What is the best way to learn Calculus?

Updated: Sep 26, 2019

With your busy schedule, you need to know the best way to learn Calculus so you’re using your time efficiently.


I received an email from a parent last week. I tutored her daughter in Calculus the past school year.


“Thank you for your hard work ensuring Emma understood Calculus this year and helping her prepare for the AP Calculus exam. She just checked her AP score…”

When I met Emma last fall, her goal was to pass the AP® Calculus exam. She daydreamed of the morning her AP® scores were released. She jumped out of bed at the sound of the alarm, turning off the alarm as she scurried to her computer. She drummed her fingers impatiently on her desk as the website loaded. She hoped to earn college credit for the difficult high school course.



With each passing second of waiting for the grades to load, Emma's heart raced faster. She hoped to see a passing score. Photo by NordWood Themes.

The Challenge of AP® Calculus


She realized the first week of school that she was missing prerequisite knowledge from Algebra, Geometry, and Pre-Calculus. The first test covered only prerequisite skills, and no Calculus.


She failed that first test.


She’s excelled in every math class. She never failed a math test before!


The next test on limits had similar results.


After the first two tests, her failing grade suggested that perhaps AP® Calculus BC may not be a good fit for her. She was tired of sitting at her desk for hours, working on her Calculus homework. After every odd problem she solved, she quickly flipped to the answers in the back of the textbook. Her shoulders slumped further with each incorrect answer.



She solved problem after problem to study for her tests. Photo by Steve Johnson.


Her grade did not reflect her ability.


But she didn’t want to drop the class. She asked me how she could improve her understanding and ultimately improve her grade.


How to Learn Calculus


Some suggestions I gave Emma (many of which don't take any extra time!):


· Write down the steps of every problem solved during class, whether it was a problem from the notes or homework

Why did your teacher do each step?

Can you recreate the process without looking at your notes and get the same answer?


· If you don’t understand a step, write a question mark in the margin where you got lost


· Attend office hours/help sessions with your teacher to get more individual help

Ask questions about any problem solving steps that don’t make sense.

If you need further help, find an effective Calculus tutor. Make sure the tutor plans tutoring sessions aligned with your goals


· Solve every assigned homework problem, even if it’s not for a grade

If you’re not getting the correct answer, find a video on Khan Academy.

When studying for chapter tests, go back and try to solve the problems you missed the first time through.


· I gave her tips on how to pass Calculus

If you have time, John Marsh suggests reviewing Algebra, Geometry, and Trigonometry before jumping into Calculus


· I told her that I believed in her. I knew that she could learn Calculus if she wanted to; she wouldn’t be in the class if she couldn’t handle it.



Could she turn her failing Calculus grade around?


She took my advice to heart.


She stayed after school to work with her teacher. But she realized she couldn’t get the individual help she needed, with other students also requiring help. So we set up one hour of tutoring each week.


I was able to explain concepts to Emma in other ways than she was presented in class. I learned what teaching methods resonated with her. We were able to cover as much in one hour of tutoring as an entire week of class because of the personalization tutoring allows.


In between tutoring sessions, she always completed her class’s homework assignments and any optional task I suggested to fill in gaps in her understanding.



What will you give up to successfully learn Calculus?


She got a C on her next test. She continued to spend at least an hour each day, watching videos and solving Calculus problems. Her grade started to improve along with her confidence in problem solving.


Do you have an hour a day to spend on mastering Calculus? If not, what are you willing to give up in order to reach your goal?


Math is just like any sport, game, or hobby—in order to improve you must consistently dedicate time to practicing. There is no quick solution to mastering Calculus. Even though Scott Young shares how he learned Calculus in 5 days, he dedicated nearly 12 hours each day to Calculus. You must practice solving and resolving problems to study math.


Emma chose to turn down social events so she could study. It was worth it.

In the email Emma’s mom sent, I read that she earned a 4 on the AP® Calculus BC exam.



Emma didn’t let the low test grades in the beginning deter her from her goal of passing the exam. Photo by Brooke Cagle.


With the beginning of a new school year approaching, start with the mindset that you’ll need to dedicate time to studying math. Spend most of that time solving problems. If you find that you need extra help from a teacher or tutor, you’ll have a better understanding what you know and what you need further help with. By putting the time and effort into practicing solving problems, I know you can learn Calculus.


For more tips for learning Calculus, subscribe to my website. You'll receive my monthly blog post and a list I created of "Approved Calculus Videos by Topic."

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