Concrete Thinking

If abstract thinking is a sign of maturity, then it follows that young children prefer concrete thinking, thinking about actual things rather than ideas. When children start to add and subtract they use their fingers to count on. This is a perfectly legitimate way for them to aid their counting. Unfortunately, it can be slow, and it introduces a limit in their minds that it is easy to add on any number up to 5, but that it's hard to add a bigger one - an impression created solely by the need to put down their pencil to use both hands to counnt on, and having no free hand to point to the fingers while counting.
To encourge children to move on and do their sums without using their fingers, pupils are told not to count on their fingers. Many children, at this point, think that they are expected to add and subtract numbers without using any sort of framework to count up/down the numbers. They can remember the first few like 2+3 which they know add up to 5, but they do not remember bigger ones like 7+8 (which was more than hard enough when they were using their fingers to count on). "How on Earth,"? they ask themselves, "do I add these big nummbers?". What's more, numbers go on up for ever and ever, and the child, quite sensibly, realises that they won't be able to learn all the combinations of all of them. And they give up.

Children need to be given some other way of counting something concrete, which they can do in their mind's eye (or on a scrap of paper) that will enable them to add/subbtract numbers up to 9. Because of the way the number system has been built, addition and subtraction only requires manipulation of numbers up to 19, another fact that isn't immediately apparent to the child. At Puppet Maths, by using puppets, we tap into the children's imagination, we get them to use that part of their brain which is so important when they're doing maths.