The introduction of the times tables test has reignited the debate about the optimum way to teach children basic multiplication. Learning by rote is the traditional approach, but that might not be the best solution, academics tell Grainne Hallahan
What is the best way to teach times tables? To answer that, we may want to look at the work of the Babylonians. Around 4,000 years ago, they were using multiplication grids regularly, so must have had an in-depth understanding of teaching such a skill.
Unfortunately, they didn’t leave us much in the way of a manual on how best to use their method – or any other – to teach multiples.
Which is a shame, because such information might have prevented some long-standing arguments. Times tables are widely viewed as one of the foundation stones of primary maths, and since their assessment through a standardised test began in 2018, the best way of teaching them has been even more of a topic of conversation in staffrooms.
The multiplication tables check (MTC) aims to determine whether pupils can recall their two to 12 times tables “fluently”. The 25-question test for nine-year-olds gives students six seconds to respond with an answer to each question. Despite the fact that the test won’t be going ahead this year, it continues to influence how this element of primary maths is taught – with rote learning approaches favoured by many as the simplest way to prepare students for those 25 questions.
But are the approaches that the test inspires really the best way to ensure that all pupils have secure knowledge in this area? According to Lorna Earle, senior lecturer in maths education at the University of Chichester, the picture is complicated.
“Testing [of this nature] establishes whether a child can or can’t give a certain fact within a certain time frame, yet assesses nothing about the connected nature of their knowledge,” she says.
Jo Boaler, who teaches maths graduates at Stanford Graduate School of Education, agrees. In 2015, she published the paper Fluency without fear: research evidence on the best ways to learn math facts, and says that teaching of multiplication tables should focus less on automatic recall and more on building connections.
“Blind memorisation is the weakest form of memory,” says Boaler. “When the brain tries to access that memory, it doesn’t have a lot to go on, whereas if you teach math facts as patterns and visuals, the brain is much more able to think about that math fact.”
While children do need to know what Boaler calls “math facts”, Earle argues that it is also important that they develop good maths sense. “Children need to understand the links and relationship between the sums, not just be able to recite 144 facts,” she says.
By placing too much emphasis on children’s ability to recall those 144 facts, she continues, we inflate the status of times tables, which can lead children to interpret that they are “good” or “bad” at maths based purely on how quickly they can recall the answer to 4 x 6.
But actually, Earle argues, whether someone knows their times tables off by heart isn’t a very good indicator of their overall mathematical ability because the speedy recall of math facts and understanding the meaning behind them are two different things.
“A better indicator of maths skills is confidence and assuredness in their knowledge,” she says.
So, does that mean that teachers are wasting their time teaching pupils to recall times tables from memory? Mahnaz Siddiqui, a senior lecturer in initial teacher education at Liverpool John Moores University and a maths specialist, says that it is not quite that simple. Learning by rote does have its benefits, and memorising the times tables can help to make children more efficient mathematicians, she explains.
“If a child has memorised the multiplication tables, it could be argued that they have freed up working memory that can be replaced by new facts and information. [This then] speeds up the problem-solving process,” she says.
In other words, if children aren’t able to recall their times tables automatically, they will need to take the additional step of multiplying out the numbers in the process of solving a problem.
However, learning times tables by rote devoid of context is also unhelpful, Siddiqui notes. “Long term, teaching for conceptual and relational understanding has more benefits than relying on memory for recall and accuracy,” she says. “If a child needs to calculate 7 x 9 but has forgotten the answer or needs to check for accuracy, drawing on other known facts like 7 x 10 can help.
“Even better is if a child has memorised the facts, and can also retrieve and explain other ways of solving a multiplication question.”
So, there needs to be balance in any approach we take, Siddiqui argues. Her view is supported by research from the Education Endowment Foundation (EEF). In 2019, it published a report called Improving Times Table Fluency. This was based on a trial the EEF conducted with 876 Year 4 children, who were taught through a mixture of “conceptual and procedural activities” for 12 weeks, and were then tested to see which method had the most success.
The report found that “no one balance of practice activities was more effective than another” and concluded that “times tables may be best taught by using a balanced approach – teaching both the concepts behind them and practising them in a range of ways with low-stakes testing”.
What might such a balanced approach to teaching times tables look like in practice? The academics say that some of the more traditional rote-learning methods, such as singing and chanting, shouldn’t be ditched just yet, providing they are supplemented with approaches that aim to develop greater understanding.
“Rote learning the times tables is often helped by songs and makes the maths facts more memorable,” says Earle. But such approaches can’t be used in isolation, she adds.
Boaler agrees that rote-learning approaches will need to be supported with the explicit teaching of strategies that will allow pupils to build on their knowledge going forwards.
“Research has shown that kids who learn strategies and kids who blindly memorise have the same speed. But the ones who are taught strategies performed better in a wider range of situations,” she explains.
As for what those strategies might look like, she gives the example of doubling and halving. When asked to solve 18 x 5, even a child who can confidently recall the first 12 times tables might struggle to respond. But if that child has been taught strategies to solve problems like this, they will have the tools to break the question down and find the answer by doing 9 x 5 and then doubling it, or 18 x 10 and then halving it.
The foundations for these strategic approaches can be laid early, Siddiqui points out – well before children even encounter times tables. “The early years [are] a great place for children to start to develop their mathematical thinking and pattern spotting,” she says. “Some children, I think, pattern spot more naturally, and others can be encouraged and nurtured to be curious about patterns. That is where a teacher might need to lead the exploration and model investigating in a curious and questioning way.”
Showing learners in the early years foundation stage pictorial representations of abstract number calculations is a good starting point, she adds.
But whichever methods you are using to teach times tables, academics agree that it is crucial for teachers to be aware of the risks of contributing to maths anxiety and to do what they can to reduce this. That means avoiding unnecessary time pressures in the classroom as far as possible, regardless of the time limits that will be placed on children during the multiplication tables check.
Shannen Doherty, a Year 2 teacher and maths lead, agrees. Just because the MTC involves a time limit doesn’t mean that teachers should base all times tables practice around that, she says.
“I don’t think the timed aspect of the test is necessarily a bad thing, but I don’t think it needs to be shared with the children,” she says. “There’s no need to go in on day one and say ‘you’ve only got six seconds to answer’.”
Ultimately, taking an approach that focuses not on speed of recall but on depth of understanding will be of most use to pupils in the long term, confirms Earle.
“Timed times table testing causes anxiety,” she says, “But if you remove the timed element, then it becomes a more useful activity.”
That way, she says, you “take the emphasis off speed and on to exploration and valuing deeper learning”.
Grainne Hallahan is senior content writer at Tes
This article originally appeared in the 9 April 2021 issue under the headline “Tes focus on...Times tables”