Teach Secondary Issue 14.3

I t’s easy to become confused as to what successful learning in school should look like. Let’s suppose a child comes home from school one day and tells their carer, “ I got 80% in a maths test today! ” According to many people’s thinking, this would place them in a category of mathematical genius. The person at home is likely to say, “ Well done, that’s great – let’s celebrate! ” But before they crack open the chocolate biscuits, we should think about this scenario a little more carefully. Let’s suppose that this test result wasn’t a fluke. Let’s imagine that they consistently obtainmarks of around 80% on their mathematics tests, week after week. A bright mathematical future surely awaits them, no? Maybe – but maybe not. What I’m going to discuss here isn’t specific to mathematics. It could just as easily apply to any other subject that’s hierarchical – where what you learn next week will be built upon what you’ve learnt today. Focusing on the gaps I’m going to adopt a ‘glass half empty’ perspective when considering this student’s success, by focusing on the 20% of content they didn’t get right. Those missed marks may have been an accumulation of little slips. Why mastery MATTERS A high level of success on a daily basis is necessary if we want students to achieve well in the long run, says Colin Foster Perhaps they related to content covered in class that the student missed, due to absence. Or it could have just been down to a tricky topic that none of the class really quite got, whereupon the teacher told them ‘ not to worry, ’ since they’d understood ‘ the majority of the topic ’. The problemhere is that if the next bit of learning depends on this bit being understood, then that missing 20%may set a ceiling of 80% on whatever the student goes on to learn next. With the best will in the world, the student might then not have much chance of getting more than 80% of the next topic right, if 20% of it depends on things they already didn’t make sense of in the first topic. Even if theymanage to maintain their achievements, theymight still end up with only 80%of 80%on their next assessment, amounting to a distinctly less impressive 64%. The sad thing about how these percentage changes accumulate is that ‘80% of 80% of 80%’ amounts to only 51%. By the time our student has covered three topics, they’ll be barely managing half the content. After 10 topics, that proportion drops to 11%. And that’s assuming the student is absolutely perfect , in the sense that they work hard at everything, and never forget anything that they’ve successfully learnt. Even if we assume that they’ll keep earning those 80% scores forever – which is highly optimistic – they’ll still end up down to 51% after just three topics. This might perhaps explain why so many students seem to begin a school year or unit of work quite successfully, before things start to trail off all too quickly. It can sometimes be less obvious that this is happening, however, due to switches in the content that’s being studied. For the sake of variety, school subjects will tend to move quite frequently between different areas of content. If our student’s 80%was earned after studying algebra, and the curriculum then suddenly shifts over to geometry, we might not pick up on the problem quite yet. But once we return to algebra, that’s when they’ll start to suffer for that missing 20%. “Complacencyover‘sort of getting’thingsmaybe setting students up formore serious problems furtherdown the line” 22 teachwire.net/secondary