At the end of last year we published Improving Mathematics in Key Stages 2 and 3, a guidance report offering 8 practical, evidence-based recommendations that are relevant to teaching all pupils, but particularly to those struggling with their maths. Over 35,000 people have so far read it online.

Today we’ve published a supporting report that looks at the best available international research on teaching maths to children aged 9 – 14 (Key Stages 2 and 3) to find out what makes effective maths teaching.

This report highlights some areas of maths teaching – like feedback, collaborative learning, and different types of textbooks – that are backed up by good evidence, as well as some that aren’t.

One area where there is strong evidence – which we have highlighted here – is how calculators can be used to support learning. The basic message is this: taught well, calculators help rather than hinder provided pupils are taught mental methods alongside calculator and other methods.

Here we answer some of the most frequently asked questions about this finding…

Do calculators help or hinder learning?

We looked at the best available evidence on what makes good maths teaching and (contrary to what is sometimes supposed) we found that using calculators in maths lessons can improve pupils’ calculation and problem-solving skills.

How should calculators be used in lesson?

The report stresses that, for calculators to be helpful, teachers need to teach pupils how to use them in a thoughtful and considered way

Here are a couple of examples of how they can be used to help learning:

- No-one in the real world would think of calculating 4271.3 x 289.6 in their heads, but, BEFORE using the calculator, pupils should know that it’s roughly 4000 x 300, which is 400,000 x 3 which is 1,200,000. And then they should be able to spot that they’ve miskeyed and the calculator is wrong if it displays an answer of around 123,000.
- We know that highly numerate people know many ways to calculate mentally. Take 12 x 15; we know that’s 180 because it’s 10 x 15 plus two more lots of 15. But highly numerate people can also spot that it’s the same as 6 x 30 or that it’s the same as 12 x 1.5 multiplied by 10. A great classroom activity is to use the calculator to figure out different ways of calculating, then to challenge pupils to use them mentally, and eventually see whether they can use the method on similar problems to beat the calculator.

What about mental arithmetic? Shouldn’t pupils know their times tables too?

Yes, pupils should know and be able to use their number facts. The evidence tells us that pupils need to have good mental arithmetic skills – as the examples above illustrate – so that they’re able to recall number facts efficiently and quickly. Those who are unable to do this may have difficulty with harder maths later in school.

Should teachers let their pupils use calculators in every lesson?

That can depend on how old the pupils are. The evidence suggests primary school pupils should use calculators regularly, but not every day. Secondary school students should have more frequent access to calculators so that they’re able to make decisions about when, and when not, to use them.

So, were ministers right to ban calculators for Key Stage 2 SATs?

Our review finds that while they can boost learning, it is important that calculators are used in a careful way. Generally, pupils don’t take dictionaries into English spelling tests but they should know how to use them, and doing so can improve their fluency. The same principle can be applied to calculators.

What else does today’s report tell us about learning maths?

We looked at the evidence behind many different areas of maths teaching. We’re particularly looking at what we can do to boost learning for low-attaining pupils, who are disproportionately drawn from poorer homes and who are more likely to leave school without attaining the expected level in maths.

We also found:

- maths homework tends to benefit older pupils, but not those in primary school;
- teacher subject knowledge is crucial for realising the potential of maths resources and interventions to raise attainment;
- high-quality feedback tends to have a large effect on learning, but it should be used sparingly and mainly for more complex tasks.

This report – and the EEF’s guidance on maths teaching – is about making sure that all young people, regardless of background, have access to great maths teaching in primary and secondary school.

* Our thanks to two of the report’s authors, Prof. Jeremy Hodgen (University College London) and Dr Colin Foster (University of Leicester), for the examples used in this blog.