I'm currently a Calculus III student. I enjoy math a lot, but only when I understand its beauty and meaning. However, so many times I have no idea what it is I am learning about, althought I am still able to solve problems pertaining to those topics. I'm memorizing the sounds this language makes, but I dont understand them. I think a big reason why most children and teenagers really dread math over any other subject is because the only thing that is taught to them is equations and numbers, and to them is not being explained its significance. For if people really knew what it all meant, then they'd realize it's probably the most important think they should ever study. Even in college, at this relatively high level of math, they still do not preach its meaning, but rather scare you into cramming pages after pages of material so you can pass the next exam. When you have passed the exam, then it is safe for you to forget the material you just absorbed. This is the reason I often find myself bored of studying my current topics. For some things, I see the intuition behind it, and those are the things that keep me interested in calculus, but its often so hard to come up with a good meaning of what I'm learning all by myself.
It took mankind hundreds and thousands of years to come to where we are with math, so I dont expect to understand its true meaning in an hour, but I'd really like to. The school curriculum, here in America at least, doesnt teach meaning or utility. This is the reason so many youngsters always ask "when will we ever need to use this stuff?"-what a naive question this I learned to be. So I guess what I'm trying to say is that I've grown bored of this material, as we often cram 2 full sections of a topic in one day. Its impossible to keep up with its meaning, but if I am to survive this course along with more advanced courses to come, I must be able to understand its meaning. My textbook doesn't help me with this issue though- no math book can really teach intuition, but they dont even attempt to. They barely even go into the history of the current topic, and thats one of my favorite parts-I like to read about how a normal man came up with this theory that revolutionized the world. It makes math feel human to me, and that I too can understand it like men before me.
Most of the question answerers on this site are mathematicians, if not at least one in training. This means you have come to where you are by understanding what you have learned in the past. How have you done this? How have you been able to connect all the pieces? What are some good resources that will help in what I hope to do? How do I stop being a robot, and actually connect with what I'm learning?