Did you know that if you shrink one parallel side of a trapezium, eventually you get a triangle? And, that if you enter a = 0 into the area formula for a trapezium, you get the area formula for a triangle?

\(\text{Area} = \frac{(a + b)h}{2}\)

\(\text{Area} = \frac{(0 + b)h}{2}\)

\(\text{Area} = \frac{bh}{2}\)

Small steps doesn’t reveal these relationships.

Conceptual atomisation does.

Routine atomisation provides the opportunity to explore then in depth.

Small steps are not atomisation.

If you’re interested in learning more about how to both guarantee 100% success for 100% of your students, every day, and inspire a deep love of mathematics that stems from a deep knowledge of its rich interconnectedness, subscribe below.