“We are usually convinced more easily by reasons we have found ourselves than by those which have occurred to others.” Pascal, Pensées (1670)
Ten years of teaching has led me to believe that pupils are much more likely to understand ideas which they have created themselves.
I was lucky to start my career with two outstanding mentors, Robert Wilne and Dan Abramson, from whom many of my resources originate. They insisted that pupils should do every bit of maths that you write on the board, as both a tool for ensuring focus and a method of assessment.
The more I read, from Jo Boaler’s inspiring Elephant in the classroom to hearing Dan Meyer’s TED talk convinced me of the merits of problem-based learning. I started to teach more and more “from the floor” rather than “from the front”, noticing a significant improvement in pupil motivation. With this mindset, a standard maths curriculum contains huge scope for investigation and problem solving as approaches to introducing ideas: I rarely stray far from the curriculum even with the highest-attaining pupils.
Discovery learning has come under some criticism in recent years, notably from Daisy Christodoulou in Seven Myths about education and on Greg Ashman’s blog. Of course it’s not appropriate in many situations and a balance needs to be struck, but the logical structure of mathematics lends itself particularly well to discovery. I also feel that if pupils never discover anything, they have never played the game of maths, so can they really understand what maths is about?
That said, recreating theories that were developed over centuries is clearly not easy and so guidance is needed. The resources I share on this blog aim to provide the structure required for pupils to create some of the great ideas in mathematics for themselves and experience the joy of discovery.
Through using this approach I have seen so many amazing ideas and approaches from students that I would never have thought of myself and may have stifled in a less open environment. One of the great joy’s of teaching is seeing that young minds are so creative.