“We are usually convinced more easily by reasons we have found ourselves than by those which have occurred to others.” Pascal, Pensées (1670)
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. As the pupils had come up with the ideas themselves, they were forced to understand why methods work, not just how to use them. Over time, I developed my teaching to try to give this as many pupils as possible the chance to make the steps themselves. I named my blog ‘discovery maths’; I don’t think I knew that ‘discovery learning’ was a thing until I joined Twitter, 8 years into my career.
This led me to learn that this approach has come under significant criticism, notably from Daisy Christodoulou in Seven Myths about education, on Greg Ashman’s blog and more recently by the prolific and influencial Craig Barton.
Of course, it’s not appropriate in many situations (I much better understand Daisy’s objection, as she teaches English) and a balance needs to be struck. I am not advocating only or always using discovery approaches; my lessons still involve worked examples, structured practice and regular testing and so I decided to change the name of my blog.
However, I feel that if pupils never discover anything, they have never played the game of maths. How many adults do you know who say they hated maths because it was just about remembering methods off by heart and involved no creativity? So, I will continue to make some use of discovery in my classroom, particularly as a way of extending the most able pupils. I know that recreating theories that were developed over centuries is clearly not easy and so guidance is needed. Some of 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.
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 been stifled in a less open environment. For me, one of the great joys of teaching is seeing that young minds are so creative.