Calculus is one of those things that takes awhile to wrap your head around, but if you put in the work, it starts to open the world for you. The problem is that the second you stop maintaining your advanced math skills, it all goes away, and you realize you wasted a lot of time learning something you'd forget quicker than it took you to learn it.
I'm sure there's some change in the brain that remains long after you've forgotten everything you once knew about calculus, which makes it all worth it. I just can't prove it and have no desire to. I subscribe to the movement that statistics is more useful to more people, thus should be taught in place of calculus, even though many people are as scared of stats as they are of calculus. Engineers and others requiring advanced math can study calculus if they need it. We would all do well to know a little stats.
But this is about calculus, so I'll save the stats rant for later. My AP Calculus course was taught by a guy who had been teaching at the same high school since my dad became part of the first class when the school was formed 30 years previously. He was old school. Our administration declared that unlike some of our rival schools who banned hats, they would only follow when it was shown that hats prevent learning. Well, except if your calculus teacher bans hats from his own classroom. There were a lot of hat heads in there.
We had to learn to juggle. It was required. I don't remember if there was a penalty for not doing it, but it was required, even if you had to juggle pieces of tissue paper. I got decent at it as my friends and I practiced. Juggling was always a good diversion from a particularly hard problem, and it was okay, since it was a required part of the class. At the end of the year when it came time to show off our talents, our teacher brought home the object lesson that you can do hard things if you just work hard at it. Then he proceeded to tell us that he couldn't juggle himself. Oh.
A couple classmates had written an awesome program on the TI-85s that we used in class, and which we were allowed to use on the AP test, that automated almost everything you needed to do. I actually had my own graphing calculator that I used, a Sharp, I believe. I was used to mine, so I used that primarily on the test, but they allowed me to bring one of the loaded TI-85s as well, so I actually used two graphing calculators during the test. It worked out, and I got a 5 on the test, the highest of any of the AP tests I had taken.
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