A Problem: Actually Doing Math

[Cfire]

I suppose the best place to start would be with some background information.

From pre-school through eighth grade, I went to a private Montessori school. After that, I went to a public high school. I absolutely did not like it. I did well in 9th grade (A's), but was quickly fed up with how I was treated by the system (and some retrospectively inane personal issues) and, in what may have been the most immature decision I've ever made, I stopped paying attention all class for almost every class. What's worse, I stopped doing most of my homework and never paid attention to when tests were coming up, subsequently getting by with half learning the material on the test by looking at the test and working my way through. I graduated high school taking all honors and AP courses, but with probably the most mundane record I could have thrown together.

This is all a very general story which only comes into play when looking at the context in which I find myself. I am currently in my third year of university, and after being an absolutely empty, unmotivated student (getting decent grades, fortunately) focusing in law, I have been awesomely inspired by astrophysics. EDIT (clarification): I am actually an astrophysics major now.

For the sake of the people reading this and clenching their teeth at the dullness of my academic history, adequate context has now been provided to get to my point.

In high school, I went through calculus I.
In high school, I did not pay attention in math since Algebra II.

I'm currently taking precalc at my university, and I understand the concepts very well. Nothing is a mystery to me (so far), I always follow what the professor is doing in class, and I can do problems in the textbook relatively easily. There is some deficit in my mathematics when it comes to a lot of rules of algebra that I forgot and am quickly relearning, which have lead to a number of very stupid mistakes that I doubt I'll make again.

The problem is that I believe I understand the mathematical concepts, but have received terrible grades on the test and two quizzes that we've had so far.

Generally, I'll be reviewing for a test and will have the following thought process:

"Well, I really think I understand all of this. I suppose I should do practice problems just to make sure. Alright, I'm rather confident that I know this." Fast forward to the test or quiz, and I start to think, "Wait, I understand the concept of this problem but I just don't know how to do this particular one. Man, why did the professor have to make this slightly harder than most of the problems in the book and most of the problems we've done in class?"

I'm not under the delusion that this is an external lotus of control (as the psychology term goes), and am well aware that the responsibility lies on me to make sure that I do well.

It seems to me that the best way to fix my problem would be to practice a lot of problems. Many more than I've practiced so far. Hours of problems a day.

My question is this: would you recommend that I just bust out problems until my brain gives way, or is there some sort of procedure (systematic or otherwise) that you think I should try in order to solidify my ability to do this math?

I'd appreciate any help/advice/comments, be they understanding or critical, short or long, soft or blunt.

P.S. The creation of this post in itself was rather reflective, and in writing it I have somewhat clarified my problem for myself. If my post seems to flutter between issues, I may just not even have a grasp of my True Problem. If this is the case, I hope that someone older and wiser than I am may be able to call me out on it.

P.P.S. I like to think of myself as being somewhat familiar with the forum rules (although I admit I have not read all of the rules thoroughly, and none of them recently), but this may not be the proper place for this thread. I apologize if I indeed made a mistake in where I posted this.
-Cfire

 

[IttyBittyBit]

If the road to studying well is 100 steps long, by knowing you have a problem and realizing that you have to rectify it, you've already taken 99 steps.

You already basically know what your problem is. You just need to solve more problems. There are really no shortcuts here; just pick up your textbooks and start solving away.
Now some people might come in here and say 'oh such-and-such book is obviously superior, it has better problems, easier to read, etc.' but the reality is that your professor is probably going to be giving you problems out of your textbook anyway, and treatment of topics varies slightly between books (for example, different books often give widely different definitions for certain polynomial sequences) so your best bet is to stick to your course textbooks, and try to solve all the problems there if you can. Learning math is a gradual process and you can't rush it. I have a degree in math and I remember sometimes solving hundreds of problems in preparation for an exam.
Also, one issue that many people have is that they try to learn math by just reading the book. That won't work. You have to have a pen and paper in one hand at all times, and use it to try to verify things you have trouble on, for example. Learning math is all about learning the techniques. It's more like art than anything else. You can never become a painter just by walking around in art galleries all day.

I hope I've helped.

 

[Cfire]

I hope I've helped.

Cognitively, I know you've helped a lot. Speaking from experience, probably more than I realize as I'm writing this.

I can't understate how much I appreciate a good response, especially when you could look the other way.