# “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…

by Jemma Sherwood
PrimarySecondary

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.