With hard work aided by smart strategies, calculus can be vanquished! Here are study tips to help students not just through calculus but with algebra, geometry, trigonometry, and other levels of math.

by Gerald Dlubala

Mention the subject of calculus around a group of students, and you’re likely to get rolled eyes, blank looks, or stares of “deer in the headlights” terror.

Calculus, the branch of mathematics that deals with continuously changing quantities and motion, has for many students developed into an intimidating though necessary evil. It is a class to “get through” in the grand plan of their education. It is the subject most to be feared, conquered only by the math wizards.

However, calculus—as well as math in general—can be vital in gaining successful employment in many top professions: actuary, civil engineer, computer scientist, cryptologist, economist, operations research analyst, physician, statistician, research scientist, robotics engineer.

And calculus can be mastered, as evidenced by the number of people who have succeeded in these professions.

So is there a trick to calculus comprehension? Are certain kids just born to understand math?

There are no secrets—but there are some strategies for getting a jump on calculus.

Some of the simplest and best strategies around are found in an article created and made widely available for internet “reprint” by Susan Hermiller, Melanie Martin, and Eric York while on staff at New Mexico State University. Many universities have adapted the trio’s guidelines for their student-help websites. The tips listed below were culled from the version from the University of Nebraska at Lincoln, where Hermiller is currently a professor of mathematics.

If you're parenting children who have trouble with math, you might want to print these guidelines and post them on your refrigerator—and tuck a copy into your child’s math book! Though some of the tips are specific to calculus, these strategies can go a long way in helping a student master any level of math.

Strategies for mastering math (especially calculus)

●  Make the time. One of the advantages of mathematics is that you can work on it virtually anywhere, anytime. You can use time when you are in the shower or waiting in line to be thinking about problems or going over new concepts you learned in class. Visualize your success!

●  Take the time. Expect to have to do more work. Calculus will require that you make a substantial investment of time, probably a minimum of three hours outside class for every hour you spend in class. Build this into your life, expect it, and work on it every day, whether you have class or not and whether anything is due or not.

●  Get involved and actively participate. Expect to have to think hard about problems and pulling concepts together. Some of the problems you'll encounter will teach you new techniques. You may not see the point of these activities immediately, but they are strengthening you so that everything will come together when it counts. Think of them as a workout for the brain and practice them often. Take some time with difficult problems, talk about them, and take breaks if you are getting frustrated. Ask for help if you get stuck. Try to enjoy the process. After all, you are learning.

●  Never erase your work. If you hit a “dead end” in your work and want to start over, cross out the work you don't want with a big “X.” Do not erase it. It might turn out later to be correct!  It will certainly provide a road map for your problem-solving and allow you to retrace your steps if needed. Also, erasing can be a big time-waster on tests, where time is very valuable.

●  Learn the vocabulary and symbols. It is vitally important to communicate in the language of mathematics and understand the meaning and usage. As you read or participate in class, pay particular attention to the meaning of each new term and symbol.

●  Review constantly. Don't hesitate to go back to review or seek help on algebra, geometry, and trigonometry skills that you may not have mastered sufficiently in earlier courses. The majority of errors that students make on tests and quizzes are not calculus mistakes; they are algebra, geometry, and trigonometry mistakes.

●  Become proficient at using a graphing calculator. Your calculator is a valuable tool for visualizing and solving problems of all sorts. Learn to use it well. Become familiar with all the ways your calculator can be used to solve a problem.

●  Become proficient at not using a graphing calculator. In some situations, you may be required to provide exact symbolic solutions for many problems, and you should be able to explain your solutions using correct mathematical symbolism and vocabulary.

●  Practice, practice, practice. Just as you must play sports or musical instrument continually to master them, you must do a lot of calculus in order to be successful. If you are having trouble and need more practice, work other problems in that section or get another book and work problems out of it. Many texts have additional or review problems at the end of each chapter.

●  Analyze both your mistakes and your successes. If you are having trouble getting a correct answer to a problem, think about what is going wrong. This will allow you to learn something new and also will prevent you from making the same error in the future. Likewise, don’t settle for a correct answer that you don’t understand.

 

A lifelong St. Louis resident, Gerald Dlubala has spent the last 15 years writing about topics including health and wellness; education; family matters; and the wonder, humor, and lessons of everyday life.

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