How to learn mathematics: the asterisk method
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How to learn mathematics: the asterisk method
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Re: How to learn mathematics: the asterisk method
#2I’ve been doing this for 25+ years without knowing it had a name
Re: How to learn mathematics: the asterisk method
#3This 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 how to crank through rote computations, and a few harder ones to learn how to think through novel applications.
If you can't solve problems with the material you've supposedly learned, you haven't actually learned it. (Otherwise, what did reading all that stuff really accomplish? You picked up some cool vocabulary words?)
Re: How to learn mathematics: the asterisk method
#4I love it. and it also applies to all kinds of learnings. I even love how the captcha is just a link.
Re: How to learn mathematics: the asterisk method
#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).
Re: How to learn mathematics: the asterisk method
#6I 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 start the Q&A part of the software, which would ask me all the questions in either random order or sequentially (it was an option).
- at first, it would only show the question and wait for a key press to show the answer. After the answer was shown, I could mark whether I knew the answer or not. If not, it would mark that question to be asked in the next loop. This is basically the same as the asterisk method.
- once I got through all the questions, it would go into next pass, asking only those questions that I didn't know the answer to. And then filter out the remaining ones, and loop again and again until the all answers are known.
- then I would restart the whole system with all the questions to check.
What I learned after using this for about 2 years, is that there's a short term memory problem. Often I would know some of the answers on the first pass, but a week later I might forget it.
I found a way that works much better: Even if you mark that you know the answer, it will come up once again in the next pass. If you mark that you know it twice in a row, only then it would be removed. For some reason, this made the knowledge stick much better.
Re: How to learn mathematics: the asterisk method
#7I 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…
You've implement some lite version of Spaced Repetition! There's a tool that does exactly that and it's called Anki
Re: How to learn mathematics: the asterisk method
#8Unrelated, 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.
Re: How to learn mathematics: the asterisk method
#9> If you read something which is difficult to understand, stop and think about it until you understand it clearly.
Ahh, ok.
Re: How to learn mathematics: the asterisk method
#10I love that there's a focus on improving learning methods in general and how it can apply to anything. Even captchas are utilized in a way that shows their potential when they're given less of a burden!