HOW TO STUDY MATHEMATICS

These notes © by Professor Clare Hemenway, Department of Mathematics.

The original version of these notes, with full graphics, is available from Professor Burger's web pages.

Before beginning you should review some general advice on studying.
 
 

GET POSITIVE!
You may be thinking to yourself "I hate math" or "I was never good at math". You may have heard the term "math anxiety" and feel that you fall in this category. I know it is a difficult thing to do, but you need to control your mind and change your attitude.

Give the course and more importantly yourself a fair chance. The way to do this is to agree to work in your mathematics course. Many of you are more mature than when you took previous mathematics courses. This maturity factor and the desire to learn are extremely important and can make a tremendous difference.
 

PREPARE FOR CLASS
Do the "homework" assigned and be sure to look it over before you come to class. The material presented in class usually builds on the material presented in the previous class. If you have not understood the previous material, you will quickly become confused. If you could not get the homework done because you "got stuck" ask questions at the beginning of class or get help from other sources as soon as possible before class in the Tutoring Lab.

Prior to class, it can also sometimes help to spend a few minutes previewing any new material. At this point you do not have to understand everything completely, but this quick preview will help you to understand your instructor's explanations.
 

ATTEND CLASS!
Every time you miss a class, you miss important information. If you must miss a class, contact your instructor or fellow classmate to get the reading assignment and homework. But the latter is no substitue for attending: if you attend you get the best notes for yourself and you get a jump start on understanding and learning the new material. You can also ask questions right there and then if you do not understand something.
 

PARTICIPATE IN CLASS
Pay attention and if you do not understand something, do not be afraid to ask for clarification. If you don't understand, neither do several other students. Many students are afraid to do so because they think that they are asking a "stupid" question. Most instructors do not feel this way; they want feedback from, and interaction with the students. This makes the class more interesting for everyone.

Also, while in class, you should take careful notes (not just copy the math from the board). Write legibly so that you can understand the notes and procedures later.You need not write down everything the instructor says. You need to find a balance between understanding the lecture and understandable notes. This varies with individual learning styles.
 

DO THE HOMEWORK!
This is the most critical commitment you must make and it involves many facets. Don't wait until the hour before class and move directly to the exercise set. In general, this is not a successful strategy. Be prepared to spend 2 to 4 hours of homework for each class meeting.

• First, review your notes as soon as possible after class.

Fill in any details which will make your notes clearer, or put question marks where you are confused.
• Next, read the text.

A mathematics text is not a novel. Mathematics texts should be read slowly and carefully. If you do not understand something, reread it. Do not just skim the examples. Work them out yourself on the side and check your work as you go. In general, you should read a mathematics text with a pencil in your hand.
• Now you are ready to tackle the homework.

Learning algebra is like learning to play the piano or learning to play basketball. You cannot become skilled by simply watching someone else do it. You must do it yourself. Your assignments must be worked conscientiously and completely. Make sure you write it neatly and carefully.
• Do your homework in a step-by-step manner and include all the steps.

Most mistakes are made because a student tries to do too much in their head. Write the steps in longhand, so that a friend could understand what you are doing. Most importantly, make sure you read the question, write the question and understand it is okay to be slow at first, but you should through practice, pick up speed at solving problems.
• Check your answers.

Many books contain answers to some of the exercises and you should check your answers. Sometimes, you can just estimate if your answer makes sense and sometimes in an algebra problem you can substitute your answer into the original problem and see if it works. Or you and a friend could check each other's work.
• This, along with doing the homework, is the most important ingredient for success in mathematics.

However, all too often, students complete the assignment and put the book away. It is critical that you take some time to reflect on the work you have just done and that you understand why you solved the problem the way you did and that you understand all the steps involved. Then, write down your reflections!
If you simply mimicked the instructor's work and did not bother to understand why you followed a specific process, you will not be able to understand how to transfer this process to similar problems. Also, you will encounter difficulty when you take an exam covering a variety of concepts. Your reflections will probably be one of the first things you look at when it comes time to review for a test.

WHEN YOU GET STUCK ....
Everyone who has ever taken a mathematics course has had this experience. Either you are confused by a concept, the reading, cannot see how to solve a problem or you thought you solved the problem but your solution is incorrect. There are a variety of options here:

• Carefully go through your work again,
• Take a break to clear your thoughts and then rework the problem,
• Ask for help.
• Move on. Perhaps you made a small error and this will become clear later. The important thing here is not to get too frustrated or to spend too much time on a problem.

WORK IN A GROUP
Like most endeavors, learning mathematics is more fun if you do it with a study partner or in a study group. You learn that others make mistakes similar to you so that you do not feel isolated; you benefit from the knowledge of others and they benefit from your knowledge. Even if you feel you are giving more help than you are getting, you will find that an excellent way to learn is by teaching others.
 

KEEP UP WITH WORK OF THE CLASS.
This can be very difficult given your many responsibilities. There will be times, I'm sure, that you will fall a little behind. But, get caught up as quickly as possible. You should never be more than a day or two behind. Advice on time management is available here.
 

ANALYZE QUIZZES AND TESTS.
When a test is returned to you do not simply look at the score and shove it in your notebook, no matter how bad (or good) the grade. Try to find and correct your mistakes so that you will not make those same mistakes again.

Advice on how to study for math tests is available here.

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