In this article, I’m going to help you achieve perfect grades in Calculus class. If you have great determination, 100% is reachable, and you won’t have to sell your soul to get there.
Today, I’m going to focus on the art of practising intelligently.
I consider this the most important piece of advice, yet also the most obvious, that I can offer you. You aren’t born with great mathematics abilities, you need to develop them! Scientists are learning more and more that the brain is very adaptable, and never stops changing. By practising calculus often, you’re creating new connections, reinforcing good habits, and speeding up the logical thinking necessary to solve problems efficiently.
Like any habit, the more often you exercise it, the more your brain makes it natural. This means practising at different times of day, and practising on a consistent basis.
Textbooks contain thousands of problems for a very good reason; because you’ll need to drill the fundamentals of calculus into your head. It isn’t sufficient to understand why a certain theorem or law exists; you need to use it over and over again until you know it and understand it personally & intuitively.
In calculus textbooks, you’ll often have different types of problems for each chapter:
Problems that help you understand a theorem or technique
These are very important to do. They’ll let you know if you understand the basic premise of the chapter.
Problems that give you the opportunity to put it into practice
This is the meat of the chapter. It’s the drill that will commit the technique to your mind. Do all of these.
Problems that apply the technique to real-world problems
I personally don’t find these very important. They might be helpful if you’re having a hard time finding the practical application of a technique. It will probably be more helpful to kinesthetic learners.
Challenging or integrative problems
These are very useful as review problems. They will let you know if you’re ready for an exam, or to move on to the next chapter.
How to Practice
I follow these steps when going through the problems section of my textbook:
- Start from the beginning
- Do each problem one after another, checking to see if you have the right answer after each
- If you make a mistake, redo the problem the right way. Otherwise, you’re not learning from your mistakes.
- Don’t move on to the next problem until you 100% understand your mistakes in the last one
- You may skip a question only if the answer comes very naturally to you
Don’t get frustrated from your mistakes. You have to understand that making mistakes is one of the most important parts of learning. In other words, you must make mistakes. Everybody, even the most gifted, make mistakes.
Also, try to always end a practice session if you’re too tired to concentrate well. Pressing on when you brain is not in an awareness state is like trying to clean a spill using a water saturated cloth. All you’ll end up doing is spreading the spill.
I hope I’ve helped you become a better math student. I appreciate any feedback.