It depend on context. It's more of a judgement call based on experience rather than a process I follow.
For example, for an especially able class, I might just go straight for the full chain.
When one teacher I worked with pointed out that his kids were struggling with the rearranging atom in basic trig function questions where he gave them:
- the triangle with sides labelled
- the trig function to use
So all they had to do was:
- identify the known values
- substitute
- rearrange
and stop there - but 50% were still getting the rearranging wrong, despite getting it right when it was treated as a single atom, my suggestion was to also identify the values to substitute for them, so all they had to do was:
- substitute
- rearrange
Which then worked for them (and later that chain could be extended. This was a bottom set Year 9 class.)
So I just choose what seems right - a meaningful start and end point that I think the class can cope with, and then adjust based on the feedback from their responses.
I also try to avoid things like calculation steps quite a lot, so that we can get loads more practice with the more meaningful atoms that reveal mathematical structures, like identifying the values needed, retrieving form memory any formulae needed, setting up equations, perhaps working the equations, but not necessarily including much trivial arithmetic, which is often slow to process and not directly relevant to what we're learning. I just make sure to do 'a few chains' with the the arithmetic included to be sure they can do it - and then might practice that more rigorously if actually they consistently make errors.
Brilliant post! One question: how do you decide which atoms to include in the sub-chain, i.e. where it starts and where it ends?
Thanks Henrik.
It depend on context. It's more of a judgement call based on experience rather than a process I follow.
For example, for an especially able class, I might just go straight for the full chain.
When one teacher I worked with pointed out that his kids were struggling with the rearranging atom in basic trig function questions where he gave them:
- the triangle with sides labelled
- the trig function to use
So all they had to do was:
- identify the known values
- substitute
- rearrange
and stop there - but 50% were still getting the rearranging wrong, despite getting it right when it was treated as a single atom, my suggestion was to also identify the values to substitute for them, so all they had to do was:
- substitute
- rearrange
Which then worked for them (and later that chain could be extended. This was a bottom set Year 9 class.)
So I just choose what seems right - a meaningful start and end point that I think the class can cope with, and then adjust based on the feedback from their responses.
I also try to avoid things like calculation steps quite a lot, so that we can get loads more practice with the more meaningful atoms that reveal mathematical structures, like identifying the values needed, retrieving form memory any formulae needed, setting up equations, perhaps working the equations, but not necessarily including much trivial arithmetic, which is often slow to process and not directly relevant to what we're learning. I just make sure to do 'a few chains' with the the arithmetic included to be sure they can do it - and then might practice that more rigorously if actually they consistently make errors.
Am I making much sense?
Thank you, that was very enlightening. Thank you for responding!