March 13, 2020

Playful pedagogy in college calculus

Ben Mardell

While playful learning is most often associated with young children, it can be a valuable resource for older learners as well. In previous posts we have shared examples of playful learning in middle and high school and for adult learners. What about college?

I’ve just finished Paul Tough’s book The Years That Matter Most: How College Makes Or Breaks Us. It is a powerful call to reform American higher education—the admission process and the undergraduate experience. And embedded in it is a story of playful teaching and learning in a college classroom. A calculus class no less.

The teacher is Uri Treisman. Treisman teaches an introductory calculus course at the University of Texas at Austin. In the year Tough chronicles, Ivonne Martinez is in Treisman’s class. A first generation college student from San Antonio, Martinez aspires to be a mathematician. For Martinez, Introduction to Calculus is an essential step towards this dream. Martinez starts her first year at college unsure about her abilities, and is, objectively less prepared than many of her classmates who attended high schools with far superior math programs.

While Treisman does not explicitly call his pedagogy playful, in his mission to make sure all his students succeed, he deploys key playful learning practices that were described in the last post: enabling experimentation and risk-taking; establishing the conditions for learning with one another; encouraging learners to lead their own learning; and embracing the range of emotions play produces (in particular, supporting learners in working through frustration).

How are these practices manifested in a college course? Treisman begins the first class session with music – the Colombian band Monsieur Perine (subsequent classes began with Linda Ronstadt and Copeland’s Fanfare for the Common Man). As the music plays, Treisman circulates among his 100 students, greeting them by name. This first class is a mix of high level calculus and the message:

You are a mathematician. This is hard and you can do it. You belong here.

During the semester Martinez and her classmates are exposed to complex mathematics that go beyond what is typical in Calculus 101. Treisman knows this is stressful and disorienting and explains that, “Almost every student in calculus gets their self-confidence destroyed at some point. I want to be there when they have this crisis.”

As the semester proceeds, Martinez certainly has her crisis. On the first test she scores a 67. Test two: 59. The mid-term is even worse. By mid-semester she worries, “Maybe kids from the west side of San Antonio aren’t cut out for calculus.”

Maybe too much disorientation, Treisman wonders. In conversations with his Teaching Assistants (TAs), they conclude that their teaching had fallen out of balance; students were relying too much on the instructors rather than discovering on their own and teaching each other. So Treisman announces that the class is switching to “workshop mode.” In study group sessions Martinez and her classmates work on problems in small groups. TAs explain that students have to come up with their own ideas of how to solve the problems, noting, as way of encouragement, “Rarely the first thing I try is correct. I’m almost always wrong at the beginning…That’s why we use pencils.”


Where do I see playful learning practices in all of this? First, experimentation and risk-taking is enabled: “that’s why we use pencils.” The study groups help establish the conditions for learning with one another and encourage learners to lead their own learning. And in supporting learners to work through their frustration, Treisman and his TAs embrace the range of emotions play produces. This is something that is challenging to figure out how to do well. It is something Treisman does masterfully, so it is worth sharing a conversation he and Martinez had during office hours where he provides lovely support by shifting the burden of learning onto himself, normalizing struggles with calculus, and giving an effective pep talk. In part, he tells Martinez:

My problem is that I have a group of students in the class who did advanced AP calculus in junior year and they went to really rigorous high schools. You’re going to catch up with them in a few weeks or in a month. But because you always did well, and now you’re struggling, you’re saying to yourself  “maybe I’m not good enough to be here.”
The question of how to teach this class so that everyone struggles, without students losing their confidence—this is my struggle. Because you guys are such incredible students. You’re really accomplished. You’re hardworking and serious. And I have to push you so that you can learn, but I have to get better at making sure you don’t come out of this and say, “struggle means I’m not good.” We can’t lose you. We need more mathematicians. We need more woman mathematicians. And it wouldn’t hurt to have more Latina mathematicians.

This support with frustration, along with the help in study group sessions where Martinez begins taking the lead in solving problems, pays off. She starts feeling more confident in her understanding of the material. Martinez takes the final exam. It is the end of her first semester at college and that afternoon her parents pick her up. On the drive home she receives this email from Professor Treisman:

I wonder if you understand how talented you are and how that talent is enriched by your amazing work ethic. You earned one of the highest grades on the final—391 out of 400, which is of course, a high A. It was a real privilege to have you in our course.

Enable experimentation and risk-taking. Establish the conditions for learning with one another. Encourage learners to lead their own learning. Embrace the range of emotions play produces. Teaching practices that can be useful in kindergarten through college to foster playful learning. And it doesn’t hurt to start class with a song.