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“Mastery” of Mathematics

December 11th, 2014 (by Nicky Bishop)

The new National Curriculum for Maths is built upon the concept of Mastery. The D of E notes that countries with the highest attainment in maths use a mastery approach to teaching mathematics. So what is it?

“Mastery” is a compound of “deep understanding of concepts” and “procedural fluency”. It’s clear to me, as a tutor of many children struggling with maths, that conceptual understanding is absolutely vital to making progress.

For example, children can be taught how to calculate fractions of a given quantity, but without understanding they quickly forget how to do this, and are completely stuck if they meet a type of problem they haven’t dealt with before. Without understanding they won’t be able to apply the same technique to help them calculate percentages of a given quantity. And without understanding they won’t be able to work from a specified percentage or fraction back to the original quantity. As D of E puts it, “conceptual understanding is essential to enable connections to be made between mathematical ideas.”

Developing understanding in school children requires teachers who themselves are totally secure with the concepts, and also have the skills to communicate those sometimes abstract ideas to young people. Many non-specialist primary teachers sadly do not have this confidence, and who are therefore unable to pass on understanding to their pupils. The result is that many of my pupils can carry out laborious processes (such as the grid method of multiplication or the chunking method of division) without the faintest clue how or why those methods work. No wonder they come unstuck later on and need specialist tutoring.

Of course, deep conceptual understanding is only half the story. Mastery also requires “procedural fluency”, in other words the ability to apply a calculation process quickly and accurately, again and again, to a range of different questions and problems.

The D of E knows there’s only one way to achieve this and that is through lots and lots of practice, with carefully designed variation built in. This means giving up a lot of lesson time for simply using new skills, trying them out on a variety of familiar and unfamiliar questions. And it means practice at home as well. Five minutes individual practice every day for a week will really help to consolidate a new procedure, and is more effective than 1 hour all at once.

The new National Curriculum for Maths recognises that conceptual understanding provides the foundations for progress. In practice, this means that steps must be carefully sequenced, and that children should not move on to the next step until they have mastered the earlier steps. It also means that teacher must provide quick feedback to pupils, along with high quality interventions to help all pupils keep pace with the rest of the class. And it means creating an environment in which pupils are unafraid to grapple with new mathematical challenges. Without these, specialist tutors will continue to be in demand.

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