What Order Should You Communicate Atoms?
It's not small steps. It's not I do / We do
Podcast is AI generated, and will make mistakes. Interactive transcript available in the podcast post.
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In the last post in this series, we saw how the atomic view reveals that we have much less to teach than we think:
This is because stage two for teaching cognitive routines - communicate - grants us the powerful ability to focus instruction on only what is new.
Now, a second thing that atomisation reveals, is that it’s not always the first atom in the routine that is new.
For example, let’s compare two routines: one for rounding to the nearest whole, and one for rounding to a given number of decimal places, both shown in the Full-Chain view to start:
If you already learnt the routine on the left, then only two atoms are new in the routine on the right.
First, identifying the position of a given ‘decimal place’ is something new compared with identifying the position of a place value.
Then second, we need to truncate any trailing zeroes, which doesn’t happen when rounding to whole numbers.
So, nearly all instructional time should be given to mastering these two atoms.
And then, importantly, it makes no difference which one you start with.
You could dive right in with a short instructional sequence like this one, for the last atom in the routine, and make sure students have mastered that before any talk about rounding to decimal places.
Next, here is an overtised routine for an algebraic angles problem.
If students are tackling this, then they have already learnt that shapes with four sides are quadrilaterals, and that their interior angle sum is 360 degrees.
Then Atom 4 is simplifying by collecting like terms, which again they will have learnt already before this point.
And Atoms 5-7 these are all atoms in a chain for solving two-step equations, again something they must have learnt before coming to an angles problem like this one.
So, the only new atom, the only new thing to learn is this atom…
This is where most of the instructional time needs to go, and it’s not the first atom in the routine.
So, in the rest of this post we’ll look at what this looks like in practice, and how the atomic view makes it easy for us to help students solve relatively complex geometric problems. We’ll look at examples for trapezium area, shading regions defined by inequalities, solving simultaneous equations, and percentage calculations. We’ll see how process thinking and I do / We do locks us in with end-end processes, while by contrast the atomic approach offers two further benefits: teaching any atom, in any order, and developing deep mastery of each mathematically meaningful atom before chaining begins.
To start, what does this look like in practice to design instruction for Atom 3 above?
We can see by switching to the atomic view:
