MATHS ESSENTIALS


Try the mastery approach to improve a grasp of maths


By Dr Helen Drury Maths teaching across the country is being transformed by the mastery approach. Whereas traditional methods often focus on rules or procedures, mastery teaching emphasises students’ understanding of mathematical concepts. For teachers and support staff who are new to the mastery approach, adopting new approaches to teaching can sound daunting, but it needn’t be. Visual representations are a simple but powerful way to help your students understand mathematical concepts, rather than just ‘do’ maths. Using diagrams, pictures, manipulatives (physical objects that help people learn maths) and other types of representations, known as Concrete Pictorial Abstract, will help learners visualise concepts so that they can understand the most effective calculations to carry out. This approach will also facilitate reasoning and problem solving, and allow students to demonstrate proof.


Finite Ideas


It’s sometimes easier for students to get their heads round what a maths question is really asking them to do, or to work out, if words can be used in place of symbols. One of my favourites is replacing the multiplication sign (x) with the word ‘of’. So, 25% x 160, for example, becomes 25% of 160, which many stents n easer to eal t ncoran te to tr ts tactc  te are eer ln oer o to anle a ltlcaton sn can rea benets n te long term.


Try this page on the NCETM’s website for a flavour of what they offer teachers of GCSE re-sit maths goo.gl/vgCJ5a You need to register.


In the same vein, the line in the middle of a fraction can be thought of as meaning ‘out of’. This immediately creates a way of visualising what a fraction is sometimes representing, which the students might not have used before. Discussing the use of ‘of’ and ‘out of’ together is also a neat way of underlining


the inverse nature of multiplication and division, since ‘divided by’ is another way of interpreting what the line in a fraction is saying to us.


Steve McCormack is Communications Director, National Centre for Excellence in the Teaching of Mathematics (NCETM).


INTUITION ISSUE 31 • SPRING 2018 23 Here are three tips to get


you started: • Place manipulatives on every table. Dienes blocks, bead strings and multilink cubes can not only help make lessons practical, engaging and fun, but they also help learners understand abstract concepts.


• Use pictorial representations. These can be as simple as a number line to help with positive or negative integers or bar modelling for arithmetic, proportional reasoning or algebraic problems. Bar models are particularly useful in helping students make sense of word problems – great for helping exam technique.


• Try virtual representations. ICT- supported representations can aid understanding of graphs, variables, functions and the modelling process. If your students enjoy learning with the aid of ICT, maybe give this a try? The journey to mastery takes


time, so be patient when trying out this new approach. But most of all, have fun with it!


CREATING MATHS UNDERSTANDING By Judy Maguire


The old Chinese proverb states Tell me, I’ll forget Show me, I’ll remember Involve me, I’ll understand.


This is the basis of Edgar Dale’s Cone of Experience. It tells us that learners retain 90 per cent of information they are exposed to if they are involved in its practice, as opposed to 70 per cent of what they write or 20 per cent of what they hear. It was always thought that this


applied more to practical skills, but we know now that it is equally applicable to mathematical principles. Historically it was assumed that


Dr Helen Drury is executive director of the not-for-profit organisation, Mathematics Mastery, and author of a new book, How to Teach Mathematics for Mastery, published by Oxford University Press (OUP).


learners needed to be shown how to solve a problem before they could do it for themselves and that there was only one way of doing it. Judgements were then made about how well, or otherwise, they remembered the process and put it into practice for themselves. Learners who have already been


introduced to the basic principles need to be exposed to active approaches that enable them to explore the principles and understand them. They need to work out


ateatcal eas ro rst principles and discuss the meaning of what they have discovered. Involving them in the learning process is therefore the key. Using practices such as group


puzzle solving, card-matching activities and marking each other’s exam questions will involve your learners and help them understand. Try it and see for yourself!


Judy Maguire is the Education and rann onatons  eonal Specialist Lead for Maths in the South East.


Find out your specialist maths and English lead at goo.gl/MwLErY


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