If the math lesson for the day is long division, the teacher explains the problems, assigns practice problems to do in class, and more for homework. Most kids do the problems so that they can find answers that will make the teacher happy and give him a good grade to keep his parents happy, but he does not do the problems for the sake of learning long division. This trains the student to think in terms of grades instead of learning. It puts the focus on getting the right answer, not understanding how the right answer was attained.
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The independent learner is also given a large number of long division problems, but he is also given the answers. He practices these problems until he masters them. His purpose is to understand, knowing that, when he is ready, he can meet with the teacher who asks him to show his understanding. He practices long division until he has mastered it; if he only has to do five problems, that’s fine, if it takes a hundred, then it takes a hundred. He is not working towards finishing the assignment so that he has something to turn in the next day, but rather he is working toward mastery; to learn and understand.