Learn by doing
You can't learn to play basketball by listening to lectures and reading the textbook. It's the same with doing mathematics. Going to lectures and reading the textbook are important, because they show you what you need to know. But you can't learn to do the mathematics, unless you do the worksheets and homeworks.
Finish what you start
Do every homework and worksheet problem from beginning to end. Find all of your mistakes, no matter how small, and fix them. It doesn't matter how much mathematics you know and can do, if you make arithmetic or algebra errors in your work.
KISS
If you can do a problem using only 3rd grade math, do it that way. Otherwise, use only 7th grade math. Use precalculus and calculus only if you absolutely must.
Why is it right?
In the real world, no one knows the right answer in advance. Even if you have the right answer, no one will listen to you, if you cannot explain why it is the right answer.
Trust no one
Never do anything because it is what the instructor, tutor, or book said to do. Do things only because you understand why they are right.
Put it in writing
Don't do anything in your head. Write it all down. You can find your mistakes and fix them more easily.
Plan ahead
Don't start doing calculations or writing up your answer, before you read and reread the question slowly and carefully. Make sure you understand exactly what is asked for. Sketch out a rough plan or strategy for getting the answer. Only start working after you know what the game plan is.
The tortoise wins the race
You will finish faster, if you work slowly and deliberately. If you rush, you will make more mistakes and not spot them. If you work slowly, you can check yourself as you work and catch your mistakes.
Department of Mathematics