How to Study Math
Copyright © 2003Ė2023 by Stan Brown, BrownMath.com
Copyright © 2003Ė2023 by Stan Brown, BrownMath.com
Summary: Read this page for some tips on effective studying in your math courses.
How to Succeed in Math
How to Read a Math Book
How to Work a Math Problem
If I could give just one piece of advice to math students, this would be it: Keep up with the class. Iíll say it another way: Donít fall behind. Noltlingís book makes it crystal clear: ďGetting behind is academic suicide.Ē
To an extent thatís true in any field, of course, but itís particularly true in your math courses. More than any other field, math is relentlessly cumulative. Almost every class depends on what came in the immediately preceding classes. If you donít quite get the material in one class, you need to learn it yourself right away or you can pretty much expect to be lost in the next class.
Since it takes a huge effort to catch up once you fall behind, your best strategy is not to let yourself fall behind. If you donít understand something, deal with it right away. (Very few things magically become clear over time.) In class, ask a question. Donít wait: your brain will be nibbling at the thing you didnít understand and that will distract you from the rest of the lecture.
Outside class, you have a little more time, but still make sure to get all your questions answered by the start of the next class. Start by reviewing your textbook. If you need to, visit the tutoring center if your school has one, work with your study group, visit the instructor, whatever it takes.
If you have to give one course short shrift because you donít have enough time one week for all your classes, donít slight the math class. I say this not because math is better or more important than any other class, but because the penalties for falling behind are more severe. In most classes you can usually understand most of one lecture if you didnít understand the previous one; in math thatís generally not true.
What if you do fall behind? It can happen even to good students. In this case, my advice is to put in extra effort and work through the missed material in order. Since the concepts are sequential, it will be pretty inefficient to try to study what the class is studying if you havenít mastered the previous weekís work. Stick with the same order that the class followed, but put in the extra effort to catch up as quickly as you can while still learning everything.
Be sure to let your instructor know what happened; s/he may be able to give you specific advice or help to use your time most effectively. If your instructor knows you had a problem but youíre trying to catch up, s/he will probably be willing to work with you, possibly even to cut you some slack about quizzes if the problem was beyond your control.
There are lots of benefits to studying in a (small) group:
You can organize your group however you want. You can simply get together to do homework at the same time, but youíll get the most benefit if youíve made a genuine effort to study the textbook and work most of the problems before you get together.
Some study groups try to split up the work so that each person does part and they copy from each other. The problem with that is that you donít learn what you need to know by copying someone elseís work. The way you learn to do problems is by doing problems yourself.
Most students donít spend enough time on homework. For a three-credit course, the College says you should spend an average of 6Ė9 hours a week outside of class. (In a survey in Fall 2002, the majority of my students spent four hours or less. Thatís simply not enough for many students to assimilate the material.)
For summer courses, you should expect to spend much more time. Figure 2Ė3 hours outside of class for every 50 minutes of class time.
Many students also try to do their homework for one subject in a big lump. Thatís very natural, but you will get better results from the same number of hours if you distribute them through the week. Try spending two hours three or four times a week. The material will be fresher in your mind, and you wonít be so likely to burn out. (An hour and a half six times a week is probably even better, but itís hard for most people to stick to that schedule.)
Remember that the 6Ė9 hour guideline is an average. You may need to spend more time or less than that. Be honest with yourself: spend the time you need to learn the material and do the homework. Your payoff will be better understanding, a higher grade, and a lower level of stress.
When is studying most effective for you? Most people have a particular time of day that works best for them. Think about what works for you, and try to arrange your schedule so that youíre doing your studying when itís most effective.
Some people are very strongly affected by whether theyíve eaten recently. You may find that youíre very alert after a meal, or that youíre a bit logy and ďoffĒ after you eat. Again, plan your study time (or your meal times) accordingly.
By the way, the same applies to class time. If you get sleepy early in the evening, avoid night courses; if youíre not a morning person then avoid 8 a.m. classes. If your attention span is shorter, avoid a three-credit class that meets once or twice a week.
If youíve already got class times or formats that are less than ideal, look carefully at your overall life schedule and see if you can make some adjustments. Can you change your sleep schedule or work schedule to make classes and studying work better? If not, it might be smart to lighten your load. All else being equal, it may be better to do well in a smaller number of courses than just barely pass a larger number. Your advisor can give you helpful advice on adjusting your schedule.
(It may be too late to do anything about this semesterís schedule. Make a resolution now to register as early as possible next semester so that you can pick the best class times for you.)
If you find yourself really struggling with a problem or concept, try doing some other part of the lesson. If at all possible, you want to end each study session with a success, even a small one.
If you can go to bed or to another activity with a sense of accomplishment, youíll give yourself a lift and make it psychologically easier to come back to your next math session.