A first for me in my new school is the concept of a taster visit – a pupil comes along to school for the day to help decide if they want to join the school. It’s interesting to see how children from other schools approach problems and a recent visit made me realise how important a particular feature of my Scheme of Work is… Forming Equations.
The taster-day student was tackling the problem above. He was doing the whole thing on his calculator; I could see that he had some good ideas, but there were just too many steps. I encouraged him to use pen and paper but he just started writing down the steps that he was typing into his calculator.
The problem: He couldn’t write down the sine or cosine rule, substitute and solve the resulting equation. This skill is crucial when you get to a level (which everyone does eventually) where you can’t solve problems in your head.
I wanted to shout at him… Form a Flippin’ Equation! Why do students struggle to do so? I feel that it’s because they haven’t been trained to.
My solution, as so often: Follow the Highgate way. Teach forming equations as an independent topic, at least once per year, and insist that students employ the strategy within other topics at every possible opportunity.
To find out more about the first part of this approach, see my resources on forming equations.
The second part is to reinforce this when teaching other topics. I think the first place I’d usually do this is when teaching students about circles, although this could also be applied to simpler shapes too. Perhaps another argument for teaching more number and algebra before shape?
For example, I would insist that pupils solve the following circle problem like this:
I do sometimes encounter some resistance to this level of detail – inevitably some students just want to do 12 divided by pi and write down the answer. In order to head this off, I ask students to solve the following problem before I teach this:
This is a difficult problem, which students at this level can’t normally solve, and this helps to provide the motivation to practise this strategy.
Moving forward, students can apply the same approach when applying Pythagoras’ Theorem:
If you continue to insist that pupils write their solutions like this whenever the opportunity arises, you’ll give them a powerful tool which will enable them to solve difficult problems.
Maybe I’m wrong. Maybe all schools teach this already. But based on pupils who move into my classes, I am doubtful.
I will leave you with the work of Cora, in the first term of year 10. I’ve taught her for 2 years and so she has been through the Highgate-style forming-and-solving training. I was so impressed with how she made such light work of this problem, which normally stumps even very capable students.
