Stocking the Toolkit – learning number bonds and tables
My older daughter is now in her second year of teaching. Just before she began her PGCE course two years ago, I had a lot of fun putting together a ‘teacher toolkit’ for her as a present. It contained lots of useful teacher tools: sticky notes, staplers, useful teacher books, laminator, highlighters, paper cutter, lolly sticks etc. She’s found it very useful, but it did nothing to show her how to teach (except for possibly the teacher books). She needed her PGCE course, and most importantly experience in the classroom and observation of others for that; as a thoughtful and reflective practitioner, I know she’ll be honing and adding to her skills throughout her teaching career. Similarly, my plumber could loan me his toolkit for a day and I still wouldn’t be any nearer to fixing the dodgy radiator in the bathroom.
Rapid recall of number bonds and tables facts is a very useful tool in any child’s mathematical toolbox. When tackling word problems, for instance, it reduces the cognitive load for a child if they can focus on visualising the problem and how to solve it without the distraction of having to work out number facts from scratch each time. However, there’s no point in having these tools available if the child has no idea how to use them or how they relate to the world around them. So, having learned the facts, it’s vital that we give our children lots of opportunities to use and apply them, doing this in ‘real’ contexts across the curriculum wherever possible.
It’s also crucial that children understand what these facts mean. When I was in primary school ( a frightening number of years ago), we all learned our tables by rote but I suspect many children who could find the answer to 9×7 in an instant, had no real idea that they could use the answer to work out how many days until Christmas when told they had 9 weeks to go. So, before trying to memorise any number facts, children should always have plenty of experience of combining objects in different ways, both using concrete objects and visual representations. This idea, for instance, shows how a multiplication fact can be represented as repeated addition, arrays or groups of objects and also uses the commutative rule to generate a related fact. For addition facts, children need lots of opportunity to explore numbers and the different ways they can be broken up into different parts. Activities like this one using number bond bracelets or this one using number spiders should be a staple in KS1 classrooms (and probably in KS2 for children who still haven’t got good mental pictures of numbers).
With these foundations in place, we need to think about how our children are actually going to learn the facts. For this, there really is no substitute for practice, but we can at least make this practice as painless as possible. In fact, many children enjoy the feeling of mastery as they see their mental stock of number facts increasing and become increasingly fluent and rapid in their recall. There are lots of games and activities, both concrete and online, for reinforcing number bonds and tables and my pinterest board has lots of ideas for this. One proviso I’d make though is that whilst many children respond well to working against the clock, some definitely don’t and for them activities which don’t involve time pressure will probably be best.
To make the task more manageable too, we need to explicitly teach children that lots of facts are related which cuts down significantly on the number of facts that need to be learned. Using fact family triangles and generating fact families so children learn that with number facts it’s ‘Buy One Get Three Free’ should be a regular part of the classroom routine.
If you’ve read my other posts, you might know that I’m a big fan of daily counting using a counting stick. This video shows how Jill Mansergh used a counting stick to teach a group of teachers at an ATM conference the 17 times table. Even Mr Gove doesn’t advocate us teaching the 17 times table in primary school (although give him time), but the basic process that Jill uses here could of course be used for teaching any times table and has the added benefit of linking nicely to counting along the number line in steps, which might be useful when it comes to teaching division too.
In my experience, most children are able to learn their number facts with fairly rapid recall, given sufficient practice. However, there are probably some children with specific learning difficulties who will never become very fluent with these facts. For these children all is not lost. Returning to the analogy of my daughter’s teaching toolkit, it’s worth remembering that teaching was perfectly possible before the invention of sticky notes and laminators! These children need to learn how to be able to work out the facts fairly quickly and use aids like tables squares and calculators to support them when using and applying their mathematical skills. If you have several children who have real difficulties with learning tables, Steve Chinn’s book may be worth reading.