What's the best way to think about mathematics? What's the best advice you have ever received about learning math and approaching math problems?
Ok, so I'm terrible at math. Not just terrible, but atrocious. I'm one of those people who proves that innate intelligence doesn't correlate well with all subject areas. In high school and college, I was a great student in almost all subject areas, from biology to English language and literature. However, when it came time to do math, anything with symbols and numbers, I was just atrocious at it. Not just atrocious but almost learning disabled bad.
I think that my stupidity in math isn't something innate however. At some point, I was never able to grasp just how to approach math theory and math problem solving. I am certain this is the case because there were subjects as a youngster that I was terrible at until I taught myself to look at them differently or learn them in a unique way. Let me give you some examples so you'll see what I mean.
1. I was a horrible speller in third grade. Just terrible. One day, I tried a new approach. I looked at any word I needed to spell and I would sound it out emphasizing every single syllable. So for example, if I needed to memorize "automatically" I would say outloud "AU-TO-MA-TEE-CALL-EEE"" and that one simple trick really attuned my mind to spelling in a way that all previous methods didn't.
2. When learning bio, I realized that a good to think of molecular was to conceptualize it as though the whole system was like a Rube Goldberg machine
. I would imagine in my head one process X causing Y which result in Z occurring and so on. It wasn't the best approach but it certainly changed how i thought about molecular biology and immunology. Plus, I did well in those classes, becoming one of the best students in that subject matter.
3. This doesn't have to do with scholastic subject matter but it's still worth relating to show how powerful a simple conceptual change can have in our ability to perform tasks. As a kid, I read this book called The Einstein Factor
and in it the author related a story about how a kid he knew drastically improved his batting average. The advice the kid received was to imagine a small speck or dot on the ball that was being pitched to him and try to aim for that dot when hitting the ball. As I was playing little league at the time, I tried this technique and the result was miraculous. I started hitting balls that had previously eluded. What was more incredible is that somehow by imagining this small speck or dot, I also learned to lay off the poorly pitched balls and thus build the patience to hit the best pitches to me.
These examples changed my life in one way or another and it taught me the power of concceputalization as a tool for learning and understanding. Does anybody have anything like this to offer me? Some sort of advice or perspective that will help me finally understand the basics of math and be able to solve the math problems. I know I am overlooking something in approaching math and I am certain that it's right there but I am somehow unable to see it.
So the hive mind: Please tell me of any tricks or advice you know about how to approach math (by math I mean GRE Level math