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In my experience teaching my friends and colleagues there are two ends of the learning spectrum--you can learn by example first or by theory first, or both, but
by solinent 6y ago
In my experience teaching my friends and colleagues there are two ends of the learning spectrum--you can learn by example first or by theory first, or both, but the former is by far the lion's share of the population.
I've taught people where there's absolutely no way I can teach them a generalization unless it's rote--however they can get domain-specific knowledge and beat me over the head in their domain and teach me something about my generalization as well that I might have been missing.
The best way for me to teach calculus to most people is to walk around a room explaining concepts like velocity, speed, acceleration, and position. However, I personally would never learn it this way--I prefer Spivak, during my read through I learned more than I could ever learn in a class.
It's also my belief that most people aren't like me in the sense that they learn from example first. However, most people I know are like me so it's hard to realize how needed a textbook like this is and how huge it could be for the regular person to learn something like this.
- skohan 6y agoIf you think about it, pretty much everyone learns math through example first. You learn arithmetic in elementary school, and it might only be after an additional decade or more of schooling that you actually learn the logical underpinnings which make the basic arithmetic operations work. If you actually started with boolean logic and tried to build up all of mathematics from there without at some point tying it back to a tangible example which can be understood in terms of the real world I'm not sure anyone could successfully learn it.
- solinent 6y agoSo I actually had a basic algebra system before they taught it to me, for what it's worth, probably something I figured out from the structure of the language my parents were using (both accountants). I'm a pretty rare individual, I've never had to work at math. I took a long time to learn how to learn from example, it used to be impossible but now it's almost just as natural.
- artagnon 6y agoTrue. Examples are necessary for both motivation, and for showing how the formalisms work, at this level. One good undergraduate textbook that has plenty of examples is Dummit & Foote. However, that doesn't mean that you don't define anything properly, and solely use examples to show how to crunch certain computations. The student is then stuck with a bunch of patterns in their heads, with little mathematical understanding.
- deleted 6y ago[deleted]