Calculus. Most readers who have stepped into a math class will stop reading this article at the very first word. For them, calculus is synonymous with monotony, struggle, and discomfort.
Jan Cannizzo, a faculty member of the Mathematics Department at Stevens, was the third speaker at the TedxStevensInstituteofTechnology and is a Stevens student favorite. He is an exemplary professor who strives for excellence when teaching his Calculus classes. Upon observing the missteps of his many students, Cannizzo began to realize that there is a larger issue at hand rather than the commonly accepted idea that Calculus is simply one of the most difficult and rigorous courses that a student can take.
In his talk, “Reimagining Calculus Education,” Cannizzo shares a journey that led him to the beginning of revolutionizing the modern-day Calculus classroom through various technological changes, including the implementation of the online mathematics platform known as Gradarius.
Cannizzo, relaxed and confident, prefaced his talk by explaining derivatives and integrals, known as the most important component of calculus, in a brief and engaging fashion. Throughout this, Cannizzo demonstrated that calculus can indeed be captivating and not “dry, impenetrable, and terrifying,” as his students used to describe it. He then introduced a jarring statistic: a few years ago, the D.F.W (an acronym for D grade, F grade, or Withdrawn from class) rate for Calculus classes at Stevens was 35%.
At the time, Calculus at Stevens was no different than it was anywhere else in America: a passive experience in which a professor simply lectures to his students with little to no interaction. To Cannizzo, this problem of a passive relationship became increasingly discernible.
However, despite how obvious the issue appeared to Cannizzo, the solution to the problem was not as clear. Cannizzo says that finding the solution “was very much a trial and error process that took over a number of years.”
“We looked at the education research that was out there, much of which showed that active learning methods were much more effective than traditional lectures.”
Cannizzo took advantage of faculty members that “had experience with computational group theory and developing a software that might help teach calculus,” and then proceeded to revolutionize Calculus education at Stevens. He eliminated the use of an expensive textbook and opted to simply upload PDFs of the learning material online for students to access. He changed his approach to class and made it more interactive for students and professors through the implementation of virtual in-class quizzes that are instantly graded. Additionally, Cannizzo aimed to reduce the stress students faced due to the weight that individual Calculus exams have on their final grade by increasing the number of small assignments and quizzes throughout the semester.
Most notable among the changes brought forth by Cannizzo is the online mathematics platform Gradarius. With a $20-per-course access fee, the platform provides students with homework relevant to the course material. Students are required to type in the work for their solutions for each step of a calculus problem and it restricts students from proceeding until they have solved it the right fashion, guided by hints along the way. Thus, students learn the correct procedure to solve a problem.
Many students have complained about the time that it takes to complete homework assignments and that the ins and outs of the platform come with a relatively steep learning curve. Since its conception, Gradarius has seen an improved tutorial system and Cannizzo promises that there are further updates to come: “I didn’t want to give the impression that we have made a bunch of changes and now that’s it — that’s the new model. We do think from year to year, about how we can teach differently. You can’t just settle into this system that you plan on using from time immemorial. You have to constantly rethink how you teach.”
Cannizzo states that despite all of the additional technological changes to an education that has remained virtually unchanged for over a hundred years, the social component will remain intact. Many have expressed a concern that the interaction between students and professors would become limited, with student identities being limited to various grading statistics and data. Cannizzo expressed that those concerns are valid: “I have concerns about outsourcing everything to a machine.” However, for Cannizzo the software is just one tool of many that assists in a great Calculus education: “in my class, at least, Gradarius is just one component of the class, we also have team workshops, and in lectures we try to make things active with students discussing things with each other and the professor — I think that is critical to a Calculus education.”
The culmination of Cannizzo’s efforts has resulted in an impressive 25% decrease of the D.F.W. rate for Calculus at Stevens and has increased student satisfaction for the course.
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