By Madeleine Stone @themadstone

For many bright students, the Advanced Placement Calculus BC exam is one of the most daunting hurdles of high school. But Philadelphia high school students who took University of Pennsylvania Professor Robert Ghrist’s online calculus course last year have a different perspective.

“Most of the students told me they crushed it,” says Ghrist with a smile.

Ghrist is the Andrea Mitchell Penn Integrates Knowledge Professor, with appointments in the School of Engineering and Applied Science’s Department of Electrical and Systems Engineering and in the School of Arts & Sciences’ Department of Mathematics. He is also one of a diverse group of professors who, with the support of Penn’s Open Learning Initiative, developed a massive open online course, or MOOC, that is free and accessible through Coursera’s online platform.

Not only has Ghrist’s course, Single Variable Calculus, offered tens of thousands of people around the world access to integrals and derivatives, but, in a pilot outreach effort that began last year, it’s also becoming a part of the education of students at high schools practically in Penn’s backyard.

“The students who took this course did very well,” says Abbi Smith, a math teacher and chair of the Mathematics Department at Friends Select School, in Philadelphia’s Center City. “They have a much better appreciation of calculus applications and a deeper conceptual understanding of some of the toughest concepts.” 

Ghrist has been testing novel approaches to teaching calculus in his classrooms at Penn for more than 10 years. His teaching drew the attention of the Open Learning Initiative. 

“Rob was one of the early innovators in this space,” says Amy Bennett, director of course operations for open learning at Penn. “We knew through his teaching that he was going to have a significant impact on STEM learning.”

In 2012, Ghrist, along with several other Penn professors, received support to start building a MOOC. To deepen students’ conceptual understanding of calculus, Ghrist felt a radical departure from textbooks was needed. 

“Calculus is the mathematics of motion,” Ghrist says. “You can’t really talk about motion at a high conceptual level with static text on a page.”

Instead, Ghrist created a visually engaging experience, in which a 13-week lesson presents calculus concepts through hand-drawn graphics and animations. The lessons are intended to emphasize core concepts and practical applications. The course was offered for the first time in January 2013. 

Smith, of Friends Select, was intrigued by what she had heard about Ghrist’s approach to teaching calculus and decided to take the first run of the course herself. 

“I signed up mostly out of curiosity,” she says. “I went in thinking I’d just do it in my free time, as a side project. It ended up being much more rigorous than I expected. But I loved it.”

In the 2013-14 academic year, 10 Philadelphia-area high schooll math teachers, Smith included, piloted Single Variable Calculus in their classrooms. Each teacher was able to implement the course material in his or her own way as a supplement to what they were teaching in class.

“These high school classes are typically very dynamic and hands-on,” says Ghrist. “The online course is not intended to replace classrooms but to facilitate deeper learning.”

In addition to deepening students’ conceptual understanding of calculus, Ghrist’s course allowed exceptionally talented students to push themselves further.

“Several of my students were seeking challenges in mathematics," says Smith. “With this course, they were provided ample opportunities to stretch their skills.”

At the end of the school year, high school students who had taken Ghrist’s course as part of the classroom pilot were invited to visit Penn for a day.

“It was great to see these students work so hard and wonderful to meet them in person and get their feedback,” says Ghrist.

Bennett agrees.

“The students loved Ghrist; he was their superstar. Visiting Penn and meeting him were very important to them.”

Ghrist says he is excited to see whether high school students come to college better prepared for math after taking his class. One of the students who took the course at Norristown Area High School will be attending Penn Engineering this fall.

Beyond Philadelphia, thousands around the world are learning or re-learning calculus through Ghrist’s free open learning course. Sixty thousand students have been actively enrolled since Single Variable Calculus’s online release. Only a third of these students are from the United States, with many more from Brazil, China, India and the United Kingdom.

“It’s a very diverse crowd,” says Ghrist. “Some are in grad school, many are working professionals and many more are retirees who want to continue learning. And there are some talented youngsters.”

Among these are Pakistani twins Khadija and Muhammad Niazi, who passed the course in 2013 at age 12. Muhammad Niazi says, “Ghrist's course really made my foundation in calculus stronger. The most interesting feature of the course for me were the animations and the non-graded homework. 

Some international students are even taking the course to improve their English, a testament to Ghrist’s clear, deliberate speech and his choice to avoid using culturally contextual references.

“I wanted to make a course that could be watched and understood by anyone,” says Ghrist. “What matters most for me is that 1.5 million videos have been watched. At 15 minutes each, that’s a lot of learning hours across the world.”

The open learning initiative represents part of Penn’s broader mission to increase access to the high-quality education offered on campus in alignment with President Amy Gutmann’s Penn Compact 2020.