What's the Problem?

By K. Clare, Lead Teacher of Mathematics

The new GCSE in mathematics that will be taken this year by our current Year 11 students is far more challenging than in previous years, with additional content and more emphasis on problem solving.

"A problem is something that you probably will not immediately see how to tackle or which once started will challenge your thinking. This means that at some point you are likely to get stuck and this is OK. In fact it is important that you get stuck so that we can talk about possible ways of getting unstuck" (source: nrich).

As part of their Subject Knowledge CPD and in order to prepare them for integrating problem solving activities in to their lessons, this year, I have been working with three SCITT students, Simon, David and David. Each week, they work collaboratively on a problem solving task that they can either use or adapt with one of their classes.

The following are some of problems that the SCITT students have attempted:

This problem is very concise in that you have to find the radius of the circle.

The problem could take minutes or hours to solve. It's certainly suitable to challenge bright GCSE level students, but with resilience all Higher Tier students could have a go at it. At first look, it's one of those "where on earth do I start questions" and our SCITT trainees initially went down the wrong route. However, with further discussion and the drawing in of a few lines, 'Eureka!' the problem was solved.

The second problem asks what fraction of the cylinder is the sphere. For our SCITT students this problem highlighted to them the need to learn the many maths formulae that are no longer given in the GCSE paper. This sort of problem would be demanding for many of our students as no measurements are given. It is a good example of a problem where many students would not know where to start. Fortunately, after a little struggle in remembering the formulae for the volume of a sphere, the trainees with a little algebraic manipulation were able to come up with the correct solution.

The final problem produced some interesting discussions between the trainees.

 

How many pairs of prime numbers add up to give 381?

 

They are so used to me giving them challenging problems that initially they thought the problem was more complicated than it was. The problem was certainly suitable for Year 7 students! However, after three or four minutes the lightbulb moment came and the problem was solved.

The trainees certainly value our weekly sessions and realise that not only do teachers require good knowledge of maths- they also need good knowledge of teaching maths.

If you would like to have a go at these three problems there is a prize for the first person with three correct solutions (maths teachers not included, although you can still have a go).