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What is the best way to learn Calculus?

Updated: Oct 26, 2023

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 AP Calculus this 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.

The Challenge of AP® Calculus

She realized in 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. In an ideal world, she would have spent time reviewing Algebra in the summer leading up to AP Calculus, but most students realize this a little too late...

She failed the 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.

Best way to learn calculus
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.

The Best Way to Learn Calculus

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

1. Learn the basic concepts of Calculus

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

-Notice what the question is asking and how that prompts a certain problem solving process

-Why did your teacher do each step?

-Can you recreate the process without looking at your notes and get the same answer? Sometimes those challenging questions appear on tests!

· If you don’t understand a step, write a question mark in the margin where you got lost so you remember to ask about it

· 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.

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

-The BEST way to learn math is to practice. The more problems you can solve, the better, especially in AP Calculus when they ask questions is many different contexts (given functions, graphs, tables, word problems)

-If you’re not getting the correct answer, find a video on Khan Academy on the topic to see if it helps

2. Learn the advanced applications of Calculus

· I gave her tips on how to pass Calculus, including reviewing daily and analyzing topics from multiple representations

· When studying for chapter tests, go back and try to solve the problems you missed the first time through. Once you're able to do those, practice more challenging questions from the best resources to study for AP Calculus tests. It includes several websites with past AP questions to match the rigor of class tests. Again, make sure you're looking at problems given functions, graphs, tables, word problems!

· 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.

Get Better Results in Calculus

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.

She got a B 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.

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.

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

And her results are common. To date, for my AP Calculus students who reported their results in an anonymous survey, 100% of students passed the AP exam: 61% earned a 5, 22% earned a 4, and 17% earned a 3. Additionally, 80% earned an A in class and 20% earned a B.

You, too, can be successful in Calculus.

Interested in learning Calculus concepts and practicing more advanced application questions? Join me for individual tutoring or in Calculus Crew! I'll answer any questions you have, and challenge you with AP level questions like you'll see on tests.


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