So, I'm now out of college (English degree), but I work with engineers daily (I'm a technical writer). I would like to become better at algebra/calculus so that I can understand what's going on better. I was talking with my boss about how odd it was to work with engineers when I'm so bad at math and he asked me to explain how I "see" math. Apparently I "see" it "discreetly." For example, if you ask me how I see 2+2=4 I say I see 2 dots, I put 2 more dots on, and now there are 4 dots. I multiply by adding in groups. When you get to square roots and (especially) imaginary numbers, I instantly become lost because I can't see how you can do that to an object. Apparently he and the other engineers on staff see numbers on a continual line and there are rules you use on how to manipulate things on this line. So they see 2+2=4 by actually going up this line. There are many lines that relate to this main number line and that is where imaginary numbers apparently come in (I may be butchering what he said, it quickly got beyond me).
I don't know if this helps or not, but as horrible as I was at algebra I was GREAT at geometry. I'm also great at memorization, literature, philosophy, and other humanities (except I can't draw or paint to save my life). I can discuss all sorts of abstract philosophical questions, but when it comes to math, if I can't see it, I can't do it.
What I want to know is if there is a way I can teach myself to think of math on these lines instead of always having to have a concrete object to manipulate. If I could lose the dependency on having to work with a concrete object, maybe I could teach myself algebra again and understand these complex ideas that you cannot tangibly do to an object, but in theory can be used to reach tangible results.
Sorry if I didn't make myself clear. I have not studied any math in years. I loved it in elementary (I can still multiply 3 digit numbers in my head), but once we broke into algebra, it was like hitting a brick wall. Now trying to tear that wall down.