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“Those who suggest scrapping rote learning are missing something important”

The choice of whether to focus on memorisation or understanding when it comes to teaching maths is a false one, argues Jemma Sherwood – students ultimately need both…

Jemma Sherwood
by Jemma Sherwood
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It’s a common error that many people make – setting up the ‘rote memorisation of mathematical facts’ in opposition to ‘understanding the underlying concepts’, as if the two are mutually exclusive.

Those who present this dichotomy suggest that maths teachers should focus their efforts on developing students’ conceptual understanding in order to help them to learn the content more deeply – often while using the word ‘rote’ pejoratively.

One of the areas in which these arguments are presented most strongly is with multiplication tables. Stanford University’s Jo Boaler last year went so far as to suggest that children suffer from ‘maths anxiety’, specifically because of teachers who focus on rote learning over understanding.

A false dichotomy

The problem is that this dichotomy is a false one. It is extremely important to have a strong number sense; to know, for instance, that to calculate 6 x 8 we could find 3 x 8 then double it, or 6 x 4 then double it. But how much easier and quicker it is if we just know that 6 x 8 is 48!

This is where those who suggest scrapping rote learning are missing something important. It is perfectly possible to teach number sense – to give students strategies for complex calculations – and to also expect them to learn certain facts to quick recall and fluency. It should be the aim of every maths teacher to do both of these things.

Research into long-term and working memory is beginning to gain traction in the education sphere. Many teachers are now becoming more aware of the fact that our working memory (the part of our brain we use to think about something in the here and now) is very limited and can quickly become overloaded. To reduce the load on our working memory and free it up to do more, we need to have as much as we can stored in our long-term memory.

For instance, if we want to factorise the quadratic x² + 2x – 63, the task becomes significantly easier if we can quickly spot the pair of numbers with a sum of 2 and a product of -63. If, however, we have poor recall of the 9 or 7 times table, our working memory will be taken up with finding the correct numbers, rather than learning how to factorise the quadratic and thinking about why the method works.

In this example, and many others, one of the keys to conceptual understanding is the instant recall of number facts.

Gradgrind be gone

Rote learning doesn’t have to be Gradgrindian or fear-inducing. Chanting, low-stakes testing, regular whole-class repetition – even singing – can be a staple of both secondary and primary maths classrooms, and should be until all students know their times tables.

With quick recall of times tables facts, moving onto things like simplifying fractions, factorising linear and quadratic expressions or resolving problems with ratio and proportion becomes significantly easier. Limited working memory is freed up to focus solely on the new problem at hand. From my experience, I would even argue that the best number sense is achieved when students know maths facts like number bonds and times tables by heart, because they can then work with that knowledge – which is a whole lot easier than working without it.

I therefore tentatively welcome the recently announced focus on mastery at primary. I am hopeful that students will be given significant time to develop strong number sense concurrently with memorisation of the number facts that underlie a successful grasp of future mathematical concepts. I am hopeful that they will become fluent in written methods of multiplication (and the other operations), so that when presented with more complex problems they do not find themselves up against unnecessary barriers.

Above all, I am hopeful that mathematics will no longer be a cause of mass anxiety, with our students instead leaving primary school fluent in the essential building blocks, and leaving secondary as able and confident mathematicians.

Jemma Sherwood is head of mathematics at Haybridge High School and Sixth Form, an SLE and previously a finalist for Teacher of the Year in a Secondary School at the Pearson Teaching Awards; she blogs at and tweets as @jemmaths

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