Part II of the thesis

Have you ever:

  • Started singing or playing one song to find yourself playing a different song by the end?
  • Found yourself walking or driving the route you take everyday, even if today it isn't the route you wanted to take?
  • Found yourself dialing the phone and being connected to the wrong person -- often to another friend who you call more often?
  • These are all capture errors. You spend so much of your life doing something one particular way that it can mess up those times when you want to do something similar, but not quite the same. Your behaviour is captured (pulled into) another similar, and more often practiced, behaviour.

    That's the way I think some children's errors in arithmetic occur. Children spend lots of time practicing one kind of problem that it can result in errors when they move on to other arithmetic problems.

    The thesis (well, the second part) models children's errors using neural computing and borrowing some terminology and graphs from dynamic systems. While solving a problem children traverse a number of states. Learning is all about making states distinct from each other, but sometimes a child will be solving a problem and will be "attracted" into a state that produces the wrong answer. And these states will be similar because they play a role in similar arithmetic problems. The child has started out trying to solve one kind of problem and has been capture by a more familiar problem.

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