What is the best way to study mathematics

Once open a time a lady wanted to hire a cook for her restaurant. She interviewed many candidates and finally she selected the one who impressed her in the interview. Lady was very impressed with his knowledge of cooking. He was like a cooking encyclopedia.

On his first day of the job, lady thought of taking his trial. She asked him to cook “Kadai Chicken“. She started eagerly waiting for the food. Food was served and she had her first bite. It was pathetic in taste. She could not swallow even a single bite of it. The lady was shocked and asked the man “It is so horrible in taste. Are you sure you can cook food?” He replied, “Madam, sorry for the food. Actually I have never done cooking before. I just had taken lessons on cooking from experts and during my training classes, I saw the instructor cooking. Also, I have read and learned all the recipes of making excellent food.”

Moral of the story is, there is a difference in knowing how to do things and actually being able to do things. By merely just knowing how to do things does not make you expert on actually doing it yourself.

Learning Mathematics is like learning the art of solving problems (actually doing) and not just knowing formulae and concepts (acquiring knowledge). So if you want to improve your mathematics, you need to focus more and more on problem solving instead of just reading theories, formulae, and solutions.

Following are some instructions/tips that would definitely help you learn mathematics better:

Always study Mathematics sitting on a study table with paper and pen to use: More you write, better you remember. Even if you are reading concepts and learning formulae, write it and learn it. Mathematics needs a higher level of concentration. Whether you are solving a problem or reading mathematical steps of a solution you need better concentration and focus. So my suggestion would be to sit on a table chair with no disturbance around. If your room is noisy, you can put cotton balls in your ears.

Spend more time on solve problem instead of reading solutions/theories/formulae: More you practice, better you would learn. It is very important that you solve problems to learn topics in mathematics. Just understanding concepts and learning formulae would not be sufficient to be able to solve questions in exam. In mathematics more than 50% of the knowledge comes through tricks/methods involved in solving problems. If you don’t practice questions, you don’t acquire this knowledge. In fact learning in Mathematics starts the day you start solving problems with pen and paper.

Step by Step learning:Learn theory and formulae first. Practice them in written. You should start reading solved-examples only after learning the concepts and formulae. This is must for easy understanding of the solved-examples as in every questions you use multiple formulae. If you don’t remember formulae well, you will take more time to understand the solution. After finishing examples, you need to solve level-1 (easy-to-average level) problems.

How to decide level? If you are not able to solve, go through solution. If you can understand the solution by just glancing it (as a hint), then it is level-1 (easy-to-difficult) problem. If you have to go through complete solution step by step and then finally you can understand the solution, then it is a level-2 (average-to-difficult) problem. If you find it hard to understand solution, it means it is level-3 (difficult-to-very difficult) problem. These levels are relative as every student has his own potential.

Once you have solved 30-40 level-1 problems and have thoroughly revised them to a level that you remember the ideas of most of them, you can then move to level-2 problems. Practice at least 30-40 level-2 problems. Don’t solve level-3 problems. They are not important and you can confidently leave them. Trying to solve them can be negative as they can break your confidence in the topic.

Revision and Re-Learning: Generally when you are not able to solve problems, you see their solutions. But you do nothing after that. In 1-2 weeks time you forget the solution. I am sure if you face that question again, you would not be able to solve it. So what is the point spending time on the question at first stage.

I suggest after reading the solution, you try to solve it yourself with paper and pen. Don’t worry if you know the solution now as you have read the solution. Mind will retain only if you do it with your hands. Then, mark the level of the question for future revision. After few week, try all questions again which are level -1 and Level-2. Do them like a test. Shortlist 50 such questions and take a 2-hours test. Even before exam, when you are confused what to revise, take out Level-1 and Level-2 (or just level-2) problems and revise them. If you don’t mark them, you cannot revise them.

Don’t refer solutions without trying problems: With all the books and study material around, most students have a tendency to read a question and immediately jump to see the solution. This is totally wrong and if you continue this for a long time, you will become dependent on solutions and you develop a bad habit of surrendering. Where as in mathematics, you need a fighting attitude. Try hard to crack the trick. I know you don’t have too much time to spend on each question but at least in each 60-70% questions you should attempt yourself first (spend 10-15 minutes average time on each question) and then refer solution. It is very important to try first as your brain develops only when you put stress on it.

Generate your Interest to perform better: No doubt, People who like mathematics perform better than others. As it involves applying tricks (like in puzzles and games) to solve problems, you perform better if you are liking what you are doing. You need to do problem solving when you are willing to do it. Feel proud if you are able to solve a question, feel thrilled rather than feeling frustrated when you take help of solutions (or help of others) to solve the problems. As I suggested in “Revision and Re-Learning”, those questions which you are able to solve through solutions, solve them again. When you are able to solve them again, you will feel good and that will help in generating interest.

Make Flash Cards for better learning: To learn formulae and even tricks involved in problem solving, make paper based card (paper sheets) and keep them with you. You can memorize them even when you are not at your desk, may be when you in a car/bus, in school, while walking, etc. This helps in building your knowledge, generates interest and above all you are utilizing your non productive time.

Help others if you get chance: If somebody needs your help in solving a problem and you know how to solve it, never miss the opportunity to help her. This generates confidence in you as well as your interest would also go up. More confident you are, better you can think.

-Manmohan Gupta
(HOD Mathematics, VMC)
Mathematics is Fun