Chaining
Bringing it all together
Podcast is AI generated, and will make mistakes. Interactive transcript available in the podcast post.
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Once two or more atoms from a cognitive routine have been communicated we can begin the process of chaining.
A chain is just two or more atoms completed one after the other.
And to chain, we simply ask students to complete one atom and then another immediately after it.
Ultimately, a cognitive routine is a chain of atoms.
A chain of atoms is a set of mathematically meaningful activities that can be executed one after another in sequence.
Individually, the atoms can be communicated in any order, but when presented as a sequence, they almost always have to progress in the same order, with no option to skip over atoms.
However, the whole chain does not have to be presented all at once.
For example, the full-chain view for expanding a pair of brackets above consists of three atoms – three transformations – that must be executed one after another.
But instead of working through all three steps in sequence, you might present students with this prompt.
This asks them to expand all brackets and then simplify. No need to complete atom 1 in the full chain.
Or you could present them with this prompt.
This now asks them to complete atom 1 in the full chain and then move on to atom 2… but go no further. It asks them to leave their response like this, in an unsimplified form.
Why would we do this?
Now that we know 100% of our students have mastered each atom in the chain, why not just ask them to complete all three atoms in the chain?
The answer is that when we chain, we run into one of the high-risk points in learning cognitive routines.
Chaining requires students to both recall to working memory each individual atom and…
