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Math Strategies & Study Tips

MINDSET FOR COLLEGE MATH

Although you took plenty of math courses in high school, you will probably have to adjust your approach for your college courses, especially if you have always been impatient about explanations, preferring simple instructions about how to work the problems. In college, you will need to understand the concepts behind the formulas if you want to receive a decent grade.
If you find yourself struggling in a math class, don’t begin to doubt your ability. It might be that your foundation in math is not as strong as it is for other students, regardless of how many math courses you took. Make use of various kinds of resources such as review books, tutoring, help from the TA or professor, and/or help from a classmate. Most importantly, increase the amount of time you spend on your homework.

HOW TO STUDY IN A MATH CLASS

  1. Try to take your math courses back-to-back without skipping a semester. Before starting a new course, review the math from your previous course.
  2. Never let yourself fall behind. If the class seems too easy, remember that all math classes start with some review. But at a certain point, the classes kick into high gear and if you haven't been keeping up, you will quickly become lost.
  3. Read or at least scan the chapter before your lecture and read it again afterwards. But don't read a math book with the goal of memorizing; instead, think of it as a reference book that will help you understand different kinds of math problems.
  4. As you read your text, do the computations along with the book. Work on the problems section by section as you read the text.
  5. In your lecture, write down everything the professor writes down, and if he/she uses different colors of ink, do likewise. Even if you think you understand a problem, write down each step! You may find yourself confused two weeks later and need those notes for the test.
  6. It’s fine to memorize math symbols and definitions, but try to understand the underlying processes and concepts. When you look at a process, ask yourself the purpose for each step. Think of analogies and try to visualize applications. Finally, it may help to explain (or at least try to explain) a concept to a friend or family member. Having to organize your thoughts and verbalize them deepens your understanding.
  7. If you find yourself confused by a topic, try some of the following resources: a review book, a high school textbook (your own or from the library), a tutor, the T.A., or the instructor. Tutors can be extremely helpful, especially if you use them soon enough. Don't wait until you get a D on an exam! Free tutoring is available through a variety of programs on campus: Honors College (Burnham Hall), Math Learning Center (430 SEO), AAAN (996-5040), and ACE (413-0032).

HOMEWORK

Nobody will be looking over your shoulder to see whether you’ve done all your homework, and it can be easy to talk yourself into thinking that you understand the material because you had it in high school. And hey, if you’re planning on running in the Chicago Marathon, nobody is going to check on whether you’ve been going out jogging five times a week You get the idea: if you’re getting ready for a competition (the test), you need to put in some practice time by doing plenty of homework problems. Practice helps you deal with the stress of the exam and it also helps you work through the problems more quickly so can finish the exam in time.

  1. Do your math homework as soon after class as possible while the concepts are still fresh. If you find yourself confused, seek clarification right away by talking to a classmate or tutor. Never wait to do your homework until after the next class, promising yourself you will catch up on the weekend. (The weekend is a great time to write an essay, but during the week you should be keeping up with your math.)
  2. Begin by reviewing your lecture notes. Take a separate sheet of paper and try to work the example problems on your own, then check your answers with the ones in your notes.
  3. Try sitting down with a classmate to do your homework, each of you working on your own but consulting with each other when you get confused. At the very least, get a classmate's phone number so you have someone to call when you’re stuck.
  4. Check your first answers in a given section before going on to do a whole set of problems. When you make a mistake, determine the source of the error, and make a mental note of a method for avoiding that kind of error in the future (ie. double check all positive and negative signs). If you can't find your error for a problem after two tries or 15 minutes, don't get stuck. Consult with another student or a tutor.
  5. When working on homework, try to do all of the assigned problems, but in an emergency, do at least a representative sampling of each kind of problem.
  6. Read each problem slowly and carefully, running a pencil under the words to make sure you notice and understand each word (ie. find the length of the smaller leg of the triangle).
  7. Summarize word problems by drawing a diagram or setting up the information in a table. Sort out the problem into given, find, need.
  8. For a very difficult word problem or when you forget a formula, substitute simpler numbers. Once you understand the nature of the problem, use the same process with the real numbers in the problem.
  9. At the end of a homework session, mentally review the most important concepts you've just learned.

STUDYING FOR TESTS

  1. Your first test will be easiest, but don't get over confident and "blow it off." You may need that A on the first test in order to offset lower grades later in the semester.
  2. Remember that doing well on homework and/or quizzes is no guarantee of doing well on an exam. Quizzes are often easier to finish in time and do not contain such a variety of concepts mixed together.
  3. Don't just memorize formulas; make sure you understand the concepts. Concepts will stay in your memory longer and are less likely to be forgotten under the stress of a test.
  4. Write up a summary sheet of key formulas and definitions.
  5. Attend any review sessions that are offered and take plenty of notes.
  6. Review all of your quizzes and rework the problems.
  7. Study for your math test by working mixed sets of problems. Use chapter reviews, old tests the professor has made available, and/or review books. It's not enough to be familiar with the material; you should have worked so many problems that the material is now easy for you.
  8. Do some timed practice tests or sets of problems. Try to find some application problems with difficult or confusing wording (you will need practice in deciphering this kind of problem). In other words, mimic the testing situation as closely as you can while you work on practice exams.
    Important Note: Taking a math test without ever taking a practice test is like going into an important basketball game without ever playing a scrimmage game. It’s not enough to work on your dribbling and shooting; you also need the experience of a practice game. The same is true for math.
  9. During your practice tests, check all results, just as you will during the test. Use some of the following methods:
    • Plug you answer back into the problem to make sure it works (this is particularly important for word problems).
    • Estimate the answer to make sure your answer is in the right ball park.
    • Double check and + and - signs.
    • If time allows at the end of the test, rework some of the problems using an alternative method.

TAKING MATH TESTS

  1. Get plenty of sleep the night before the test. Sleep is essential for higher order thinking.
  2. When you first get the actual test, write down any formulas you might forget. Next, look at the number of points given for each problem and think about how to get the most points in the quickest amount of time. Apportion your time and begin work on the easiest problems. (If you do happen to run out of time, you don’t want to leave the easiest problems undone.)
  3. Write out each step. This way, even if you miss the answer, you may get partial credit.
  4. When your test is returned, rework any problems you missed and find out what went wrong. (This is analogous to a sports team watching the tape of a prior game when preparing for an upcoming game.)

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