My maths trainees have been teaching problem solving. These are the rules we have developed:
Rule #1: Don’t give your students problems that you haven’t taught them how to solve.
The pupils who solve the problem won’t have learnt much from it (see here). The pupils who don’t solve it have learnt nothing.
Rule #2: Show them exactly how you want them to solve it.
Don’t ask the class questions as you go – just do it as clearly and quickly as you can. We rehearse it first.
Rule #3 Pupils copy down the neat version on the board.
One of my trainee teachers convinced me that getting the learners to copy down the clear version is time well spent. Later, when the pupils got to solve their own versions of the problem, they all presented their working just at the teacher had done. There was no effort wasted on working out how to write it down (no extraneous load). It was marvelous.
Rule #4: Do a second version of the same problem together.
One modelled question won’t be enough. Solve a second example using the same strategy, but this time using Q+A or talk partners. It is a bridge to doing the problem independently.
Rule #5: Have many variations of the problem ready.
This is usually simple in maths – change a couple of numbers in the question or change the context slightly). They will need to use this strategy dozens of times.
Rule #6: Come back to similar problems over the coming weeks and months.
Like all knowledge, spaced practice is the key. If you want them to learn a method, plan to practice it over time.
Rule #7: Gradually change the context of the problem.
Each problem-solving strategy is suitable for many problems. The trick is matching the problem to the strategy. So pupils need to see the strategy used in as many situations as possible. If your initial question was about the number of feet in a field full of animals, change it to legs on tables, branches on trees, planets around stars, vertices on shapes. You can’t do too many.
The pupils get a real buzz from solving problems. Make sure all of them get the buzz, and not just the fastest two or three.
Many thanks to Jonathan, Lyndsay and Ryan.