today I had a talk with a friend which told me that according to him, it is possible to "destroy" someone's abilities in doing maths for his entire life: take the person at age 5, learn him something totally wrong (for instance that the digits used for decimal numeration system are in order something like 8, 5, 4, 9, 2, 3, 0, 6, 1, 7 and call them respectively "three", "seven", "one", "six" and so on) so that once the wrong information has been assimilated in the long-term memory, it would be impossible for the person to correct and "overwrite" something that has been learn by heart.
Of course this example is exaggerated, but I was wondering whether this would explain some difficulties with people writing hundreds of time the same mathematical errors like (a+b)^2=a^2+b^2 and other stuff like this, even after many mathematical teachers explain them they are wrong (my assumption here is that the "correct" way has not reach yet the long term memory, so it would done less harm than in the first situation).
Do you agree with this idea or it has been challenged by cognitive studies? I'd be very happy with more readings; thanks in advance for your comments and suggested readings if you have :)
