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 Ghristâ€™s online calculus course last year have a different perspective.
â€śMost of the students told me they crushed it,â€ť says Ghrist with a smile.
Ghrist is the Andrea Mitchell Penn Integrates Knowledge Professor, with appointments in the School of Engineering and Applied Scienceâ€™s Department of Electrical and Systems Engineering and in the School of Arts & Sciencesâ€™ Department of Mathematics. He is also one of a diverse group of professors who, with the support of Pennâ€™s Open Learning Initiative, developed a massive open online course, or MOOC, that is free and accessible through Courseraâ€™s online platform.
Not only has Ghristâ€™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, itâ€™s also becoming a part of the education of students at high schools practically in Pennâ€™s backyard.
â€śThe students who took this course did very well,â€ť says Abbi Smith, a math teacher and chair of the Mathematics Department at Friends Select School, in Philadelphiaâ€™s Center City. â€śThey have a much better appreciation of calculus applications and a deeper conceptual understanding of some of the toughest concepts.â€ť
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.
â€śRob was one of the early innovators in this space,â€ť says Amy Bennett, director of course operations for open learning at Penn. â€śWe knew through his teaching that he was going to have a significant impact on STEM learning.â€ť
In 2012, Ghrist, along with several other Penn professors, received support to start building a MOOC. To deepen studentsâ€™ conceptual understanding of calculus, Ghrist felt a radical departure from textbooks was needed.
â€śCalculus is the mathematics of motion,â€ť Ghrist says. â€śYou canâ€™t really talk about motion at a high conceptual level with static text on a page.â€ť
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 Ghristâ€™s approach to teaching calculus and decided to take the first run of the course herself.
â€śI signed up mostly out of curiosity,â€ť she says. â€śI went in thinking Iâ€™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.â€ť
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.
â€śThese high school classes are typically very dynamic and hands-on,â€ť says Ghrist. â€śThe online course is not intended to replace classrooms but to facilitate deeper learning.â€ť
In addition to deepening studentsâ€™ conceptual understanding of calculus, Ghristâ€™s course allowed exceptionally talented students to push themselves further.
â€śSeveral of my students were seeking challenges in mathematics," says Smith. â€śWith this course, they were provided ample opportunities to stretch their skills.â€ť
At the end of the school year, high school students who had taken Ghristâ€™s course as part of the classroom pilot were invited to visit Penn for a day.
â€śIt was great to see these students work so hard and wonderful to meet them in person and get their feedback,â€ť says Ghrist.
â€śThe students loved Ghrist; he was their superstar. Visiting Penn and meeting him were very important to them.â€ť
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 Ghristâ€™s free open learning course. Sixty thousand students have been actively enrolled since Single Variable Calculusâ€™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.
â€śItâ€™s a very diverse crowd,â€ť says Ghrist. â€śSome are in grad school, many are working professionals and many more are retirees who want to continue learning. And there are some talented youngsters.â€ť
Among these are Pakistani twins Khadija and Muhammad Niazi, who passed the course in 2013 at age 12. Muhammad Niazi says, â€śGhrist'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 Ghristâ€™s clear, deliberate speech and his choice to avoid using culturally contextual references.
â€śI wanted to make a course that could be watched and understood by anyone,â€ť says Ghrist. â€śWhat matters most for me is that 1.5 million videos have been watched. At 15 minutes each, thatâ€™s a lot of learning hours across the world.â€ť
The open learning initiative represents part of Pennâ€™s broader mission to increase access to the high-quality education offered on campus in alignment with President Amy Gutmannâ€™s Penn Compact 2020.