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by DigitalJack
4421 days ago
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I remember struggling greatly in algebra because it was like a boatload of recipes to remember. There was never much discussion on what these actions meant or why you do them. There is this awful commercial in the states for an online tutoring project where the student asks "how do I find the area if a triangle?" The response is "well, Cindy, the formula for the area of a triangle is 1/2 b*h, so you take half the base and multiply by the height and that's how you find the area of a triangle." Non of that is false, but all the poor girl in the commercial learned was yet another reasonless recipe. |
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Recipe's are a very helpful fallback where you might be struggling with understanding the origins of material in a rigorous manner. You can inspect a triangle all you like, but at the end of the day it's much easier to simply remember the formula.
This, I am finding, is the only way I'm managing to actually understand complex analysis - take the formulas for the results, and remember how to apply them. It's revealing to me that what looks complex gets very simple in that manner (and also that I still get tripped up by elements of basic integration).
If I couldn't do this, then I'd be lost - and in a test simplification remembering how to work through the definition isn't possible (and isn't required thank god) because that's a path which leads to me spending 6 hours figuring out and trying to picture something in a way which makes sense.