By Brian Murray, co-author of Oxford Mathematics
At the start of trivia night I recently attended, the organisers requested that all participants’ smartphones should be switched off. This was not because the phones might cause a disturbance, but because those running the quiz could not trust us to resist the temptation to cheat.
In this, the smartphone era, we are seemingly only seconds away from being able to find the answer to any problem. Whether we want to translate a sentence into another language, find our way home or divide a restaurant bill equally between six, technology provides a quick and easy solution.
With the advent of the smartphone, some people have begun to question whether encouraging students to have an instant recall of basic mathematical facts is a waste of time and effort. The argument goes along the lines of Why would you want to bother learning your seven times table by heart when the answer is only a Google-search away?
We could ask, ‘Why bother to learn anything that requires recall – a foreign language, the words of a favourite song, or the answer to 9 x 7?’ The solution to all these is easily at hand without the need to tax our memories. The simple counter-argument is that it is useful, and even pleasurable, to have an instant recall of many things in our everyday lives. Recall is not a necessity, but it is a definite convenience and can also be a source of satisfaction.
Therefore, if someone questions whether the learning of basic facts, such as times tables, is necessary, the short answer is no. However, if we ask ourselves whetherthe learning of times tables is useful, the answer is a resounding YES.
Once, in a bakery, I asked for six croissants. They were $2.50 each. The server looked up from the till perplexed, saying that she was sorry but the calculator on the till wasn’t working. She reached for her smartphone to calculate the sum, proving that not only is the recall of maths facts useful, it can save us from potential embarrassment.
In the UK, the department charged with the regulation of educational standards, OFSTED, has no doubt about the importance of learning basic maths facts by heart. It has stated, as a matter of fact, that primary schools that fail to teach times tables by heart are condemning children to a lifetime of struggling with numbers.
The UK national curriculum now specifies that pupils should be taught to recall the multiplication tables up to 12 x 12 by the end of Year 4. To this end, national online testing of students’ ability to recall times tables facts is scheduled to begin in the UK in 2020, with individual schools being held to account for any deficiency that is revealed.
To some, this approach is reminiscent of the Dickensian era, when inspectors would visit schools, randomly demanding an immediate recall of multiplication facts from student after student. The argument that formal, online testing of times tables recall is putting too much pressure on young students may have merit. However, the fact remains that the instant recall of basic maths facts is, at the very least, a useful skill to have. (It is an entirely different matter for students who aim to work in a field that involves regular exposure to mathematics – who would suffer from a lack of recall of these basics.)
There is no doubt that in some situations it is far preferable to rely on technology. For example, there are not many jobs in which someone who has to multiply 984 x 47 would reach for a pen and paper. But imagine two people having to write down the answer to 9 x 7, with one having to arrive at the answer using their phone and the other their memory. The person who knew their seven times table would write ‘63’ in a flash and there is no doubt that the smartphone user would lose by a country mile.
One way to explain to students the advantage of learning their times tables is to use a floor sweeping analogy. It is possible to complete the job by getting down on hands and knees and picking up the pieces by hand, but why would anyone bother when it’s so much quicker and easier with a vacuum cleaner?
In maths, students who do not know the answer to 7 x 6, could draw 7 rows of 6 dots and count the dots to find the answer. Of course, it would be quicker to reach for a calculator and key in the problem, but even quicker still if we can instantly recall that 7 x 6 = 42. If we use the floor cleaning analogy, drawing an array is like picking up the pieces one by one, using a calculator would be the equivalent of using a brush and pan, and relying on instant recall would be like using a vacuum cleaner.
It’s also worth explaining to students who are not easily motivated that learning the times tables is like learning to swim or to ride a bike – once learned, it’s there for life. Students who say I can’t learn them – I already tried! probably need to be reminded that If you can learn the words of a song, or the names of the people in the class, you can learn your times tables – it may be less interesting, but it’s not more difficult.
I would assert that the ability to recall basic facts instantly, whether the order of the alphabet or times tables, is an integral part of our development as humans and to deny this part of their education to our students would do them a disservice. Electronically generated answers do play an important role in the modern world, but to suggest that reliance on technology is preferable to using our ability to recall basic facts is nonsense.