Calculus can often be an intimidating class for students. The subject matter can feel like the culmination of all a student’s previous courses, and in many ways, it is. Many students struggle with calculus as a result of weak mathematics fundamentals. These weaknesses are where every good tutor must start when helping a student master his or her calculus class.
Calculus Tutoring: First Steps
A calculus tutor should initiate the sessions with a student by assessing which of the building blocks of calculus –algebra, geometry, and pre-algebra – are weakest by providing the student with problems that test these skills. The topics of functions, slopes, limits, trigonometry, graphing, and logs are among the most important to review as these are the key topics learned in pre-calculus and a mastery of these requires a mastery of the lower level material as well. At this point in time, it is beneficial for a tutor to introduce how these topics will relate to the work being learned in the calculus course itself. This provides the student with a strong foundation on which to stand for their upcoming work as well as a new way to frame the concepts.
Using Calculus Tutoring to Overcome Challenges with Motivation
A second issue students often encounter is motivation. Calculus has developed a reputation for something only aerospace engineers should be using but nothing could be further from the truth! An MIT course in calculus offers a calculus tutor an excellent jumping off point for helping a student recognize the importance (and the fun, though that’s a harder sell) of learning the material. The issue of motivation often stems from the seemingly esoteric nature of the methods involved in applying calculus to problems. For this, a good tutor must have an arsenal of analogies such as this one for explaining the application of a derivative or this one to elucidate an integral. Understanding how a student likes to solve problems – visually, logically, or by trial and error – can cue a tutor to what kind of analogies work best on an individual basis.
All students will learn calculus best not by memorizing the theorems of calculus but by working through, and many times struggling through, problems. Lots and lots of problems! However, it is difficult for even the best tutor to generate calculus practice work on the spot. The material is too complex and the potential for mid-problem error is high. In light of this, one of the best preparations a tutor can make to help his or her student is to amass an arsenal of resources from which he or she can draw problems from any part of the calculus curriculum. Because we live in this wonderfully digital age, tutors can find these kinds of problems for free from highly reputable sources such as Khan Academy, MIT Open Course Ware, and if the level of the course permits, the College Board AP Calculus site.
Having a wide variety of problems can also assist in any motivation issues a student can have. There are many real world examples that can be solved by calculus. A good tutor will take the time to learn which of these kinds of problems is of most interest to a student. In this way, a tutor can select problems that challenge a student’s weaknesses while simultaneously piquing his or her attention. One of the most popular, and perhaps most practical, kinds of problems is the application of compounding interest on an investment to teach of the concept of infinitesimal steps and review the concepts of limits.
The complexity of calculus and the intimidation students feel about the subject makes it a unique subject to tutor and requires the extra skills of a well-experienced tutor. Calculus starts off as a sprint, with a rapid review of nearly every mathematical concept a student has learned to date. From there the course becomes an obstacle course with the student encountering a new, more challenging, and seemingly different obstacle each week. A good tutor will be able to help the student move seamlessly through each of these obstacles by employing an arsenal of analogies to help explain the concepts along with problems to help teach them. Thus a good tutor is like an integral in this way, using many small infinitesimal steps to help the student get from point A to B. Better still, a good tutor will use these steps to get a student from a B to an A!
By Liz Iffrig
Lizz Iffrig grew up in Philadelphia, PA before attending MIT in Cambridge, MA. She graduated in June 2010 with a Bachelor’s of Science, double majoring in Chemistry and Biology with an unregistered minor in Literature focusing on classical literature. She recently completed her graduate studies, in which she simultaneously pursued a medical degree (MD) from Emory University and a PhD in Biological Engineering from Georgia Tech. During her graduate studies, Lizz tutored for Atlanta Tutors. Now she regularly contributes to our blog.