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At the time of writing, a video is doing the rounds of a Scottish lad, caught by his mum, getting Alexa to do his homework by him reading out loud some multiplication questions.
I wonder if future generations will look back and see the memorising of multiplication facts as being as obsolete as we now regard the teaching of using a slide rule?
But we are a long way from that, and although I think the testing that children are going to be subjected to is not far short of cruel, it is going to happen and we need to support pupils and reduce its stress.
So here are my top five tips for supporting learning multiplication facts.
Knowing that for every multiplication fact you know you also get one free reduces the load. Know 4 x 6 is 24, then 6 x 4 is 24.
The array is the best image for helping children, right from the start, get a sense of how and why multiplication is commutative.
An image of a four by six array is transformed into a six by four array simply by rotating it through 90 degrees.
While it is popular to show multiplication as jumps on a number line, it is not quite so obvious why four jumps of six should land on the same final number as six jumps of four.
Being confident in the ‘low hanging fruits’ of 2s, 10s, 5s and 4s facts provides a strong foundation for the remaining facts. Working on doubling is central to two times facts, and doubling twice gives you four times facts. Ten is easy, and halving helps ground the five times facts.
Pupils in Japan are explicitly taught to reverse multiplications calculations if the smaller number is second. Seven times four? Do not do that; do four times seven.
This has a double pay-off. Firstly, you are often going to end up with 2, 4, 5 or 3 as the first number – and they are easy (see tip 2).
Second, if you need to do some skip counting to get the answer, then that is going to be quicker with the smaller number first.
Seven times two means counting “two, four, six, eight, ten, twelve, fourteen”. But two times seven, hey, it is just seven, fourteen.
The astute reader may have noticed that I have not used the words ‘times tables’ so far. That is because I am not convinced that chanting tables is the best way of getting to know your multiplication facts.
I would much rather a child knew that, say, four times nine is 18 (double nine), 36 (double again), than have to chant through the four times table.
But if you think tables help, the Chinese versions are rather more sensible that ours. In China, the two times table is:
And that’s it! Three times and four times tables:
Each table only goes up as far as the square of the table number, so the seven times table is:
So, you might ask, if the two times tables ends at 2 x 2, when do the children learn what 9 x 2 is?
Well, they do not directly, but they work a lot on multiplication being commutative (tip 1) and putting the smaller number first (tip 3), so given 9 x 2 they know that is equivalent to 2 x 9 and, hey, that is 18.
Our tables put an extra burden on children by asking them to memorise each multiplication fact twice, once as 9 x 2 in the two times table and again as 2 x 9 in the nine times table!
There is some truth to the adage of ‘use it or lose it’. We cannot assume that the child who knew some multiplication facts last year is still confident with them this year.
Overlearning is important – repeatedly going back, just for a few minutes, to recap on the multiplication facts that children know and building their confidence.
Mike Askew is adjunct professor of education at Monash University, Melbourne. A former primary teacher, he now researches, speaks and writes on teaching and learning mathematics. Find him at mikeaskew.net and follow him on Twitter at @mikeaskew26.
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