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"but later in college when they finally get to hear all this stuff, they’ll really appreciate all the work they did in high school.” So painfully spot-on. My mathematical education was horrible. Meanwhile I had been writing code since I was a little kid. It wasn't until I was an adult that I realized how much math I had been learning while programming. And worse, that I had been completely miseducated about what math…
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Interestingly, the converse is also true. I was always into computers and tech but never really programming. I was a math major in college, however, and after graduating I started programming. The transition was almost seamless, I picked up programming really quickly, it was surprising to me how much the "ways of thinking" are alike.
One of the key mistakes of educational strategy is dividing up knowledge into a bunch of subjects like "Language", "Math", and so on. You can find linkages in just about everything; this siloing really only serves to make people think they're particularly good at one thing and not another, when really it's a preference for one perspective over another.
He is 100% right. We should not be teaching the formulaic rules of basic arithmetic until high school, and only then as a part of life skills class. It should be taught as the art form that it is.
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One of the key mistakes of educational strategy is dividing up knowledge into a bunch of subjects like "Language", "Math", and so on. You can find linkages in just about everything; this siloing really only serves to make people think they're particularly good at one thing and not another, when really it's a preference for one perspective over another.
So the pragmatists question is then naturally, how do you teach it? How do you shard the curriculum if not by subject? It seems a bit overbearing to ask each teacher to have the proper renaissance man's education of knowing a bit of everything.
As I understand, classifying classes into "disciplines" is for the convenience of administrative systems, like university deans. This classification is not a law of the universe, nor of the human mind. One can imagine the negatives of fitting learning into hierarchical administrative models.
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Can't vouch for this book, but coincidentally just read about it today-- "The Essential Knuth" by Knuth, Daylight, and DeGrave. Donald E. Knuth lived two separate lives in the late 1950s. During daylight he ran down the visible and respectable lane of mathematics. During nighttime, he trod the unpaved road of computer programming and compiler writing. Both roads intersected! -- as Knuth discovered while reading Noam…
> (...) while reading Noam Chomsky's book Syntactic Structures on his honeymoon in 1961 Which makes you wonder, what kind of person reads this stuff on the honeymoon.
"There is such breathtaking depth and heartbreaking beauty in this ancient art form. How ironic that people dismiss mathematics as the antithesis of creativity. They are missing out on an art form older than any book, more profound than any poem, and more abstract than any abstract. And it is school that has done this! What a sad endless cycle of innocent teachers inflicting damage upon innocent students. We could al…
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This kind of approach simply doesn't make sense It was poorly explained there, but essentially that style of reasoning does work: http://www.amazon.com/Primer-Infinitesimal-Analysis-John-Bel... And I at least find that approach easier and more useful. (I learned it from the Feynman lectures on physics, where he didn't axiomatize it; the above link does.)
I find the logically sound version of the infinitesimals approach to be much more difficult to understand than the approach using limits. For example, you have to introduce hyperreals to make it work (most common approach): http://en.wikipedia.org/wiki/Hyperreal_number
Most of them could get a better intuitive understanding of Calculus. (We should of course conduct a rigorous study comparing the effects of using different approaches to teach Introductory Calculus.) Then those who need to use the limits approach for other courses could use the intuition to learn it faster. In addition, they would understand Calculus from two different angles and could select the more suitable approach for each problem.
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yet struggle to convince "artsy" persons that what I do is creative. As another mathematician I've almost found the exact opposite. As soon as I mention math to an arts person they instantly start babbling about fractals and chaos and Fibonacci and all kinds of other vague pop-culture terms they've heard of but don't really understand. Artsy types almost seem to find math much more artistic than I do.
They look at fractals and spirals and enjoy seeing the pretty pictures with all the symmetry and colors. However when an explanation of how the series is generated and how it can vary is presented, interest is feigned and the core concepts still elude them. It's almost as if they don't like getting their hands dirty in a different medium.
"There is such breathtaking depth and heartbreaking beauty in this ancient art form. How ironic that people dismiss mathematics as the antithesis of creativity. They are missing out on an art form older than any book, more profound than any poem, and more abstract than any abstract. And it is school that has done this! What a sad endless cycle of innocent teachers inflicting damage upon innocent students. We could al…
"Music is a stupid way of art, usually for stupid people. If you are writing literature or poetry, then you should be an intellectual; as a really good musician, that's not a must." -Holger Czukay So there is this idea of different arts being more or less accessible to the general population.