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Children learn by getting things wrong. A child doing the sum and getting the wrong answer may be learning as much as a child doing the sum and getting the right answer.

http://www.bbc.co.uk/programmes/b04dwbkt

Most relevant is probably this one: http://www.bbc.co.uk/programmes/b04gw6rh

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Yes exactly. That's the reason so much practice is necessary. When you learn subtraction, you need to see lots and lots of number combinations, many of which you'll initially get wrong, but soon learn to do correctly, then recognize instantly, and finally use as building blocks.

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