Mastery: HOW and WHY

My last week’s blog focused on learning as fun! If we are to encourage school children of all ages and abilities to take learning further independently – we must change the way we do it. Yes – we want children to master learning – but HOW?

This is what I would say to a clever Year 9 pupil in a top set – aiming to stay there and achieve at the highest point possible. Mastery is about:
– Diving down to explore the inner workings of topics
– Problem solving – using logical deduction based on previous learning
– Making connections between topics and concepts
– Identifying short cuts – for speed, flexibility and efficiency
– Tools and rules – for keeping on the right track.

I would offer the same advice for any subject but let’s see how some of these apply to maths – because if you have read my previous blogs, you will know that I love maths and find it fun. Let’s explore a mathematical problem – to place in descending order: 1/3, 3/8 and 7/12. A pupil might immediately start to find the common denominator – which is the correct (taught) method for sequencing fractions. But, wait a moment! Look at these particular examples. In less than a minute, the logical deducer notices that 7/12 is more than half, while the others are not, that 1/3 equates to 3/9 (same numerator as 3/8) – and knows that ninths are smaller than eighths. We (and the logical deducer) see immediately the descending order as: 7/12, 3/8, 1/3 – saving time in exams by increasing speed. Thus, identifying short cuts pays off in some types of problems.

Let’s think about algebra. We have to, as it looms large at Year 9 and beyond and often causes much frustration – as young people meet difficult linear equations. Problem: solve the following equation by finding K :

2(K + 1) = 3K – 41. This becomes: 2K + 2 = 3K – 41. This becomes: 2K – 3K = -41 -2.
This then becomes: -K = -43 which then becomes: K = 43. Proving this by substituting 43 for K in the original equation, both sides equal 88. So we know it works.

Okay – for pupils struggling with these types of problems, where is the mastery? The HOW and WHY? The logical deducer knows that the brackets must be expanded first (got rid of) because of BIDMAS (brackets, indices, division, multiplication, addition, subtraction). Tools and rules have also come into play, for example, knowing that when we move a value to the other side of an equation – the sign changes to its inverse – hence, 3K and +2 both change to minus. The basic idea is to isolate letters and numbers onto opposite sides – to enable simplifying. If in doubt, pupils should at least stare at it for a while and try to see deep down, inside the problem. It really works! Eureka! Like switching on the Blackpool Illuminations inside our brains.

Let’s be honest, though. Only a small proportion of Year 9 pupils are in that top set. What about those pupils who aspire to be up there – but struggle to achieve average? The advice is basically the same. One thing that will NEVER work is for pupils to simply try to remember taught methods, without understanding at the heart. Memories fail when they have nothing to attach themselves to inside our brains. When memories fail – without that logical deduction that comes from some level of understanding – staring at the problem to tease out its meaning will simply not work. Frustration. Maths is no longer fun, or even interesting – it’s a total switch off – pulling the plug on those illuminations – staring into perpetual darkness.

I’m not finished with mastery yet because many more children need to reach it. The National Curriculum aims towards it for as many pupils who CAN. So parents, help your child to achieve mastery. Start by finding out WHAT your child learns and HOW. My books will help – Supporting Children at the various Key Stages by Sylvia Edwards are available from Lulu in printed form, and from Amazon, in printed form and as ebooks.

Next week – let’s explore mastery in a different way – is mastering writing based solely on grammar? Mmmmm?

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