I regularly watch the Child Genius programme on Channel 4. What has perturbed me was that even at this high level of education the children have no concept about the methodology of mental arithmetic and maths, whether or not they arrived at the correct answer, they did not seem to know how they arrived at it. The expressions on the children’s faces told stories.
It is not just about knowing the times table up to 12. There are methods for adding up long lists of numbers in one’s head-digits can be counted by using a base of 10, so that 7+3=1, 6+4=another 1 etc. The figures do not even have to be adjacent in a row, they can be a few digits apart, and the eye will scan each base of 10. I once had a race in a maths classroom as several columns of digits were listed on the board and while the pupils used their calculators, I summed everything using my head. I not only won the race with the correct answer, but very few pupils arrived at the correct answer. When I was an accountancy student (16 years old), I timed myself to add up a day book in my head, and could do 100 pages in 30 minutes. The client of the Estate Agents where this too place, complained to my boss, accusing me of being asleep.
For multiplication, one child was asked the sum of 37 times 12. 37 is one of the easiest numbers to multiply. Times 3 is 111, times 6 is 222, times 9 is 333, times 12 is 444 etc. The 11 times table is very easy with large numbers. For two digit numbers 11 times 45 is 495, you add the digits together 4+5 and put the result in the middle. This works throughout with 11. Dividing by 3 is easy-add the figures together and if they total a sum divisible by 3, then the whole number is also divisible by 3. Nine is another such number (3 times 3). Dividing by 5 will only work out exactly if a figure ends with 5 or 0.
There are lots of games that can be played with numbers, and many numbers can be remembered through being significant and having a connection with something else such as with history or sport. Teachers can make their maths classes interesting-remember 147, the maximum break in snooker etc., or zero not being used in any form of maths until 1300 years ago, first used in India.