Times tables have been a hot potato politically for a long time, there seems to be a slightly rose-tinted view that once upon a time every child in Britain learned them by heart and still remember every fact today. Yet clearly not, if the famous example of politicians such as Stephen Byers and George Osbourne are anything to go by then even the great and the mighty parliamentarians have a wobble now and then. Those halcyon days just did not exist; it has ever been true that some pupils find learning their tables harder than others – we can give you roomfuls of teachers, teaching assistants and parents from all walk of life who can bear testament to this, most of whom can name the fact that remained a blindspot. Last week Nick Gibb announced that there would after all be a times table test for Y6 pupils beginning in 2019. Inevitably this is likely to increase the emphasis on the learning of these facts – no bad thing as recall of these facts reduces the cognitive load enabling the focus of learning to be attended to, but it pays to be mindful that we build in meaningful learning sequences before we introduce the low stakes tests that allow teachers and pupils to identify gaps in fact recall and teach for them.
The following blog considers one such possible approach.
Kate Kellner-Dilks is a Primary Mathematics Adviser at Herts for Learning
In many of the schools I have the opportunity to visit and work with, the age old questions of multiplication facts comes up. Lots of schools have a ‘times tables challenge’ or variation of, which usually equates to some level of weekly testing. In my last blog ‘Are the boys really better at mathematics?’ I questioned whether multiplication facts (times tables) needed to be tested before they are learned, particularly against the clock, because of the anxiety you see in those pupils who don’t (yet) know them. These children often end up using inefficient strategies based on counting, to figure them out, rather than the intended memory recall. The test does not necessarily help build their memory recall and often, in my experience, reinforces their counting strategies, (a child said to me her ‘mind goes blank’, so she panics and counts up rather than using memory).
So, how should we teach times tables, in a way that helps build memory recall? And I do mean teach. Not practice recall through games (which comes later), or testing (which comes later still, if at all). The problem that we’re up against is that there will be a test introduced as part of Key Stage 2 SATs at some future point, which had originally been planned for introduction later this year but is now planned for 2019 and will affect our current Year 4 pupils.
Original DfE press release:
First we should return to the purpose: Why do we want children to learn the multiplication facts? They are part of an essential underpinning of our mathematics system, like counting, number bonds and place value. If children have this knowledge secure, they are better able to carry out calculations (or parts of calculations) quickly, accurately and with confidence. Leaving the time and energy, particularly in upper Key Stage 2, for the more challenging aspects of a problem or calculation. In a nutshell, they are also part of what is likely to make a child more successful in their Key Stage 2 SATs for mathematics (whether multiplication facts are tested separately or not). Understanding multiplication facts and having the recall means a child can manipulate questions such as 71 x 8 with ease. This came up in the Key Stage 2 arithmetic paper in 2016, and for some children was an ‘easy’ question, based on their knowledge of 7×8 (x10), and 1×8. All too quickly though, in my experience, we skip through the phase of exploration and learning, not giving enough time for children to properly understand how these groups of facts build up and many children did not find this question easy.
In the National Curriculum it states that children should learn, with recall, the multiplication facts for the 2s, 5s and 10s in Year 2, then the 3s, 4s and 8s in Year 3 and finally know all facts to 12×12 (and corresponding division facts) by the end of Year 4. This is a challenge for many Year 2, 3 and 4 children, their teachers and parents. It then continues to be a challenge for Years 5 and 6.
So, having pondered this on and off for a while, I have developed some strategies alongside some of the teachers and schools I’m working with. Early feedback from the adults and children has been extremely positive and some school have gone on to (with my help) share this with parents, to support them in understanding how you might learn a times table at home.
It uses the CPA approach (Concrete-Pictorial-Abstract) to underpin the steps, which basically means that you have a better chance of creating a long term memory, based on manipulation of physical resources and constructing images before or alongside the abstract e.g. the facts written as numbers; 6 x 7 = 42.
In reality I have actually used these strategies for years now, but to be sure of my ideas before committing them to an eternal life on the internet via this blog, I tested the sequence out again (in January 2017), in a 50 minute session with four children from Year 4. I asked the school to select me a small group of children not yet confident with the multiplication tables expected for their age. The school chose children in Year 4, but still working towards the Year 3 expectation of knowing their 3s and 4s. My session was split over a school playtime and the Teaching Assistant who works within the year group stayed with us to see the session in action. We carried out a brief random quick recall test at the beginning and end of the session as a crude measure, but the most telling feedback was from the Teaching Assistant who, knowing the children well, was impressed by how much better their memory and rapid recall of the facts became in such a short space of time, as well as all four children increasing their scores in the random recall test, two children scoring 100% correct in the exit random recall test. The pictures used below are from this group.
How it works: The basic approach starts with physically building a multiplication table as an array which grows, each time you add a new row, creating a new fact.
I ask children to start by making me 1 group of the multiplication table we are working on. In this case 1 group of 4 for 1 x 4.
We then use this to discuss 0 x 4: If 1 x 4 = 4, this means when we have 1 group of 4 cubes we have a total of 4 cubes, then it must also mean 0 x 4 = 0, because 0 groups of 4 cubes means 0 cubes.
We then build on the next fact; the second group: 2 x 4 = 8. And so on. By simply making the facts with cubes or something similarly concrete, so that you can see a growing array, and using this to build the list you can also make points clearly – each time you add a group you are adding the next fact, which links to multiplication being repeated addition. The array can be physically turned to show the corresponding fact e.g. 5 x 4 = 4 x 5 = 20, building the understanding of commutativity.
Children continue until they have the full array built to 12x and have recorded the full list alongside, from 0x to 12x. We check everyone has a correct and full set, just in case. We then pause at this point to talk, led by questions: “What do you notice?” It’s adding 4 each time, I can count in 4s, they are all even numbers, and so on. “Which facts do you think you already remember?” Children opting for 1x, 2x, 5x and 10x with a couple of others. “Which do you think will be hardest to remember?” And then discussing how we will remember these ones, or what strategies would help us to work them out.
At this point I would suggest reading through the list in full – but the emphasis being that it can be reading from the list – as our focus is still on building their memory recall. You can add in a further step of drawing an array for each fact, if this is a valuable step for the particular children you are working with.
We are now ready to turn this into a card game. Each fact is tuned into a small card, with the multiplication on the front and answer on the back. Children make the cards themselves, based on their list and their array. At this point they are still internalising what the facts are.
The cards are played with in order first, multiplication fact side facing up (0 x 4, 1 x 4, 2 x 4), to be secure that you can remember what is on the reverse, before playing games with the cards out of order and against a partner, or with the answer showing to see if you can recall the related question. This may take a few sessions, before children have a recall memory of the facts. I often return to similar quesitons; “Which facts do you think you already remember?” “Which facts are harder to learn?” “Why is that?” “How can we remember them?”
I’ve found it also helps to allow or encourage the children to take the cards home to play with, playing against a parent, friend or sibling. The important thing is that this is building a rapid recall memory that will last. My feeling is that this is the precursor to other rehearsal games and activities: Colouring the numbers on a hundred square to spot patterns or playing Fizz Buzz, even using a counting stick for times tables rehearsal probably needs to be based on some learning first. Otherwise I’m not sure what we’re expecting children to draw upon when we do these things. But, once they do have recall, based on this understanding and exploration, children will need to continue to rehease so that they stay fresh.
Teachers I’ve worked with have told me that they’ve gone on to personalise the process for themselves and the children they work with – developing division recall strategies, or adapting other elements, which is great. It’s important that this is ‘owned’ by whoever uses it. It takes time for most children to develop their memory recall of the full set to 12×12 and so developing and personalising the approach is important.
So is the test element simply to satisfy the adult that they child has learned the required information with rapid recall and to identify gaps in fact recall that still persist? In which case it can then be used (or not used), as appropriate. We need to remember it’s even more important to teach the multiplication facts properly, to develop rapid recall, as testing and recall games on their own, to prepare for any new test, won’t cut it I’m afraid.