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I tried taking a trigonometry couse. Something I aced in college. Some parts were easy. But I kept running into references that I could not remember.
Eventually I just had to back to pre-algebra. Most of it is trivial but I do keep finding things I had completely forgotten.
"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?
This technique is often criticized for teaching only the writing and rough meaning of characters, while ignoring actual usage and pronunciation. However, for me it was an absolute revelation that allowed me to finally break through and eventually achieve something close to fluency in the language (passing the highest level of proficiency exam, the JLPT N1).
Later, I began to comprehend how the method itself--which is kind of abstract and involves quite a bit of raw repetition--achieved its amazing results by building a rock-solid scaffolding in my brain upon which I could hang all of my Japanese language knowledge. If learning is the process of building new knowledge structures in the brain, then understanding is the process of linking existing structures into tightly integrated patterns which can support higher-level reasoning. The stronger the base structures, the deeper the understanding that one can develop on top of them.
As for the "backdoor", I believe the original comment was referring to the way that the brain seems to naturally (and sometimes effortlessly) work to strengthen the connections between knowledge structures that are sufficiently "exercised". So, one can use conscious efforts to simply reinforce the raw knowledge as much as possible, and then trust in the "backdoor" to reveal the important insights and connections as they are uncovered.
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This is the essence of the method described in the link, and the ability to pull it off is called "mathematical maturity". How one acquires mathematical maturity is the matter of some debate.
> How one acquires mathematical maturity is the matter of some debate. The asterisk method just reminded me about this (how to draw an owl): https://www.reddit.com/r/funny/comments/eccj2/how_to_draw_an...
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…
(I am not affiliated in any way apart from being a happy user)
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.
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> How one acquires mathematical maturity is the matter of some debate. The asterisk method just reminded me about this (how to draw an owl): https://www.reddit.com/r/funny/comments/eccj2/how_to_draw_an...
If you stop at step 5 and ignore the rest, including step 10 which includes asking people who can help you understand.
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This. There's also Mnemosyne, SuperMemo, and others. More here: https://www.gwern.net/Spaced-repetition
This site has many useful methods and lists its technicality in details. Thanks.
[1] https://www.gwern.net/Nicotine
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You've implement some lite version of Spaced Repetition! There's a tool that does exactly that and it's called Anki
This. There's also Mnemosyne, SuperMemo, and others. More here: https://www.gwern.net/Spaced-repetition
Lots of great Flashcard apps out there. Definitely a great way to learn - especially things that fade quickly if not using them regularly (looking at you, Powershell ;-p ).
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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 was also better at solving problems involving trigonometry than anyone I knew - including my professors.
You could, of course, argue that if you needed to use it every week, you would know all the identities merely by using them so much. Don't assume this is correct, though. One of the reasons I used them so much is because I had memorized them. My colleagues who used them as often as I did and who didn't memorize them did not, in fact, have them burnt into memory after so much usage.