After only three meetings with my math instructor I have learned why many math students don't do well in the class. Math requires "thinking outside of the box," to use the common administrative cliche. You have to approach problems using all of the standard processes, but then you've got to come up with completely new methods. Students don't want to do this, it requires too much effort and can take up too much time. Why try and figure out a formula that some ancient mathematician has already done 1,000 years ago? Why prove something that's already been proven? These thought patterns alone hold students back from success.
To do well students need to be active during lectures and participate. Students should ask questions rather than accept what is given to them by the instructor without any thought. Give the teacher a problem to work out on the board. Do the problem along with the teacher, working out each step in a collaborative effort. Instead, students will just sit back and wait for class to end by watching the teacher write various runes on the board.
Math isn't just about completing homework assignments. When students are at home they should research on the internet topics that were brought up in class. The library has plenty of resources on the history of math, mathematicians, and the wide range of math subjects. Students don't want to do this, because again, it takes up too much time and effort.
Students forget anything they've learned, hoping that they will never see it again. Unfortunately, they do see it again, but they don't remember seeing it in the first place. In math, there are basic skills that students shouldn't forget. They should use these techniques and apply them to future problems. These methods serve as a springboard for solving a problem that the student hasn't seen before. If every problem is approached like it's an alien script then the student won't know where to start and what to try, ultimately failing.
Confessions
I'm just like every other math student. Most of the time I sit in class, copy down what the instructor writes on the board, and accept whatever statements s/he makes. At home I do my assignment, skip the hard problems, check my answers (the solutions are usually in the back of the book or in the solution manual), and forget about what I've just done. However, I found that when I "cheated" on my lazy strategy of apathy toward the subject, and become more involved, I did better.
I have survived math courses by taking the Dr. Jekyll and Mr. Hyde method. Sometimes I'm the lazy student, other times I'm the active math pupil. As of now I'm the lazy student, probably due to the long summer. If only I could be one of those kids that just gets math automatically, then I'd be set.
