There is no doubt that knowing times tables up to ten is a good thing. Very few people get through life without having to do some multiplication and having that knowledge makes it easier. But beyond ten, there is a question mark. The new National Curriculum seems intent on making the eleven and twelve times table de rigueur for all primary school children, returning to how tables were taught when I was a child.
The post Is There Any Point to the 12 Times Table? looked at the efficiency of learning the 11’s and 12’s and concluded not. This was, of course, a rather simplistic study of the benefits of knowing the 11’s and 12’s, only taking into account the benefits of the multiplication knowledge. Possibly if the issues of factors were also considered then this may change the balance.
For me, what is important here is not so much which number to stop at, but how to learn the higher numbers.
One to ten, it’s simple. Learn them. Yes, I know it’s a chore, but it will pay back. It is an efficient process. Take X hours to learn this, save Y hours in the future. Mostly, Y will be larger than X.
Once you go beyond ten then I have issues with the “rote” learning. The issue is where do you stop? Yes, there are societal reason that knowing the 12’s (time and angles being just two of them), but what about 11? Or 13? 15 could be useful, 14 and 16 for weights, but not 17 surely?
I would suggest that once you get beyond ten then tables multiplication should be taught as a process. Teach the idea that 12 x 7 is the same as 10 x 7 plus 2 x 7. This has the benefit of showing children why learning the tables up to ten is useful, and is extensible to any further numbers they want to multiply. For the cognitive science aficionados out there it is also starting to get students to be more efficient by adopting chunking strategies for larger problems.
To try to learn the twelve times table by rote is a missed opportunity.