Gone are the days when the only way you could learn a new skill was in a classroom. Between online classes, learning platforms like Udemy and Khan Academy, and resources like YouTube, you can learn just about anything online. But can you teach yourself a challenging subject like calculus?
You can teach yourself calculus if you have a growth mindset instead of believing in misconceptions about how difficult it is to learn math. You should be familiar with Algebra, Geometry, and Trigonometry, choose your sources, come up with a schedule, and stick to it.
Calculus is the mathematics of change. If you don’t think you can teach yourself calculus, we want to change your mind. We will explain why people believe Calculus is too challenging and why they are wrong. Then we will give you tips on resources to use and steps to take so you can get started.
Why Do People Think Teaching Yourself Calculus Is Impossible?
The word calculus strikes fear in many people. If someone were to ask, “can you teach yourself bookkeeping?” or “can you teach yourself to program?” the reaction is not the same. For some reason, people hear the word calculus and assume it’s difficult, without even taking a calculus class.
Some people suffer from what Professor Jennifer Ruef calls “math trauma.” According to some studies, over a third of young adults think they aren’t good at math. If you are one of those people, you could believe one or more of these misconceptions:
- Not everyone can learn math. We used to think that intelligence is fixed, but researchers have shown that it is false. Psychologists like Carol Dweck have shown that believing that you can increase your intelligence will lead to more success. Some have called this belief a “growth mindset,” but “the effort effect” is another way of thinking about it.
- Math is about solving problems quickly. If you think that being fast is a sign of being good at math, you are setting yourself up for failure. Researchers at the University of Chicago have demonstrated that anxiety even affects students who excel in math. By focusing on how fast you can solve problems, the increased anxiety can lead to “brain freeze.”
- Math is rules and procedures. Knowing how to solve a problem is important, but knowing why that solution works is more important. If you learn only the rules and procedures without learning why they work, what will you do if you forget it?
Numerous studies, such as this one by Alan Schoenfeld, professor at the University of California, have shown that math instruction that focuses on rules leads to a poor understanding of math.
There is no disputing that calculus is difficult. But if you adopt a growth mindset and are willing to let go of common misconceptions about math, you can successfully teach yourself calculus.
Why Should You Teach Yourself Calculus?
Geometry is the study of shapes and space, while algebra is the study of relationships. Calculus is the study of change and how change can be measured over time. Being able to measure how something will change is essential in fields such as economics, engineering, biology, medicine, and more.
Beyond those practical reasons, if you teach yourself calculus, you might be able to apply the concepts to other things you are interested in. You will also have bragging rights that you taught yourself a topic many people think is impossible to learn on your own. You’ll increase your confidence in yourself.
And maybe you’ll come to love calculus. Who knows?
What Are the Prerequisites to Teaching Yourself Calculus?
Calculus builds on algebra, geometry, and trigonometry, so you need some background in those subjects. Before you get started, you should brush up on these essential skills:
- Algebra. Be able to solve polynomial, linear, and quadratic equations. Understand the properties of exponents. Know the properties of logarithms.
- Functions. Understand what a function is and how to represent it on a graph. Know how to manipulate functions and be familiar with terms related to functions, like domain, intercepts, and range.
- Geometry. Be able to compute the area of shapes and volume of shapes. Be able to reason about a coordinate plane and equations for parallel and perpendicular lines.
- Trigonometry. Know what sin(x), cos(x), and tan(x) functions represent and how they are represented on a graph.
You can find many online calculus readiness tests. However, many are paper and pencil. If you want an online test, check out the Free Test Online Calculus Test.
What Steps Should You Take to Master Calculus?
The first step is to get started. As the Chinese philosopher Lao Tzu said, “a journey of a thousand miles begins with a single step.” If you have read this far, you have already taken that first step. These are the next steps on your journey.
Pick Your Sources
For learning Calculus, you have three options for sources—books, free online resources, or self-paced courses that you need to pay for.
|Books||•Easy to find good used books|
•Practice exercises included
|•Difficult to teach yourself from books alone|
•Books usually do not have answers to all the problems
|Free online||•Lots of resources on many platforms|
•Ability to watch videos repeatedly until you understand the concept
•Multiple resources if you need a concept explained differently
|•Require a lot of time evaluating resources|
•Without a set curriculum, you might not know which essential concepts you are missing, leading to frustration
•Interaction with others is limited
|Paid online courses (like Udemy)||•Engaging content taught by professors|
•Courses structured so that you don’t miss important concepts
•You can augment with free content
•Interaction with others still limited
There are a few free online resources that come close to paid courses like Udemy. Here are some to check out:
- Khan Academy. This popular site features courses in everything from Art History to Physics. This link will take you to the Calculus page. Many of the courses on the website start with middle school concepts and work up, so this could be a useful resource if you need to review a prerequisite subject.
- MIT OpenCourseware. MIT was one of the first universities to upload courses with lecture videos. Some courses include homework assignments, notes, and tests.
- Calculus.Org. This is a hodge-podge site with everything from problems, animations, online textbooks, tutorials, and videos. An excellent resource for additional problems, explanations, and tools.
- Calculus for Beginners and Artists. A straight-forward approach. It is a text-only resource, but the writing is clear, and the course is well-organized. If you want to use YouTube, this resource would be an excellent way to ensure you are logically hitting the concepts.
Come Up With a Schedule
Without a schedule, chances are good that other things will keep coming up. Before you know it, a month has come and gone, and you are still in Chapter Two.
There are two approaches to a schedule. One is to see how long a course is, and then decide how much time you plan to spend per day or week. Let’s say you pick one of the MIT courses, which is 120 hours of videos. If you plan to devote 2 hours a day to the course, you will finish in 8-10 weeks (depending on whether you will take days off or not).
You can also set yourself a deadline and then work towards that. Say you plan to finish in a month. There are 19 chapters in the Calculus for Beginners Course. That’s five chapters a week.
You know yourself, and which approach would work best for you. As to keeping yourself on track, check out the many apps and sites that let you set goals. Check out Joe’s Goals—it looks like it was designed in the late 1990s, but that’s part of the charm. Goal-Buddy is another site to check out. If you are interested in a phone app, most of those available have a free-trial period.
Maybe you already have a support group or circle of friends who will keep you on your toes and share your successes. However, if none of them are strong in math, you might need someone to study. In a college course, finding study partners is easy. But what to do if you are teaching yourself?
One resource is MoocLab. This community site provides forums for online learners. You can get a free trial to try it out. Check out Reddit—post a request and wait for someone to respond. If you just want someone to keep you on track, you can find accountability partners on Reddit as well.
Plan to Reward Yourself
Decide how and when to reward yourself. Gretchen Rubin writes about creating a “Schedule of Treats” as a way to keep yourself motivated. Studies show that without treats, we start to burn-out and resentful. But people who treat themselves become better at self-control. That is a skill anyone who plans to teach themselves something like calculus needs.
You can teach yourself calculus. It won’t be easy and requires self-discipline and knowledge in algebra, geometry, and trig. However, the resources are out there, but the motivation must come from within. So what are you waiting for?
- Huffpost: 6 Free to Low-Cost Resources to Teach You Calculus
- Farnam Street: The Feynman Technique: The Best Way to Learn Anything
- The Muse: The Pomodoro Technique Actually Works
- Live Science: What is Calculus?
- MIT: Calculus for Beginners and Artists
- University of California: Calculus.org
- The Conversation: Think you’re bad at math? You may suffer from ‘math trauma’
- HuicHawaii.org: It’s Not the Math They Hate
- USA Today: Math Can-do: Column
- Stanford Magazine: The Effort Effect
- University of Chicago News: Anxiety Affects Test Scores Even Among Students Who Excel at Math