Calculus is one of the most challenging subjects for college students. It involves understanding derivatives and solving integrals, which can be quite a source of anxiety for students. So why is it so difficult?
Let's examine what makes calculus so challenging for most students, identify the common issues they face, and consider how tutors can help with academic support.
We'll also include some tips for getting the most out of your college calculus class and how to make studying calculus more manageable.
What Is Calculus, Why Is It So Important, and Why Is It So Challenging?
If hearing calculus has already made you nervous, we'll start by simply explaining what it is.
Calculus is the branch of mathematics that studies change over time. It focuses on rates of change (derivatives) and cumulative quantities (integrals).
Students will come across calculus in various STEM (science, technology, engineering, and math) programs like physics, engineering, economics, and biology.
Understanding calculus is important. It can open doors for a better understanding of the world mathematically. For example, you can use it to predict population growth and analyze physical motion.
It's usually a stepping stone for more advanced math courses. Still, it often feels like such a leap from any math you've studied thus far that students can feel overwhelmed.
So why do so many students find calculus daunting and why is it so important? Let's have a look at the reasons.
Calculus Builds on Previous Math Courses
Calculus is a step from all the math you'll have studied. It builds upon core concepts from algebra, trigonometry, and geometry.
The area of math that deals with variables and numbers for solving problems substituting letters for values.
The branch of math that is concerned mainly with triangles, their sides, their angles, and the relationships between them.
The field of math that studies the properties of points, lines, surfaces, solids, and higher-dimensional analogs.
Calculus requires a solid understanding of these areas of math and many other core mathematical concepts for you to understand it. Any student who struggled in any way with any of these is likely to find calculus challenging.
While students might continue to pass their math classes in high school, they'll likely end up with knowledge gaps in their math education. These gaps can be circumvented in certain areas, especially where students can excel in everything else to get a passing grade, but they may be essential components of calculus.
Students who have a weak or less-than-perfect understanding of polynomial expressions, quadratic equations, or trigonometric functions can face worse problems later on.
Remember that tutors can always help with gaps or lacunae, especially in math and calculus.
Calculus Includes Abstract Concepts That Are Hard to Grasp
The abstract ideas and concepts featured in a calculus class are also problematic for students. Many of the concepts in calculus are intangible and difficult to visualize.
A limit, for example, describes how a function behaves as it approaches a certain value, which provides a new way of abstract thinking for students.
Students need to think conceptually and deal with infinitesimal changes, which can be tricky to grasp initially. Then, you need to understand the reasoning behind these abstract concepts, which is more than simply memorizing formulas like you may have done in math classes beforehand.
Weak Fundamentals in Math
Students who lack strong math fundamentals, particularly in algebra, trigonometry, and pre-calculus, will likely struggle in calculus.
For example, students will need a strong foundation and understanding of concepts like logarithms, sine, cosine, and tangent to solve calculus problems. A student who isn't particularly strong in these areas will find calculus particularly difficult.
As mentioned earlier, any gaps in your knowledge can lead to problems in later math classes, especially calculus. It's always worthwhile preparing for your calculus class by brushing up on these areas of math.
Complex Formulas and Techniques
College calculus classes introduce students to various formulas and techniques, including the power, product, and chain rules for derivatives. These formulas include multiple variables and operations, and students typically need help memorizing and applying them correctly at first.
Calculus problems often include multiple steps with different mathematical operations. Students need to recognize which method is used in certain problems and know both when and how to use these techniques.
Students in college calculus classes may feel overwhelmed by the sheer number of formulas, steps, and rules they need to follow.
Be sure to ask for additional help from professors or private calculus tutors for key concepts like Rolle's Theorem, the Mean Value Theorem, and integration techniques.
Time-Intensive Calculus Courses
College calculus courses ask a lot of their students. It would be best if you regularly practiced and studied calculus to stay on top of what you'll learn in class.
Calculus involves memorization, but you also need to read and understand calculus, regularly referring to your notes from class to internalize the material.
Right from your first calculus class, you should review all your notes and study until you've understood everything. Even if your professor starts the course at a manageable pace, getting into this habit is a good idea for when the requirements start ramping up.
If you aren't regularly brushing up on your notes from class, it can be very easy to start falling behind. If you have to go back over things you should have studied in earlier classes when your schedule is busier, you'll likely struggle with more classes than just calculus.
studying calculus every week!
Over-reliance on Calculators
Calculators are helpful, and we're not here to say that you can't ever use them. However, there are a few pitfalls to overusing calculators, especially in a college calculus class.
Students who use calculators too much will start struggling to memorize some of the more essential math skills they need for calculus, such as memorizing special angles in trigonometry or recognizing the shapes of curves when graphing.
Many professors expect their students to solve problems by hand in a college calculus class without using calculators for basic math functions.
Master these skills, and you'll avoid the trap of becoming dependent on your calculator and succeed in your calculus class.
Real-life Applications of Calculus
Calculus is hugely important because it has many practical applications. You can use calculus to understand and model real-world phenomena.
Calculus can be used for population growth, chemical reactions, computer science algorithms, and even video game design.
Students interested in a career in engineering, economics, physics, or computer science will quickly realize that calculus isn't an entirely abstract subject; they can use much of what they learn, which can help them when studying it.
Here are just some of the areas where calculus is best used.
- Engineering: In civil engineering, differential equations model stress and strain on materials. Integral calculus computes the areas and volumes of the forces acting on structures.
- Economics: The maximum and minimum values of functions are used in economics to calculate marginal costs and marginal revenue and predict market trends.
- Physics: Calculus is used to model the motion of objects, and Newton's laws of motion, for example, are based on calculus.
- Biology and Medicine: Calculus can be used to model population growth, the spread of infectious diseases, the outcome of vaccination campaigns, etc.
- Computer Science: Computer scientists use calculus to design algorithms, model networks, and solve problems with data and artificial intelligence.
Here's a great video showing calculus being applied.
Learn Calculus with Superprof
Don't get us wrong—calculus is a challenging subject. Still, you can master it with the right mindset, work towards internalizing the necessary foundational knowledge, and regularly practice and study.
It is normal to feel lost or overwhelmed by abstract concepts, deadlines, and all the new math you must tackle.
Luckily for you, there are plenty of incredibly talented and qualified math tutors out there who can help you.
On the Superprof website, you can search for tutors for math or even calculus specifically. Beyond calculus, students can also work with tutors to become better students, focusing on organization, study skills, and transferrable skills that will help them in every one of their classes.
Finding a tutor is easy. Search for what you want to learn and where you'd like to learn it. There are often plenty of academic tutors in college towns, but you can also learn online from tutors worldwide.
Online tutoring is typically cheaper as the tutors don't have travel costs to worry about. A tutor elsewhere, especially in a different time zone, could be useful for students with busy schedules.
With many of the tutors on Superprof offering the first session for free, we recommend trying a few tutors before you choose the right one for you and your academic goals.
Whether it's brushing up on the math you need for calculus, getting help with calculus itself, or becoming a better student, you'll find the right tutor on Superprof. Search for one today!
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