You may have conquered more than a few complex math concepts and problems, but math is a diverse and comprehensive topic. You need to go further to keep up with new math topics that have ever-increasing complexity. You will understand the problem better if you explain it to others. You may think that you understand a math topic, but by teaching others about the same topic, you may encounter details that you haven’t touched before. It’s a universal troth that you should be aware of. True grasp of the learning material can be achieved if you teach people about it. It feels very different when you are helping others to understand the problem.
You also need to guide the person to break things down into manageable chunks, so he will get better understand about the problem. Even if you are getting more proficient in working with math problems, you will make mistakes once in awhile. In fact, it could be a matter of time before you make another mistake. You shouldn’t see mistake as a setback, it is actually a part of your progress and learning process. After you make a mistake, regardless of your comprehension on math topics, you should know why such a mistake could happen. It may happen because there’s a gap in your understanding and you are not expecting that a math problem can be approached from a direction that you haven’t expected previously.
If you want to improve your math skill further, it is important that you have the right skill. As an example, you need to use mechanical pencils that create cleaner lines. You also need to separate eraser, so you are able to more cleanly erase mistakes. With improper eraser, you will only create smear all around the sheet of paper. Cheap eraser won’t be helpful enough in tackling with difficult math problem. In many cases, you will be able to perform better if your solutions look very neat. You need to do things in an organized manner and try to vertically work with your problems. Do this one step at a time. If the math problem is particularly challenging, you won’t get better results if you work horizontally. It is true that you may not get point for neat and well organized procedure, but this extra effort will pay off immensely.
If you want to work on difficult math problems, it is important that you choose the right time. As an example, you will only do yourself a disservice if you constantly tackle difficult calculus problems very late at night. If it’s 9.30 PM and time to prepare to sleep, then you need to stop working. You will have very slow progress if you push yourself constantly. Fatigued mind won’t perform well and you may end up staring at a problem for one hour or more with little result. You will start to make one silly mistake after another, making things slower for you. If you are facing difficult problem, you need to internalize it and find out the best way to proceed.