Mastery in Practice

This month, our Mathematics Consultant Caroline Clissold explains what mastery means in practice. 

Since the visit made by a group of teachers from the Maths Hub programme to schools in Shanghai and return visits from teachers in Shanghai in November of last year and February/March of this year, we have learned a lot about teaching mathematics in order that children can master each concept that they are taught. You might like to read this blog written by the director of NCETM or the NCETM page on teaching for mastery.

So, just as a reminder, what is mastery? If you drive a car, imagine the process you went through…

  • The very first drive, lacking the knowledge of what to do to get moving
  • The practice, gaining confidence that you are able to drive
  • The driving test, fairly competent but maybe not fully confident
  • A few years on, it’s automatic, you don’t have to think about how to change gears or use the brake
  • Later still, you could teach someone else how to drive

However not all of us know exactly how the car actually works!

Learning mathematical concepts is similar but it also involves knowing how and why it all works. It involves deep and sustainable learning, the ability to build on something already mastered and the ability to reason about a concept and make connections to other concepts.

Mastery is a continuum… mastery at a particular point of time that is sufficient mastery for that stage of learning and then built on at a later stage.

Here’s what it means in practice, and some points to consider when designing a mastery curriculum.

  • There is an expectation that all pupils are capable of achieving high standards through whole class teaching. This has implications for class groupings. These days the view is that mixed attainment groupings work best. How do you group your class? We often have preconceived ideas about which children have more or less potential. We need to think carefully about:
    • How to support children who find a concept difficult
    • How to challenge children who find it more accessible
    • Observing and questioning the children during the lesson
    • Making generalised assumptions about overall ability
  • Differentiation is achieved by emphasising deep knowledge and through individual support and intervention. The children need to be enabled to access what is being taught. How are interventions run at your school? Are they recapping, rehearsing or learning what was taught in the lesson or doing something else? Current thinking recommends that interventions work on what was taught in the lesson.
  • Questioning and scaffolding should vary and misconceptions should be dealt with immediately.
  • Fluency needs to be developed. This comes from deep knowledge and practice. The ability to recall facts and manipulate them to work out other facts is important.

Practice makes perfect - so we need to spend longer on key concepts. We need to give the children the chance to practice, but this practice needs to be intelligent. Intelligent practice involves:

  • Basic (bare or decontextualised) practice of the concept taught
  • Practice within different contexts, for example in length, mass, capacity, volume, area, perimeter, money and time
  • Practice which gives opportunities to develop fluency
  • Extended practice which goes deeper… and deeper
  • Practice to spot relationships and make connections
  • Practice to deepen conceptual understanding
  • Practice through problem solving, the children should have different problems to solve, higher attainers need to be given complex problems which deepen their knowledge of the same content.

 

Some things to think about! Get back to us if you have any thoughts.

 

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Assessment, CPD, English and Literacy, Grammar, Spelling and Punctuation, Mathematical Vocabulary eBook, Mathematics, Pupil Premium, Reading and Ebooks, Rising Stars Mathematics

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