Mastery – as flexibility

Last week’s non-fiction blog focused on thinking and problem- solving. I have just been editing my fifth book in the Parent Series: for parents of pupils at Key Stage 3; due hopefully for publication by April. The word that has jumped out at me is – flexibility. Without flexibility – thinking and problem-solving are anything but efficient. But where does flexibility with calculations come from and how does it emerge over time, through each stage of teaching and learning?

At Key Stage 1 young children are taught clear methods for calculating numbers at simple levels. From addition and subtraction, they move to multiplication and division. Over time, they practise and perfect their understanding of the four numerical rules. Gradually, fraction and decimal numbers are introduced into the mix, then percentages. As this happens, problem solving becomes more involved and the scope for flexibility becomes much broader.

From Key Stage 2, most children start to realise that there are multiple ways in which to solve problems. For example: they learn both the standard method and the grid method for multiplication, and develop these further into KS3. Most children start to recognise multiple ways of dealing with fractions, decimals and percentages (FDP). In fact, success with FDP problem-solving relies solely on recognising the interrelationships between these three areas and dealing with them in different ways.

Thinking about the best means to solve problems – in time-efficient ways, is what flexibility is all about. When time matters, such as in exams, flexibility is key to success. How does it emerge? Flexibility can emerge only through a deep and secure understanding of the reasons for particular methods. Take inverse, for example: working flexibly between the add/subtract and multiply/divide inverses depends on a thorough mastery of how and why these calculations work as they do. Back to mastery again. Too many children and young people merely accept methods for problem solving without interrogating the reasons behind the methods. Without the question WHY as part of the equation, flexibility with problem solving has no chance.

Rigidity is the opposite of flexibility. Rigid, single approaches to mathematical problem-solving limit the end goal of mastery. So, a message for all parents, encourage your young learner to know and use different methods to solve problems and to become confident with all of them. Flexibility evolves into mastery in maths.

Start by finding out WHAT your child learns and HOW. My books will help – Support Your Child with SEND (Book 1) and at successive Key Stages (Books 2 to 4), by Sylvia Edwards, are available from Lulu in printed form, and from Amazon, in printed form and ebooks. Visit my website:

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