(7) In second semester calculus, there were three chapters full of formulasthat could all be derived from the first formula in the chapter, but neitherthe book nor any of the teachers pointed out that all but the first formulawas derivative. There appeared to be much memorization needed to learneach of these individual formulas. I happened to notice the relationshipthe night before the midterm exam, purely by luck and some coincidentalreasoning about something else. I figured I was the last to see it of the1500 students in the course and that, as usual, I had been very naive aboutthe material. It turned out I was the only one to see it. I did extremelywell but everyone else did miserably on the test because memory under examconditions was no match for reasoning. Had the teachers or the book simplyspecifically said the first formula was a general principle from whichyou could derive all the others, most of the other students would havedone well on the test also.


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