It happened in calculus class. Seriously. That class I've been freaking out over for the last few weeks. The one that moves at the speed of light and covers a vast amount of material, all of which is cumulative? Yup...that one.
I was frantically taking notes as my professor was explaining Riemann sums. When I looked up, I saw that he had drawn a line on a graph, under which he'd drawn multiple rectangles. It looked like this:
He mentioned that the sum of the areas of each of the rectangles under the curve would give you the area under the curve, minus, of course, the parts under the curve not included in the rectangles. And the he said, "if we used more rectangles, the sum of the areas would be closer to the actual area under the curve." So here's where my day-maker moment happened: I thought, wouldn't that mean that when the number of rectangles under the curve approaches infinity, that the sum of them would approach the actual area under the curve?
BINGO! Wouldn't you know, that's exactly where he was going with the lesson. Now, I know this isn't news to most people. But it was damn exciting to be guided like that through the learning process, instead of feeling dragged; to arrive at a conclusion without needing to be told what conclusion I should be arriving at.
It's times like those when I feel most confident in myself...when I feel capable of understanding all of the things that I always thought were out of my reach. It's times like those that remind me of how important it is to have teachers...ones who know how to set the stage for thought and encourage it.
3 comments:
I'm suddenly MORE confused.
Your story reminds me of a story my boyfriend told me. He is an aerospace engineer, and his first time through calculus he failed it. I asked him how he overcame his problems with it and he said, "when I was taking it for the second time, one day in class, it all just clicked. I haven't had a problem since."
That's not exactly what happened to you, but it's on the same track, I think. Here's hoping it all just "clicks" for you one day! (Though it never did for me....)
Thanks Sally :) It's clicking...but sometimes we just approach a subject that feels utterly impossible to understand.
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