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Learning advanced math by drawing, playing with beach balls and knitting

smithsonianmag.com

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Re: Learning advanced math by drawing, playing with beach balls and knitting

#31

Post by geoalchimista »

kolpa wrote: post #30
geoalchimista wrote: post #27

Title is clickbait. Whatever you can learn from "drawing, playing with beach balls and knitting" is most likely not advanced math . (Otherwise professors in a math department would all be playing knitting and beach balls to get tenure.) Advanced math is hard. It is like toiling in the field under a scorching sun. Edit: Didn't see that the author of the article is a math professor. This method seems to work in a liber…

I'll defer to the math professor on this one.

I'd be curious to see what a math prof would have on this.

But IMHO, math is learned by writing proofs. That is the only solid way for building an understanding.

Re: Learning advanced math by drawing, playing with beach balls and knitting

#32

Post by Jtsummers »

geoalchimista wrote: post #31
kolpa wrote: post #30

Earlier quoted context omitted.

I'll defer to the math professor on this one.

I'd be curious to see what a math prof would have on this. But IMHO, math is learned by writing proofs . That is the only solid way for building an understanding.

The author of the linked article is a math professor.

Additionally, not all math is writing proofs. It's also applying their results (a student doesn't need to prove 2+2=4 to use 2+2=4 in some computation) and developing intuitions about the nature of mathematical objects (which can then be used to guide future development by helping to discover new hypotheses to prove).

Re: Learning advanced math by drawing, playing with beach balls and knitting

#33

Post by geoalchimista »

Jtsummers wrote: post #32
geoalchimista wrote: post #31

Earlier quoted context omitted.

I'd be curious to see what a math prof would have on this. But IMHO, math is learned by writing proofs . That is the only solid way for building an understanding.

The author of the linked article is a math professor. Additionally, not all math is writing proofs. It's also applying their results (a student doesn't need to prove 2+2=4 to use 2+2=4 in some computation) and developing intuitions about the nature of mathematical objects (which can then be used to guide future development by helping to discover new hypotheses to prove).

Fair enough. I didn't see the last line. I retract what I said earlier.

Still I am not very convinced that it is a good idea to teach STEM students that way. The author of the article works at a liberal arts college.

Re: Learning advanced math by drawing, playing with beach balls and knitting

#34

Post by Jtsummers »

geoalchimista wrote: post #33
Jtsummers wrote: post #32

Earlier quoted context omitted.

The author of the linked article is a math professor. Additionally, not all math is writing proofs. It's also applying their results (a student doesn't need to prove 2+2=4 to use 2+2=4 in some computation) and developing intuitions about the nature of mathematical objects (which can then be used to guide future development by helping to discover new hypotheses to prove).

Fair enough. I didn't see the last line. I retract what I said earlier. Still I am not very convinced that it is a good idea to teach STEM students that way. The author of the article works at a liberal arts college.

1) Science and math (though not engineering, typically) fall under the liberal arts.

2) The course is offered in "J-Term" (January), it's a supplement and meant to connect dots for students, not explicitly teaching them advanced math theory (in the sense that they'd come out of a one-month course able to understand, intimately, graduate level maths).

Re: Learning advanced math by drawing, playing with beach balls and knitting

#35

Post by j2kun »

nabla9 wrote: post #24

I can learn to understand basics of many advanced concepts outside engineering math to the level where I can read/skimp some research papers and understand the thinking behind it. But it's very hard to recognize the concept on my own and the utility 'on the wild' unless someone else is pointing it out and explains it. Take for example Sheaf[1]. The basics are not that hard if you spend some time. But once you have le…

Oh, if only I could make a career of pointing math things out :)

Joking aside, I think a lot of researchers will oversell the applications of their technology, so it's just as important to be able to recognize when a particular math thing will help, and when it's more harm than good. The first rule of statistics is: if the decision maker already has their heart set on a particular action, you shouldn't waste your time and money designing a statistical study with fancy tests and inference techniques.

Re: Learning advanced math by drawing, playing with beach balls and knitting

#36

Post by j2kun »

geoalchimista wrote: post #27

Title is clickbait. Whatever you can learn from "drawing, playing with beach balls and knitting" is most likely not advanced math . (Otherwise professors in a math department would all be playing knitting and beach balls to get tenure.) Advanced math is hard. It is like toiling in the field under a scorching sun. Edit: Didn't see that the author of the article is a math professor. This method seems to work in a liber…

It depends on your goals. Much of mathematics is training for specific goals (often narrow), while if your goal is simply to be exposed to many different things, you can get quite a lot of the intuition with knitting needles and drawings.

As a mathematician and engineer, I bet this class is more like a "film history" class than a "principles of optics" or "CGI techniques" course.

Re: Learning advanced math by drawing, playing with beach balls and knitting

#39

Post by sitkack »

geoalchimista wrote: post #27

Title is clickbait. Whatever you can learn from "drawing, playing with beach balls and knitting" is most likely not advanced math . (Otherwise professors in a math department would all be playing knitting and beach balls to get tenure.) Advanced math is hard. It is like toiling in the field under a scorching sun. Edit: Didn't see that the author of the article is a math professor. This method seems to work in a liber…

> Otherwise professors in a math department would all be playing knitting and beach balls to get tenure.

Your hyperbolic statement is not an argument.

Re: Learning advanced math by drawing, playing with beach balls and knitting

#40

Post by adenadel »

geoalchimista wrote: post #33
Jtsummers wrote: post #32

Earlier quoted context omitted.

The author of the linked article is a math professor. Additionally, not all math is writing proofs. It's also applying their results (a student doesn't need to prove 2+2=4 to use 2+2=4 in some computation) and developing intuitions about the nature of mathematical objects (which can then be used to guide future development by helping to discover new hypotheses to prove).

Fair enough. I didn't see the last line. I retract what I said earlier. Still I am not very convinced that it is a good idea to teach STEM students that way. The author of the article works at a liberal arts college.

Lots of people falsely equate the liberal arts with the humanities. This is a misconception that I try to fight in my in-person conversations with people. Math, chemistry, physics, and biology are all liberal arts. Business, engineering, nursing, and other types of professional training are not liberal arts.
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