Tips From an Irvine Calculus Tutor: The Calculus Conundrum: Why is Calculus Such a Stumbling Block?
Many students dread taking calculus. Whether it’s the final math class of high school or a required prerequisite for their college degree, calculus is often a necessary mathematical capstone in education. Calculus also tends to carry with it a reputation for being much more difficult than previous math – book your private Irvine calculus tutor today. This stereotype is supported by many students who struggle and even fail their first calculus class. Often times, these are students who completed – or even excelled in – their previous math classes. So why is calculus such a stumbling block? What makes it so different from our other math courses?
The first, likely the most significant, reason for calculus difficulties is the class’s deviation from the previous progression in math classes. Coming into calculus, students have been following progressions in their math knowledge for years. First, we learn addition, and that 2 + 3 is equal to 5. Then we learn how addition leads to multiplication, or that 2 x 3 = 2 + 2 + 2 = 6. Finally, we learn how multiplication leads to exponents, or that 23 = 2 x 2 x 2 = 8. This process took years of math classes to master and build up from addition. A similar process happens with subtraction to division to negative exponents; in algebra with one variable to single step equations to multi-step to multi-variable; and in functions from linear to quadratic, to polynomial and their graphs. These progressions build upon themselves and have students master the previous concepts before moving on to the next, usually over the course of years. You may have learned addition in the 1st grade but didn’t see an exponential until 7th. You probably did your first “find x” in middle school, but weren’t conquering complex polynomial factoring until 10th or 11th grade.
Calculus throws this timeline of progression out the window. Now you’re starting over with new concepts and new progressions, but it’s consolidated to just one class.
When you learned linear functions in middle school they teach you how to find the slope, but do they ever mention the word derivative? When you move on to quadratics, do you also learn the graph of the slope of your parabola? As your graphs approach asymptotes, was there ever a mention of limits? When you had to memorize dozens of transformations and identities in trigonometry, were any of them the derivatives or integrals of the functions?
You’ve been working with calculus concepts for years without knowing because the teachers are saving it all for calc class. And once you get to calculus, they spring it all on you and expect you to jump through all of the hurdles in a few weeks. Remember that nice progression from addition to exponents that gave your years to master the topics and become an expert? Now you have a month if you’re lucky to get from the derivative of y = 2x to deriving y = (sin(3×2 -4))3(ex+1)-5. If your teacher lost you somewhere along the way, you’re doomed for the rest of the year. Just like you would be doomed in middle school if you never mastered addition.
The same fast-track progressions happen with integrals, with limits, and with sequences and series. You’ll see symbols you’ve never seen before, doing operations that are entirely unfamiliar, and you’re expected to progress from beginner to expert in them all. And you better not try to simply memorize some equations and problem-solving steps, or the word problems will eat you alive (READ: 5 Signs You Need a Math Tutor in College).
This last idea is a common problem even for students who get an ‘A’ grade in their calculus class. Many students have the memorization capacity and studying habits to learn how to do calculus problems. They learn how to solve their integrals and manipulate their functions by sheer repetition without always understanding what’s going on. This leads to another quintessential calculus complaint: “When would I ever use this is real life?” Students have a hard time seeing any applications when all they have to rely on memorization and don’t understand what they’re doing.
Stay tuned for part two! In the meantime, book your private Irvine calculus tutor from TutorNerds. Call us for more information.
Michael C. is currently a private math, science, and standardized test tutor with TutorNerds in Irvine and Anaheim.
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