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I get it. After working in tech for 10 years, I went back to grad school for statistics recently. I came to the realization with every math class that I took

by AvAn12 5y ago

I get it. After working in tech for 10 years, I went back to grad school for statistics recently. I came to the realization with every math class that I took - after the first couple of lectures I had to say to myself, it looks like I'm just going to have to teach myself this class. I think that's the deal with math. With some other subjects, you can get quite far by knowing the gist of the material. Since math classes are generally evaluated on one's ability to grind out problems, you have to just grind out a lot of problems - no shortcuts. Like learning to play the piano - there's only one way work your way to learn to play a mozart sonata or whatever - lots of grinding away at it. Definitely think it's open to debate if this fact us USEFUL to anyone. For example, making Calculus II students learn to grind out loads of integrals by hand which can be solved by Wolfram Alpha in a fraction of a second may be of debatable value - - let the debates carry on... But I think under the current idea of what it means to "learn" math, to my eye it appears it really is the case that one has to teach it to onesself...

williamstein 5y ago
“There is no royal road to geometry.” -Euclid
rossdavidh 5y ago
Some truth here, but some of what she describes (e.g. no example problems with worked solutions to learn from) are not sensible if you want people to learn. Imagine if programmers had only the definition of what a function does, but example code using it was banned from all documentation (and no Stack Overflow). Especially in a math class intended for non-majors, it's an odd policy.
arghnoname 5y ago
There's an additional problem that you kind of glancing hit at, which in the US at least, there are at least two maths. Math for non-math major is grinding out some class of problems until you internalize the mechanism for solving that class of problems. You continue, adding a new class of problems on top of the old ones. This eventually culminates in something like calculus, where you do algebraic transforms until it's in a form you know how to mechanistically derive or integrate. Math for math majors is usually about finding proofs. This also just requires a lot of work, but it has a very different feel that the math classes for engineering students (source: was math and CS major). I found that it wasn't very difficult to learn the same mechanisms someone programmed into Wolfram Alpha (though it was tedious), but being good at proofs requires 'mathematical maturity,' and this is something else altogether. There seems to be something innate here. I was decent at it, but it took a lot of work for me to get there. Others were better than I'll ever be and they were 15 years old while I was a college junior.

by AvAn12 5y ago

williamstein 5y ago

“There is no royal road to geometry.” -Euclid

rossdavidh 5y ago

Some truth here, but some of what she describes (e.g. no example problems with worked solutions to learn from) are not sensible if you want people to learn. Imagine if programmers had only the definition of what a function does, but example code using it was banned from all documentation (and no Stack Overflow). Especially in a math class intended for non-majors, it's an odd policy.

arghnoname 5y ago

There's an additional problem that you kind of glancing hit at, which in the US at least, there are at least two maths. Math for non-math major is grinding out some class of problems until you internalize the mechanism for solving that class of problems. You continue, adding a new class of problems on top of the old ones. This eventually culminates in something like calculus, where you do algebraic transforms until it's in a form you know how to mechanistically derive or integrate. Math for math majors is usually about finding proofs. This also just requires a lot of work, but it has a very different feel that the math classes for engineering students (source: was math and CS major). I found that it wasn't very difficult to learn the same mechanisms someone programmed into Wolfram Alpha (though it was tedious), but being good at proofs requires 'mathematical maturity,' and this is something else altogether. There seems to be something innate here. I was decent at it, but it took a lot of work for me to get there. Others were better than I'll ever be and they were 15 years old while I was a college junior.