Teach Secondary Issue 14.3

ABOUT THE AUTHOR Colin Foster (@colinfoster77) is a Reader in Mathematics Education in the Department of Mathematics Education at Loughborough University, and has written many books and articles for teachers; find out more at foster77.co.uk Howmastery helps The implication of all this is that we perhaps shouldn’t have been quite so satisfied with that initial 80%. If the 80% meant that our student didn’t understand, or couldn’t do one in five areas of content – well, maybe that’s not such a great result after all. Complacency over ‘sort of getting’ things may be setting students up for more serious problems further down the line. This doesn’t mean we need to take a discouraging, negative perspective on students’ achievements. We still want to celebrate students’ achievements, praise them for their efforts and celebrate success at all levels – but if we move on to newmaterial, assuming that what we’ve just covered is secure because students’ scores were mostly around 80%, then we risk doing them a disservice. Spending the extra time needed to ensure real mastery – say, 95%– can make a huge difference. A 95% success rate over three successive areas of content, each completely dependent on the previous one, will leave us with 86% success at the end. There’s an enormous difference between settling for 80% success and striving for 95%. Cumulative subjects Granted, not all subjects are as hierarchical as mathematics; some may be more cumulative. If I had gaps inmy knowledge about the Tudors, for example, that wouldn’t hamper my learning aroundWWII. But it’s still true that an historian who makes false statements around a fifth of the time; an engineer who has seen a fifth of their buildings fall down; or a doctor who has presided over 20% of their patients dying unnecessarily isn’t exactly ideal . Being 80% right isn’t actually that good in any real-life situation where knowledge genuinely matters. We wouldn’t be happy with that success rate for any professional we’ve paid to deliver a certain level of service. We have to avoid seeing school as a kind of preparation for a pub quiz. You can guess your way through a multiple choice pub quiz without knowing all that much of the material and still do reasonably well – or even win, given that everyone else is in the same boat. And after all, it’s just a bit of fun... When preparing students for life, we should want to aim considerably higher than being right 80% of the time. We want students to know some things for sure – but also know that, like all of us, there are many more things that they don’t yet know, which they’ll need to look up or go out and discover for themselves. Knowing what you don’t know is an essential life skill. When tomove on Getting 80% on a prerequisite knowledge check may mean that you seriously need to review the content before moving on. Very often, the reason that students can’t do one thing is that they don’t know some other thing that they’re supposed to have encountered previously. They can only work with what they have available, within the limitations of whatever existing skills and knowledge they have at the time. ‘Mastery’ is a word that’s bandied about quite a lot. It takes longer to aim for mastery before moving on, but doing so is more satisfying for students because they feel that they really know something. This then raises students’ levels of self-confidence to where they should be, and lets them get used to being right most of the time – except in situations where they know that they don’t know the answer, and thus need to check. Because we don’t want to turn out students who simply coast through life by bluffing and hoping for the best, and whose utterances need constant fact-checking by others. “Being80%right isn’t actually that good inany real-life situationwhere knowledge genuinelymatters” 23 teachwire.net/secondary P E D A G O G Y