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How to learn mathematics: the asterisk method

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Re: How to learn mathematics: the asterisk method

#51

Post by pas »

timwaagh wrote: post #50

Copying stuff by hand or otherwise focuses you on writing not reading. Personally I felt experimentation with this method set me back in my studies.

It's probably an aid for attentive repetition. If you can do it faster without writing, great. Many people can't.

(Basically it's a consequence of ADHD. While it's a novelty it's easy to focus, connect it to other things, grasp the rough outline of the concepts, mash them together, be creative, talk about it, barf up ideas about it ... but when it comes to memorizing a proof glyph by glyph reading does not help, because it just makes me feel like reading something that I completely understand and remember the 1000th time. Of course it turns out without actually writing it down from memory it's hard to judge how well I could write it down from memory based on what I feel while reading it...)

Re: How to learn mathematics: the asterisk method

#52

Post by k__ »

I noticed a great overlap in learning math and programming.

Programming was easier for me to learn and now helps me to understand math a bit better.

Coding a real project is the equivalent to math's proofs, I think.

The book "Badass - Making Users Awesome" says, learning something just requires two steps. Perceptual exposure (of hundreds of correct examples) and deliberate practice.

I think, math falls short in the first step, and I don't know why, but somehow mathematicians often see much part of syntax/grammar as a given, and use different ways to describe the same thing (sqrt and power of 1/2, for example).

Re: How to learn mathematics: the asterisk method

#53

Post by MayeulC »

noduerme wrote: post #41
olau wrote: post #11

Earlier quoted context omitted.

Intuitively, it does make sense. If you only ever encounter something once, it probably does not make sense to spend brain resources storing it.

I think I've reinvented trigonometry at least fifteen times in my life when I needed to animate something roughly circular, spherical or wave-like. I still have no freakin clue which thing is a sin, cos or tan. I failed precalc (and they still let me work on video games!) But I do remember that a hypotenuse is the square root of A^2 + B^2 and from that I can pretty much figure out the rest.

I had trouble with that, always going back to the "SohCahToa" mnemonic. Nowadays, I always use the unit circle. Cos is abs[cissa] (horizontal), Sin is ordinate (vertical). Rotate the unit circle (or your drawing) to align as needed, scale with the radius: https://en.wikipedia.org/wiki/Unit_circle

You can derive that back from the Pythagorean theorem, but only if you have the sine and cosine definition in mind (SohCahToa).

Re: How to learn mathematics: the asterisk method

#54

Post by jvvw »

spekcular wrote: post #3

This is not bad advice, especially for people new to proof-based mathematics. (I've noticed more mathematically experienced people do something like the linked method intuitively, without writing things down.) But, it's only half the story. After you learn the definitions and theorems, you have to learn how to apply them to do computations and solve problems. This means working at least a few "easy" problems to learn…

One thing that is hard is that not all areas of mathematics have obvious easy problems to work through or rote computations, although you should clearly do that if those exist. I do think problem-solving and 'getting your hands dirty' is important, but you are also unlikely to manage to reinvent hundreds of years of mathematics by yourself so there is value in reading too. You do also need to learn the vocabulary that other mathematicians use.

When reading textbooks, I would often try and prove theorems myself before looking at the proof - and when I looked at it because I was stuck I would just try and see what the next insight or step and go from there.

I suppose I am thinking somewhat of reading maths papers here which don't come with a nice set of exercises, which probably isn't what we are talking about - but mathematics does move gradually in that direction from areas where the routine computations are laid out to areas where you have to work out for yourself how to make the abstract seem less abstract and where there are assumptions that you will fill in lots of details yourself.

Re: How to learn mathematics: the asterisk method

#55

Post by MayeulC »

sva_ wrote: post #19
tyilo wrote: post #16

I get a 410 Gone when visiting the page.

I'm not sure why it doesn't directly link to http://www.geometry.org/tex/conc/mathlearn.html

> (You must permit one cookie.)

What a throwback to the early days of Internet explorer when it asked you if you wanted to allow a cookie for every cookie the website asked you. I think that was available later as an option, but it became unbearable to browse with that activated later on...

Re: How to learn mathematics: the asterisk method

#56

Post by SPascareli13 »

blaeks wrote: post #5

"First learn. Then understand. Insight requires ideas to be uploaded to the mind first." Yes, our mind has a 'backdoor' which is imho a slow write/read/breathe manifold we all can summon and it's free (both as a freedom, and as a beer).

I didn't really understood this "learn then understand" concept in the article, and also didn't understood the "backdoor", can you illuminate me?

Re: How to learn mathematics: the asterisk method

#57

Post by zaik »

k__ wrote: post #52

I noticed a great overlap in learning math and programming. Programming was easier for me to learn and now helps me to understand math a bit better. Coding a real project is the equivalent to math's proofs, I think. The book "Badass - Making Users Awesome" says, learning something just requires two steps. Perceptual exposure (of hundreds of correct examples) and deliberate practice. I think, math falls short in the f…

> Coding a real project is the equivalent to math's proofs, I think.

Surprisingly, this turns out to be true: https://en.m.wikipedia.org/wiki/Curry%E2%80%93Howard_corresp...

Re: How to learn mathematics: the asterisk method

#58

Post by zimzam »

shurane wrote: post #13
babuskov wrote: post #6

I did this during university, but made it much more efficient. I wrote a program that would work like this: - while reading, instead of copying, the software would ask me to enter "facts" in form of questions with the most important piece of knowledge being the answer. I would type the question and the answer into the software - much faster than writing anyway - after I have gone through all the material, I would sta…

Have you ever tried learning a spoken language by doing this? Like another commenter mentioned, it sounds a lot like Anki Spaced Repetition. It's very cool that you just rediscovered it, though.

FluentForever is based on this method - the initial product was actually a set of Anki cards.

Re: How to learn mathematics: the asterisk method

#59

Post by jedimastert »

paulpauper wrote: post #8

Unrelated, but I am curious about the splash page and redirect. Is this good enough to thwart spiders without having to use Google's captcha? Making pages un-crawlable is a major topic of interest. I read that it's very hard to do nowadays. http://www.geometry.org/human/?i=/tex/conc/mathlearn.html

I think it just stores a cookie, then checks for a cookie before redirecting. I actually have no idea if google's crawler stores cookies or not, there would be good design arguments either way
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