“Many children are held back in their learning because they have a model of learning in which you have either ‘got it’ or ‘got it wrong.’ But when you program a computer you almost never get it right the first time. Learning to be a master programmer is learning to become highly skilled at isolating …
“Many children who have trouble understanding mathematics also have a hopelessly deficient model of what mathematical understanding is like. Particularly bad are models which expect understanding to come in a flash, all at once, ready made. This binary model is expressed by the fact that the child will admit the existence of only two states …