Resources for Problem Solving at GCSE - Michael Anderson 

Lucy TyremanBefore this workshop, I firmly believed that you could not teach problem solving. 
When we teach students the maths they need to solve problems, we can give them a nice rule or algorithm to follow that will get them the right answer every time, though of course we make sure they understand why the rule works. But this doesn’t work for problem solving. Problem solving is all in the method, not the answer. Although there may be a right answer, there is no right way of getting there. As long as the maths and logic is sound, anything goes. 

Despite having much the same opinion after the workshop, it has enlightened me to the ways in which we as teachers can develop other skills required of students when they are problem solving, particularly planning a strategy.

One hurdle facing students when problem solving is the lack of a structured method given to them. Students become used to being taught that there is one way of doing maths and following the steps they know. When this is taken away it can be a shock. However, if there’s anything I took away from this workshop it’s that dots can solve it.

20 minutes of talking about 24 dots on a page. It seems ridiculous; how could you spend so long talking about some dots? Yet, I really think this could be a crucial tool when introducing students to the many ways of solving problems. Counting dots, at its surface, is a simple task. However, when you stop and think about what you’re doing when you count and compare your method with that of other people it opens a discussion into the many ways one can perform such a simple task.

My table alone had four different ways of counting: snaking a path and counting individually, seeing it as a grid with dots missing, and grouping in two different ways. When the conversation opened to the whole group, there were even more ways shared. I found myself thinking, if there are so many ways to go about counting some dots, imagine the number ways there could be to solve a more complex problem.

Starting a problem-solving lesson with an activity like this could really help students get over the idea that there is only one way to do maths, and just because their neighbour does it differently doesn’t mean either of them are wrong.

Overall, the discussions we had during the workshop have made me see that although it may not be possible to teach problem-solving directly, as teachers we can facilitate the development of skills needed to become good problem-solvers. By getting students to slow down and think about the strategy they want to use, and realising they are a few they could try, we begin to foster the patience and planning they will need to be successful in this discipline.
By Lucy Tyreman