In Home Tutoring Services

Tips on how to study mathematics


Math Study Skills

Be actively involved in managing the learning process, the mathematics and your study time:

Take responsibility for studying, recognizing what you do and don't know, and knowing how to get your Instructor to help you with what you don't know.

Attend class every day and take complete notes. Instructors formulate test questions based on material and examples covered in class as well as on those in the text.
Be an active participant in the classroom. Get ahead in the book; try to work some of the problems before they are covered in class. Anticipate what the Instructor's next step will be.

Ask questions in class! There are usually other students wanting to know the answers to the same questions you have.
Go to office hours and ask questions. The Instructor will be pleased to see that you are interested, and you will be actively helping yourself.
Good study habits throughout the semester make it easier to study for tests.


Studying Math is Different from Studying Other Subjects

Math is learned by doing problems. Do the homework. The problems help you learn the formulas and techniques you do need to know, as well as improve your problem-solving prowess.


Study Time

You may know a rule of thumb about math (and other) classes: at least 2 hours of study time per class hour. But this may not be enough!
Take as much time as you need to do all the homework and to get complete understanding of the material.

Form a study group. Meet once or twice a week (also use the phone). Go over problems you've had trouble with. Either someone else in the group will help you, or you will discover you're all stuck on the same problems. Then it's time to get help from your Instructor.
The more challenging the material, the more time you should spend on it.



Problem Solving

The higher the math class, the more types of problems: in earlier classes, problems often required just one step to find a solution. Increasingly, you will tackle problems which require several steps to solve them. Break these problems down into smaller pieces and solve each piece - divide and conquer!


Problem types:
Problems testing memorization ("drill"),
Problems testing skills ("drill"),
Problems requiring application of skills to familiar situations ("template" problems),
Problems requiring application of skills to unfamiliar situations (you develop a strategy for a new problem type),
Problems requiring that you extend the skills or theory you know before applying them to an unfamiliar situation.

In early courses, you solved problems of types 1, 2 and 3. By College Algebra you expect to do mostly problems of types 2 and 3 and sometimes of type 4. Later courses expect you to tackle more and more problems of types 3 and 4, and (eventually) of type 5. Each problem of types 4 or 5 usually requires you to use a multi-step approach, and may involve several different math skills and techniques.
When you work problems on homework, write out complete solutions, as if you were taking a test. Don't just scratch out a few lines and check the answer in the back of the book. If your answer is not right, rework the problem; don't just do some mental gymnastics to convince yourself that you could get the correct answer. If you can't get the answer, get help.
The practice you get doing homework and reviewing will make test problems easier to tackle.


Solving an Applied Problem

First convert the problem into mathematics. This step is (usually) the most challenging part of an applied problem. If possible, start by drawing a picture. Label it with all the quantities mentioned in the problem. If a quantity in the problem is not a fixed number, name it by a variable. Identify the goal of the problem. Then complete the conversion of the problem into math, i.e., find equations which describe relationships among the variables, and describe the goal of the problem mathematically.

Solve the math problem you have generated, using whatever skills and techniques you need (refer to the four-step process above).
As a final step, you should convert the answer of your math problem back into words, so that you have now solved the original applied problem.


Studying for a Math Test

Everyday Study is a Big Part of Test Preparation.
Good study habits throughout the semester make it easier to study for tests.
Do the homework when it is assigned. You cannot hope to cram 3 or 4 weeks worth of learning into a couple of days of study.
On tests you have to solve problems; homework problems are the only way to get practice. As you do homework, make lists of formulas and techniques to use later when you study for tests.
Ask your Instructor questions as they arise; don't wait until the day or two before a test. The questions you ask right before a test should be to clear up minor details.


Asking Questions

Don't be afraid to ask questions. Any question is better than no question at all (at least your Instructor/tutor will know you are confused). But a good question will allow your helper to quickly identify exactly what you don't understand.
Not too helpful comment: "I don't understand this section." The best you can expect in reply to such a remark is a brief review of the section, and this will likely overlook the particular thing(s) which you don't understand.
Good comment: "I don't understand why f(x + h) doesn't equal f(x) + f(h)." This is a very specific remark that will get a very specific response and hopefully clear up your difficulty.
Good question: "How can you tell the difference between the equation of a circle and the equation of a line?"
Okay question: "How do you do #17?"
Better question: "Can you show me how to set up #17?" (the Instructor can let you try to finish the problem on your own), or "This is how I tried to do #17. What went wrong?" The focus of attention is on your thought process.
Right after you get help with a problem, work another similar problem by yourself.