How to Teach Anything
Routine Atomisation and Atomic Instruction
Podcast is AI generated, and will make mistakes. Interactive transcript available in the podcast post.
When you first start teaching maths it feels like there are hundreds of things to teach. Thousands. The cries that the ours is a “crowded curriculum” with “too much maths to cover” have been sung for decades, the most recent shown in the May report from the Maths Horizons programme following their surveys of teachers. The reports authors don’t agree with that diagnosis, and neither do we, but I empathise.
It certainly feels like there is far too much. We race through hundreds of topics and question variants every year. Kids forget what we taught them last week, which means by the time we get to next year we’re reteaching it all again.
We think this isn’t an issue with curriculum content, though. It’s a problem of curriculum design, easily solved through better design, something the national curriculum has no opinion on.
Curriculum design will be a feature of a future post:
Today, there is another, related, problem we teachers face: thousands of ‘things to teach’ means thousands of ‘things I have to figure out how to teach.’ Now that is a problem we’re already, so quickly, in a position to solve.
Once you start to atomise, you begin to realise that there aren’t really thousands of things to teach, there are only four.
Four atomic elements:
Learn how to teach those four elements, and you have learnt how to teach around 90% of everything you will ever have to teach in maths.
Best of all, we have already seen examples of all four elements:
In this one diagram we have an example of a categorical, a transformation, a fact, and a subroutine.
For each element there is a way to teach it that works every time. It results in what the literature calls logically faultless communication (what we call ‘unstoppable learning.’)
As the teacher quoted at the top says, once you see this, it feels like you’ve hit a button, and suddenly all the kids are getting everything right.
So now you can do the same thing each time:
If you’re teaching a cognitive routine then you atomise as we’ve already seen to unpack its constituent atoms.
Any more routines in there, like Atom 5 above? If yes, have they already mastered that atom? In this example: can they already evaluate an expression like that one? If yes, no need to teach anything. If no, atomise again (just repeat the process.)
Any new categoricals, like Atom 1? If yes, atomic instruction for categoricals.
Any new transformations, like Atoms 3 and 4? If yes, atomic instruction for transformations.
From here, once all the atoms are mastered, you can start to build and practice sub-chains and the full chain.
In summary:
Step 1 - which element is it?
Step 2 - if it’s a routine, atomise
Step 3 - what are its atoms?
Step 4 - if there’s a subroutine they haven’t mastered, atomise again
Step 5 - if there is a new categorical, atomic instruction for categoricals
Step 6 - if there is a new transformation, atomic instruction for transformations
Step 7 - (optional) once they have mastered some or all of the atoms, build and practice sub-chains
Step 8 - once they have mastered all atoms, build and practice the full-chain
This leads to two questions:
How do you identify categoricals and transformations?
How do you teach them; what is atomic instruction?
Because what we looked at before wasn’t really atomic instruction.
And it’s the atomic instruction, first and foremost, that hits the button:
Later in the week we’re going to kick off by answering these questions for categoricals.
Next week will feature the first in our series of deep-dive analyses by looking at real atomic instruction designs that have been created by practising classroom teachers.
From there, we’ll move on to do the same for transformations.
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