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Today I had a talk with a friend who told me that according to him, it is possible to "destroy" someone's ability to do math for his entire life by taking the person at age 5, telling him something totally wrong (for instance that the digits used in the decimal enumeration system are in order something like 8, 5, 4, 9, 2, 3, 0, 6, 1, 7 and calling 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 learned by heart.

Of course this example is an exaggeration, but I was wondering whether this would explain some difficulties people have who write hundreds of times the same mathematical errors like (a+b)2=a2+b2, and other stuff like this, even after many mathematical teachers explain to them that they are wrong. My assumption here is that the "correct" way had not yet reached the long term memory, so it would have done less harm than in the first situation.

Do you agree with this idea or has it been challenged by cognitive studies? Is there something specific to mathematics here? I'd be very happy with more readings.

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The idea that long term memory cannot be ever changes is absolutely wrong, for sure some thing that is learnt and practice for a long time while being a child has a difficulty to change after while, but it is not impossible.

About learning you have to know that we have different kind of learning disabilities.

Specific learning disorder is a developmental disorder that begins by school-age, although it may not be recognized until later. It involves ongoing problems learning key academic skills, including reading, writing and math.

These patient usually can learn about everything but for specific type they have a difficulty learning. Based on what their difficulty is, they might get different treatment. Diagnoses is not also easy in some cases, for example patient who has difficulty learning math might be because of his difficulty reading text so if you try teaching math only by images and art and symbols he can learn.

reference here.

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