31–40 of 158 posts
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One of my friends in HS was against calculators, and also very stubborn, and got in trouble for asking how to do sin, cos, tan functions without a calculator.
Good old taylor series, of course!
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Ever heard of new math? https://www.americanheritage.com/whatever-happened-new-math-... I agree with you, especially if you are in your 60s and have a math professor as your teacher, one would think a new math approach works best!
sure https://www.youtube.com/watch?v=UIKGV2cTgqA I used to listen to that several times a day when I was a kid.
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Right. >Fundamental understanding gives exponential results yet most courses try and get the axioms and basics out of the way as fast as possible, working through basic proofs or derivations is cute sideshow, if anything. This is so true. I was exactly like the author. I could not understand any math beyond algebra. Trigonometry was way beyond my ability. But one day, I found an old trig book lying around when I went…
Very well said! It is true that once you grok this technique, you are basically unstoppable. It does make for slow progress at first, but it's worth it. Edit: I went to grad school for math, and I got there by pretty much doing what you described!
Even more, there is research pointing that continuous learning will prolong your lifespan. Best indication is a study on how university professors tend to live longer.
Reminds me of the night terrors I had when I was younger. I remember often having dreams that involve the unknowable, unseeable or in some other way were impossible for my finite mind to comprehend. In the worst of those nightmares I was left shaken with fear — feeling as though I had peered from just over the precipice of sanity itself.
It's a shame he went to all the trouble of avoiding conventional education (for the wrong reasons), but then still ended up going down an execution rather than concept focused route. As soon as you start memorizing operations and treating math more like a narrow grind only approached through arbitrary problems solved primarily through computation or use of rote application of poorly understood technique, you lose the…
I left school at 15, never to return to education, in part because of how maths was taught. There was never an explanation of the _why_ of things. It was very frustrating, and the teaching was very poor. I ended up a programmer, in part, because I figured if teachers weren't teaching, i'd teach myself. This has been a good strategy for me, however there's serious holes in my pure maths knowledge.
Education would still have to artificially give students problems; waiting for students to naturally have a problem for which taking the derivative of a tan function and then leaping in to discuss that just doesn't scale in all sorts of ways. But if we gave them problems first, and let them chew on them for a bit, I think it would work so much better.
But that's an anathema to the current system. It would require not moving students through in cohorts because you need to give students enough time to chew on things and there's no way that will be standardized. And of course it requires admitting that Very Smart People Are Totally Wrong About Education, and I might as well ask for a pony while I'm at it. The Curriculum Must Not Be Changed. The Curriculum Must Not Be Questioned.
I wish someone would pay me for a few years to try to develop a computer-based math curriculum based on this concept. I'm still waiting for education to move to the phase where computers are used as something other than "The Old Curriculum, But On A Computer!" I thought we'd be farther along on that path by now. I seem to have underestimated the inertia of the Holy Curriculum, Hallowed be its Name and Hallowed be The Heroes Who Practice It in its infinite glory, yea verily.
In my opinion, nothing can make you smarter. Learning rationalist techniques may make you better at thinking through problems, learning memory techniques like Memory Palace may improve your memory, using learning techniques like Spaced Repetition may help you learn and retain large amounts of information with the minimum necessary effort, but nothing can make you smarter.
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I left school at 15, never to return to education, in part because of how maths was taught. There was never an explanation of the _why_ of things. It was very frustrating, and the teaching was very poor. I ended up a programmer, in part, because I figured if teachers weren't teaching, i'd teach myself. This has been a good strategy for me, however there's serious holes in my pure maths knowledge.
One of the thoughts I've been developing over the past 10 years or so is that you can't teach someone the solution to a problem they don't have. This encompasses the "why" question but even goes beyond it, because even the answer to "why" is often just another level of "why" and/or "who cares", quite reasonably. To learn something, you need a problem, you need to grapple with the problem for a bit, and then you can b…