How to Study Mathematics

by Murli M. Gupta, Professor of Mathematics, The George Washington University

Mathematics seems to be a difficult subject for many people. One often hears phrases such as: ``I was never good at math'' or ``Math is/was my worst subject''. I even hear such phrases at social gatherings where once a person discovers that I teach math at college tells me that he/she was never good at math and perhaps thinks that I must be from outer space to be able to teach math, especially at college!

I talk to many students who are taking math courses, from me or someone else, and who have difficulty with their math courses. I often hear: ``I have done all of the problems in the book''; ``I am working with a tutor''; and ``Why am I doing so poorly on my exams?''. I explain that it is you, the student, who must learn the material that is presented to you. A tutor, like your professor, can only assist you in your learning process. Working with a tutor is no guarantee of success.

What guarantees good results? What are good study habits, especially for math? Here are bits of advice that might help.

A math book is not something where you could engage in passive reading. In math learning you must do things. You should have a paper and pencil when you read any math book. Take a lot of notes. Reading the examples in your book is not enough. You should actually do those examples yourself as you read them. This would allow you to learn the manipulations and intricacies involved in getting from one step to the next, thereby improving your math skills.

It is important to do your homework. I often hear: ``I have done all of the problems in the book''. I ask: are you able to do these problems without any help? Many students leave their books and notes open when they do the problems and constantly check to see how the other problems were solved. I see this in my classroom when I give a problem and ask the class to solve it. This is fine as an initial technique but the fact is that eventually you should be able to do the problems on your own, without any help. No books, no notes, nothing!

How are you going to do this? First, select a few problems and solve them perhaps with help from your books or notes. Second, try to solve these same problems on your own with the books closed. When you get stuck at some point, check your previous work to see how you went past that point. Repeat this process until you can do the complete problem without any help whatsoever. Now find a few more problems of similar type and see if you can solve them without any help. Once you are able to do so, you have learnt the technique of solving this type of problems. This will build your confidence in your problem solving skills.

Word Problems

Word problems seem to cause a special sort of fear in many students. In your personal life, you often face situations where you have to decide what the problem is and how to go about solving that problem. The word problems are somewhat like that! You have to decide what the facts are, how to go about solving the problem, and actually doing it.

There are four crucial steps:

Get the picture (READ);
Decide what to do (MODEL);
Do it (SOLVE);
Give the solution (INTERPRET).

READ: First, you have to understand what the problem is. Don't start solving the problem until you understand the whole problem. You must READ the given word problem, at least twice. Draw pictures and/or make a mental picture of what is given and what is unknown.

MODEL: Assign some symbols to the known and unknown quantities and decide how these symbols are related. Read the given word problem again to write down the relationships between these symbols. This is your mathematical model. Check for accuracy!

SOLVE: Once you have a mathematical model of the given problem, use the appropriate techniques to find its solution. Make sure that the solutions are relevant to the physical situation described by the word problem. Check for accuracy!

INTERPRET: The last step is to interpret the solutions in terms of the original word problem. Make sure that the units are correctly stated.

A final word. When you need help, do not hesitate to go and see your professor and your TA.
Most of my colleagues are happy to help their students in any way possible. Certainly, I am. Good luck.

Author: Professor Murli M. Gupta
Mathematics Department (Monroe 221)
2115 G Street, NW
Washington, DC 20052
Office Hours for Fall 2007 semester:
Mondays and Wednesdays 11:00-- 12:30 p.m., and by appointment.
Telephone: 202-994-4857
FAX: 202-994-6760
Email: mmg@gwu.edu
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