The need for a problem solving approach in school mathematics

I have recently run some training for a group of Mathematics Subject Leaders on problem solving. I looked at the Nrich site that has so many wonderful problems that cover mathematical enquiry from the earliest investigations up to quite sophisticated problems for A Level students.

As a non-mathematician myself I found myself excited by the prospect of investigating many of these problems. Sometimes the answers were fairly obvious, often they involved many possible answers and on some occasions they were as near intractable to me as it was possible to be. Thank goodness the site includes solutions sent in by students from all over the planet who have worked out some wonderful solutions to the problems.

In my training we talked about the useful things that problem solving gave people. High on the list were that they required tenacity to stick with things even when they were wrong, that they allowed you to learn from mistakes and that they were often opportunities to work together in a collaborative way that led to more effective answers to  the problem.

The video above is like a detective story.It is the search  for a solution to a problem that had baffled mathematicians for centuries and related to  Fermat’s Last Theorem that  states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. Many years ago a young boy who lived in Cambridge, U.K. found out about the theorem and it set him on a life’s journey to solve it. The video explains how he was able to do just that, through tenacity, the help of others ands by learning from many many mistakes.

Having just re-read a chapter from Jo Boaler’s wonderful book “The Elephant In The Classroom” where she talks about making mathematics real to schoolchildren and not the artificial, dry and ultimately quite boring subject that it turns out to be for so many of them, I just wish that all trainee teachers that were going to teach mathematics in any way could see this video.

I do not suppose that we will have all our children solving Fermat’s last theorem but we can enthuse them to understand just how powerful mathematics can be and give them real life skills in working together, learning from each other, learning from mistakes and persevering even when it all looks impossible.

My colleagues left the training saying they had enjoyed the problems and looking forward to exploring some of the sites that I had suggested they look up. I hope that they will really make the effort to make problem solving a key part of their children’s mathematical experience. They will help them to develop key 21st century skills and maybe, one day, one of them may just be like Andrew Wiles and solve a really big problem… you never know!


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