Research & Innovation

Keeping Distance Learning Engaging and Effective—At a Time When Mathematics Is More Relevant Than Ever

Stevens teaching assistant professor Jan Cannizzo says the transition to online and hybrid teaching is a golden opportunity for instructors to adopt active learning methods in their classes.

Jan Cannizo helps child

Jan Cannizzo’s love of math started early in his childhood. Following periods of intense interest in astronomy and physics, he realized that mathematics was fundamental to both subjects, and abstract enough to explain almost anything.

His childhood fascination with math never ended. He went on to study math throughout college and graduate school with an end goal in mind: becoming an academic. Today, Cannizzo is a teaching assistant professor at Stevens Institute of Technology in the Department of Mathematical Sciences, focused on spreading appreciation for math among Stevens students and school-aged children.

Experiencing the joy of math, core to Cannizzo’s teaching philosophy, was the central focus of last year’s Stevens Math Olympiad. As a co-organizer of the mathematics problem-solving competition, Cannizzo shared his passion for math with students in grades three through twelve. He was looking forward to this year’s Math Olympiad. Then, the COVID-19 pandemic put a stop to it. Still, he is determined to find new ways to deliver quality distance-learning, both as part of his commitment to outreach as well as with his own students.

His quest to encourage students to pursue a mathematics education continues, undeterred by today’s difficult circumstances. Cannizzo is used to helping his students address challenges—after all, he explained,many students have difficulty with math. “Among school children and the public at large, there are widespread misconceptions about mathematics—that it’s stale, boring, and all about memorizing formulas,” he said.

He explained that math can be exciting, interesting, and deeper than most realize; and that struggling with the subject, and overcoming frustration, is a necessary part of achieving true understanding—even for mathematicians.

Sharing the excitement of math with elementary school students

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Jan Cannizzo, Ph.D.

In addition to helping organize the Stevens Math Olympiad, Cannizzo runs the Stevens Math Circle Initiative with his colleague Andrey Nikolaev, also a teaching assistant professor in the Department of Mathematical Sciences. A Math Circle is an enrichment program that reimagines math education in elementary schools, including those located in disadvantaged neighborhoods. Children enrolled in the program work to solve interesting mathematical problems and puzzles after school for up to two hours a week. They also participate in plenty of mathematical games and activities.

Math Circles, currently funded by grants from the Mathematical Association of America and the Alfred P. Sloan Foundation, are provided completely free for public schools and students.

Sharing Cannizzo’s interest in generating a love for mathematics are talented Stevens students, who are largely responsible for facilitating Math Circles in the classroom. “The kids were so excited to talk to me, and they had so much energy,” said Diana Rosado ’24, Stevens computer engineering major. For Rosado, the opportunity to make a difference in a young student’s life was personally meaningful to her. “I come from a disadvantaged background, and to have this chance to give back to the community made me happy.”

The “aha” moment was the favorite part of the experience for Julia Liszka ’21, a math major, and Yiding Yang ’23, a mechanical engineering major.

“The most rewarding part was seeing students pondering a problem and their sense of pride when they managed to complete the problem set,” says Yang. “The experience was enriching and enjoyable. I feel blessed to have engaged with students and to be a part of their educational journey.”

Liszka agreed. “It is rewarding to show these kids that math is not always just numbers, but also logic, patterns, and puzzles. The kids get excited about the games. They don’t even realize it is math because it is different from what they are used to in the classroom,” she said.

Ryan Adoni ’22, who has previous experience working as a math tutor, jumped at the opportunity to work in the Math Circles program when he learned about it. “It was rewarding to see advanced students learn new topics,” he said. He also enjoyed helping students who need additional help in math to really understand new concepts. According to Cannizzo, getting Stevens students involved provides them with a rewarding teaching experience and allows the initiative to run many Math Circles at once. “At the peak of the Math Circle program, we were running six Math Circles per semester,” he said. However, like the Math Olympiad, the COVID-19 pandemic halted the program in the spring of 2020.

Now, with public schools grappling with the challenges posed by the pandemic, and with enrichment programs often an afterthought, Cannizzo and Nikolaev are working to offer Math Circles remotely.

Shifting to active learning in online classes can help students succeed in math

Last spring, Stevens instructors were put in an unusual situation when the COVID-19 pandemic struck the New York City metropolitan area. Right across the Hudson River from Manhattan sits the Stevens campus.

“Most of us had not taught online before and had to make do as best as we could at the time,” said Cannizzo.

The shift to online learning was sudden, and Cannizzo found that his online teaching approach had its shortcomings.

“It wasn’t a disaster, but I was convinced that there was a more effective method,” he said.

He came across an active learning teaching method pioneered by David Pengelley, a mathematician and professor emeritus at New Mexico State University. The teaching approach flips the classroom, emphasizing active learning in favor of traditional lectures.

Canizzo explained that research in education has shown that lectures alone are not optimal at promoting deep learning, and a fully active learning classroom eliminates them. He took Pengelley’s ideas and adapted them to his online summer course and, now, his online fall courses. The method requires students to engage in reading, writing, and problem-solving on a topic before that topic is discussed in class, and it has the advantage of being relatively easy for instructors to implement. “The goal is for students and instructors to spend class time discussing and refining their pre-class work, so that they achieve a thorough understanding of the material by the time class ends and are prepared for higher-level work,” Cannizzo said.

After observing a high level of student engagement, more meaningful faculty–student interactions, and deeper learning, Cannizzo decided to share what he learned with Stevens faculty. Over the summer, he ran a workshop for his colleagues to demonstrate how the teaching methods he had introduced in his online course can improve learning.

Learning math is a worthy struggle

Succeeding in math can provide students with a high level of confidence. But success requires a certain amount of effort, according to Cannizzo. “If there isn’t any struggle in the course of learning, there probably isn’t much learning,” he said.

Learning math is more than memorizing formulas and solving routine exercises, he explained. “It is a process of starting from a place of confusion and, through active engagement and the asking of questions, gradually coming to understand a mathematical truth,” he said.

Cannizzo delivered a Ted Talk entitled "Reimagining Calculus Education" in September 2018, presenting calculus as an important and "riviting" area of study. He shares this enthusiasm to his students.

On a grand scale, innovative approaches to teaching math to grade-school children and college students are hugely important for preparing future generations to reason about the world, according to Cannizzo, who spends much of his time teaching calculus to Stevens students.

He explained that in the current pandemic, much of the information that is thrown at us is intimately connected with deep ideas in mathematics. “To understand the connection between a chart displaying new cases of COVID-19 per day and the total number of cases in the U.S., for example, is to understand an instance of the Fundamental Theorem of Calculus,” said Cannizzo.

He added that, when properly understood, mathematics can make sense of what is really happening in the world and help people see things in a different light—something that is critically important in today’s disruptive times.

Watch Cannizzo's Ted Talk:

Learn more about math at Stevens: