Maths teaching in Ontario has featured regularly on this blog over the years. People used to point to it as an example of good practice and yet, in recent years, Ontario’s scores on standardised assessments such as the Programme for International Student Assessment (PISA) have declined.
I have not taught maths in Ontario, but it does appear to represent a large-scale implementation of ‘fuzzy maths’. I use this term because the name used by proponents constantly shifts. To some, it is ‘reform maths’, to others it is ‘constructivist’. However, if you go around calling it ‘constructivist’ then someone else is likely to appear and inform you that constructivism is a theory of learning and not a teaching method.
However, there are a few essential points. Fuzzy maths is not a fully explicit teaching approach. No matter how scaffolded or guided it is, students are still required to figure some things out for themselves. This is the key pivot point away from explicit teaching, because the latter tends to over-explain and re-explain concepts. As such, fuzzy maths is subject to the the criticism that it overloads working memory. Fuzzy maths is perhaps epitomised by the old strapline to Dan Meyer’s maths teaching blog, “less helpful”, although this seems to have disappeared in recent times.
Fuzzy Maths proponents take relatively simple ideas and, through the application of much beard-stroking, turn them into pseudo-deep discussion points. Should we call a mistake a mistake? How do we know if students really understand the principle of equivalence, deeply? I mean, like really deeply, dude?
They also disdain what they would characterise as the rote learning of procedures and the memorisation of maths facts. Given that doing maths involves performing procedures and that knowledge of maths facts is helpful when performing procedures, fuzzy maths represents a form of maths-in-denial. The effects on students should be fairly obvious and probably do account to some degree for Ontario’s decline.
It is therefore heartening to see a change of approach from Ontario’s government. We do not yet know the details, but the Toronto Sun is reporting that memorising times tables is back on the agenda, alongside training for teachers and a generally more traditional approach. There is also an emphasis on employability. Yes, students do need to be able to read a tape measure, but I wouldn’t want maths to be reduced to just the functional.
Unfortunately, the Toronto Star, and perhaps the politicians they have been talking to, have described this reform in the language of ‘back to basics‘. This may play well with many parents, but it makes it hard to bring academics along who can dismiss it as part of a politically conservative agenda. I understand why people use this term – they mean that we must not ignore the fundamentals. However, it also has the unfortunate connotation that teaching maths is basic when it most certainly is not.
No matter, gripes aside, it looks like Ontario’s fuzzy maths experiment has finally come to a welcome end.