>>6668118 I really should have put >inb4 just studying in the OP, because I realize that is the most important part. What I'm asking I suppose is if there's anything that made everything clearer, like a fog was lifted and you suddenly understood everything a bit more intricately?
>>6668125 The most honest answer to your question is thinking of real life applications to the mathematics you are learning.
Try and find scenarios in your every day life where you could apply the concepts.
For example, think about how you'd calculate the water going down the drain as you're having a shower. How much is coming out of the shower head? How fast is it going? What integration techniques would you apply if you had solid estimates? Stuff like that really made it stick out for me and helped me get a solid undestanding.
Not sure if this is what you were looking for, but good luck.
>>6668125 Seriously just studying. Regular amounts rather than large amounts not often. The only way to be truly good at something is to do it. Some find it easier but study is the main thing. This fog you're referring to is just not enough practice.
Well, I'm still pretty early in my math career (I'm only taking Calc 1 this coming semester), but I went from having my education end at the first grade level to getting my GED and getting high A's in every math class I've taken since (and onwards to a Physics major), so maybe what I'm about to say carries weight.
Yeah, it's studying. Doing exercise after exercise to solidify your grasp on the concept is key. Looking at a problem and how it's solved and pulling it inside out to further your conceptual knowledge (versus just spitting out a memorized formula) helps a lot. What you get out of math is what you put into it, etc.
I think a large part is just having an interest in math. I actually failed math in high school because I found it so boring, but a couple of years later I aced all my college math classes and eventually started taking math classes above and beyond what I had to. It's pretty damn fun once you get into it, and that's also when it becomes easy.
>>6668115 Specifically for math, it was forming clarity over a few months where I went through Artin's algebra and a few other books on basic 'advanced' stuff. Math doesn't really fit together until you get to the 'real thing'- you just haven't seen enough.
Kind of an interesting question, I've always thought I'm pretty smart, did good in school, but then when I was in university I realised my brain wasn't mature enough, I understood what was being said, but I just would NOT let it enter my brain, then there was a period of my life where, like someone mentioned, the fog dissipated, and I UNDERSTOOD everything I wanted to learn. I am aware that my 'intelligence' does not encompass everything, though, there are things I just won't like (philosophy, for example).
But yes, as mentioned, study, read a lot, think outside the box, and most importantly, you have to WANT to learn shit, nigga.
>>6668115 I have a more out-of-the-box reply. I think that math and logic are one in the same. That said, never underestimate the power and mind-training involved with being skeptical. I have done this ever since I was a little kid, and my dad told me to question everything. It has served me well. These days, i am immediately able to view any situation in terms of the most favorable and most unfavorable results. This type of thinking uses creativity as well as logic and reason. I think to be truly good at "math" you must embrace all facets of critical thinking. In other words, "brain training" is a real thing, and you need to do it as part of your everyday life. Meditate if you need to. Do anything that really allows you to engage with your gray matter.
Everyone has a hobby, something they're really into. Try to theoretically teach yourself from a third-person point a view using metaphors related to that thing you're into. That's how I make everything click.
Also -- back to the teaching thing -- try to reach out and explain a concept to other people. If you can teach the concept, you will understand it. Doing this also helps you better wrap your mind around what you're learning.
>>6668115 If you've ever watched "The Great Debate" at ASU with some of the more renown scientists, Bill Nye explains that learning math is like learning another language: learning Chinese in America is going to take you a lot longer than learning Chinese in China. Delve into a world that requires you to know math and you will learn it much faster.
>>6668115 Don't think that you're bad at math, that's one of the first steps and don't think you're stupid because you don't understand, because you probably just need to learn what it really is.
Ex:Cos and Sin. This shit is a pain in the ass, and one day you learn about e^io, which make everything clear. Or circle in a plane, that's shit until you realize its just a cone passing through a plan. So remember, you're never bad, it's just that you don't know about the greater picture.
/fit/ crossover. I just started going to the gym 3 days ago. I can tell you without a doubt that my display of skill, strength and endurance that day as I attempted to squat, bench and row was abysmal. Legitimately struggling to maintain form just lifting the bar with no added weight.
But I like pretty much everyone who bothers to enter such a place, if I return often enough, could well be lifting 1-2x my bodyweight on those same exercises with ease.
Now, I might not have the perfect genetics for muscular aesthetic; it may turn out my abs are slightly asymmetrical or what have you, but they'll definitely get stronger as I keep working them. And your brain is pretty much like that.
Math is no different from English and grammar. I treat it like a language, I learn the vocabulary, and the more I practice it the better I am able to speak and read it fluently.
The problem with American education is that they treat Math like some kind of wild foreign beast that's TOTALLY DIFFERENT from EVERYTHING else, and then tell you if you're not doing well in it then you're just "not a Math minded person" and act like it's okay.
Good mental hygeine helps alot. Remove the unnecessary, and replace it with something mentally stimulating. There are alot of habits that can really inhibit your ability to think.
Back when i was playing league of legends and wow for 12 hours a day + constantly scanning reddit, i really struggled learning anything new. After i removed them from my life and started reading / exercising / getting involved in actual discussions, it felt like my brain actually started working again.
>>6668115 >there has to be something you did that made everything "click"? nope.
well, what probably helped was spending most of my free time in my childhood playing with legos, and having an awesome dad who read me the number devil when i was like 8 and got me a bunch of videotapes on famous math problems in middle school, and reading thousands of books as a kid, and getting put in advanced classes for all but kindergarten, 1st grade and 2 years of middle school, and making friends with other smart people rather than anti intellectual dumbfucks as a kid, and hell even spending much of my adolescence playing strategy based computer games might have contributed.
but its not like there was just one thing i did or one point at which everything clicked, it was all part of a 22 year long and still ongoing process that isnt going to end until i am dead or have accumulated enough money to stay continuously high on coke for the rest of my life.
>>6668115 I treat math like a mechanism; like a system. I love taking shit apart and seeing how it works; learning the rules. Math is pretty much nothing but rules. Those rules describe patterns. When you understand the patterns and shapes generated by the rules, math is actually quite enjoyable.
I always get this feeling that if I studied for say 1 hour per day for a week or so before some sort of test that there's still the risk of failure and I could have spent 7 hours playing vidya or otherwise enjoying myself and get the exact same result.
TL;DR There's no guarantee that I'll pass something even after studying so I'd rather play vidya than waste a few hours achieving nothing.
I'm 31. I am now going through this process. I had to shake off a lot of bad bullshit ideas from my youth and internalize the best moral ideals. I did it through continental philosophy as an antidote to Catholic dogma. The philosophical ideas and the mathematical ideas are truly inseperable. I was frustrated with unlinked, contextless rules of symbolic manipulation and did not see the connections, and was always told, you'll understand why when you take the next class. Educational striving toward a heaven that never revealed itself within their institutions. The symbols were... unimportant, disconnected. The pointless manipulation games, disjointed Theorems that promised absolute truth but delivered tranacendental functions and irrational numbers with which we were meant to reason. For me, it took ... existential experience as well as academic experience... or maybe I was just chasing dangerous pussy down dark alleys while my blood ran with the fire of youth. I don't know, man, but if you have the true will to learn the language, the way will be provided. Good luck, and Godspeed.
you have to make math personal, and not something you're just taught at school.
this is why there's a ton of good programmers out there, but only a few mathematicians. people get to get good with computers on their own, but with math it's always "teach me sempai" and that's why they suck (not dissing collaboration here, it's a different thing)
then you have to develop a taste. math can be ugly, unnecessarily wordy, useless, and convoluted, and if you won't learn how to discriminate stuff you'll get stuck and disappointed. then there's important stuff that's just complicated, or you didn't do your groundwork, and you have to suck it up. it's a balancing act, and it has to take time.
the last thing is constant revision. solved problems, learned theories, that's just minor stuff. now what's really important is how you get there, asking why were you stuck, and what made you click. there's probably less than 20 "meta-patterns" out there, the trick is to start looking for them, otherwise you won't see it. start a notebook.
>>6676856 That's somewhat true, I remember back in High School I lost 25 points on a test for having a miscalculated angle which accumulated to a wrong result, even though the method I used for solving the problem was 100% correct.
There is a genetic component, that cannot be denied, but there is also an environmental component, that cannot be denied either. People are the product of the interaction between their genetics and environment. Which is obvious.
Motivation is a folk psychology concept that should have been discarded long ago. Anything to do with the Freudian notion of "id" or "ego" should be immediately thrown in the garbage can. Skinner's work was a big step forward in terms of showing us how behaviors in animals are really established, unfortunately cognitive psychology has moved our understanding backwards significantly by undoing and dismissing all of Skinner's excellent work.
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