Perhaps controversial title, but bear with me.
The prompt for this post comes from this excellent blog post, combined with my marking of some year 9 half term tests. They are the lowest-ranked set who are currently doing the Higher syllabus.
They nearly all failed to pick up any marks on the following 5 mark estimation problems:
I taught lessons on rounding, estimation of multi step calculations that didn’t involve roots, estimating square roots; and some BIDMAS revision. Students did well during all these topics. I assumed that would be enough. It was not – with the sole exception of the highest attainer in the class, who was quick enough to put it all together.
If you haven’t already, read that excellent blog post I mentioned above. It’s exactly the same lesson. Without teaching precisely how to address such problems,
you have two kinds of pupil – the pupils who get it and the pupils who don’t. The pupils who get it feel clever; the pupils who don’t feel stupid. This is hugely damaging. It lulls the pupils who get it into a false sense of security (“I got it on my own because I’m smart”) and reinforces to the pupils who don’t get it that they never will (“I don’t get it because I’m stupid”).
Except, in my case, it’s a more serious application: my students didn’t perform as well as they or I hoped; they will be discouraged and demotivated; their relationship of maths will sour slightly.
Teach to the darn test. Or, in other words:
If we give the kids who don’t get it the algorithm, we give them the key to success. If we give the kids who do get it the algorithm, they get to practise and make it automatic. Tell the kids everything they need to know, and then give them lots of opportunities to practise. Only then will everybody be able to ‘solve the cube’.