The Art of Math Improv
Complementing Active Learning With Active Teaching
By Pedro Morales-Almazán
“I hate math!”
That was my opening line for the October session of the Santa Cruz Math Teachers’ Circle. As a mathematician, I have heard this phrase multiple times. Students, friends, family members, and even random strangers, we all have heard this expression when they discover that we do — and love — mathematics. But, how do we counter those who have such an awful attitude towards math?
Simply put: we don’t.
This counterintuitive response is no surprise for improvisers. Improv, short for improvisational theater, has become popular mainly due to comedy shows, professional development programs, and improv courses. In improv, being spontaneous and unscripted is key. The challenge is, despite this uncertainty, to develop coherent and interesting stories. More than wit, improv requires training and practice. Just as any other skill, great improvisers learn and practice techniques to better navigate the unpredictable.
Teaching as Improvisation
As teachers, we are very familiar with the unpredictable. Even in highly planned lessons, we often find unforeseen questions or situations arising from our interactions with students. No matter how the , unexpected situations are bound to happen. There is a famous saying that goes: life is improvised. This is definitely true for teaching as well. An experienced teacher has learned how to handle these uncertainties, and even, to take advantage of them. We can also learn how to deal with this in a more structured way. We can systematically study how to handle uncertainty and how to use it to our advantage. This is one of the main values of improv for us as teachers.
I started in the world of improv about five years ago. I found it to be a very enjoyable and liberating experience. The playfulness and free-flow of the activities felt very different from the typical academic environment that I was used to. This made the experience very engaging. I started to analyze and to research a bit more about improv in academic settings. There is quite a lot of literature about the benefits of improv in soft-skill development. By no means do I consider myself an expert improviser, but I am passionate about the applications of improv to teaching and learning.
There are two main approaches to improv in the classroom. One is to incorporate it as an activity with students. Playing improv games with students increases engagement in the class and develops soft skills that sometimes can be overlooked in a mathematics curriculum. This is closely related to active learning. There is plenty of research done in this area, especially for mathematics. Another approach is related to what I call active teaching. It is possible to have a classroom with many active learning strategies conducted by a passive teacher. An active teacher is responsive and adapts to what is happening in the classroom. Even if a teacher does not use improv games or activities in the classroom, they can use the lessons promoted by it.
The Rules of Improv
Some of the most important lessons from improv are known as the Rules of Improv. These so-called rules are useful techniques that help navigate uncertainty. The most common ones are:
- Yes, and
- Active listening
- Being present
- Team work
- Failure
These rules develop important skills needed to interact with students and to promote mathematical thinking. We can say that these five rules focus on perception, communication, mindfulness, cooperation, and compassion.
© Aude Vanlathem / www.audevan.com
A Math Circle Approach to Improv
At our Math Teachers’ Circle, many of our participants had expressed interest in the connections between improv and mathematics, so we made our October 2021 session about “Math Improv.”
The session was held over Zoom and we had about 15 participants. We have a very diverse group of people that attend our Circle, including high school teachers, school administrators, retired mathematicians, and math enthusiasts. This diversity in backgrounds and skill sets converges in our passion and interest for mathematics.
The first rule that we approached for our session was “Yes, and.” We started with a simple game:
Game: Yes, and
Instructions: In a circle, players go in sequence saying a statement. (To facilitate “going around circle” on Zoom, participants can use grid view and rearrange their grids to follow the same order.) Players need to add to what was said previously by starting their phrase: “yes, and.”
Goal: The goal is to collectively construct a story. It is OK if the story is not realistic or defies logic. What is important is to account for what is being said before and not denying the previous players’ statements.
The main idea of this game is to acknowledge everyone’s reality. For example, the statement “I hate math” expresses a very common perception among non-mathematicians. We can certainly deny it and tell them that math is actually beautiful. However, implicitly we are saying that their perception is wrong. Denial does not move any conversation forward. Rather, it halts any progress.
By “yes-and”-ing an idea, we can move the conversation forward into something that incorporates the different perceptions present in a discussion. Beware: “yes-and”-ing an idea does not necessarily mean automatically agreeing with it. It means to recognize that the other person thinks, believes, or feels it. When the other person states “I hate math,” we can acknowledge that feeling while at the same time adding our own perspective to the story.
A typical situation inside the classroom that many of us often encounter is when a student says, “This problem is difficult.” Even well-intentioned teachers might respond with, “Let me show you how this is easy.” This is a subtle denial that implies that the student is wrong in thinking that the problem is difficult for them. A better approach is to “yes-and” the student’s statement — not to say that the problem is difficult, but rather to acknowledge that it is difficult for the student. In this way, the student and the teacher can team up, agreeing on their mental and emotional states.
Continuing with our session, we played another variation of the “Yes, and“ game:
Game: The Alphabet
Instructions: Similar to “Yes, and” but players don’t start with the phrase “Yes, and.” Instead, players cycle through the alphabet, beginning their statements with a word that starts with the next letter of the alphabet.
Goal: The goal is to pay attention to what the previous player said, not only in meaning, but also to actively listen to their first word.
Many times we listen only to reply. Active listening promotes listening to understand. In the classroom, teachers often answer their own questions rather than the students’. By being more intentional about the way we listen, we can improve our communication. This is key in the classroom setting, as it promotes engagement and trust with students.
It is particularly important to pay close attention to the wording that students use. As novices, students often don’t have a well-articulated mathematical vocabulary, which can prevent us from correctly interpreting the actual questions that students pose in class.
A common situation occurs when a student says, “This problem doesn’t make sense.” Often, students mean different things when using this phrase. This can be “I haven’t seen a problem like this before,” or “I don’t understand some of the terminology,” or “I don’t know how to start.” Active listening helps us to pinpoint the specific difficulty that a student is facing rather than assuming it.
We played a few more improv games in our MTC session focusing on the “Yes, and” and “Active listening” rules of improv. It was very interesting to see the interactions between people with different backgrounds and interests. Even in Zoom, we experienced a very engaging session.
It is important to remark that most of these activities and strategies are not math-specific in the sense that improv activities can be used in many different contexts. However, one aspect relevant to mathematics is that improv brings a human touch to it. Traditionally we experience math classes as very fact-oriented. Even in active settings, “yes-and”ing, listening, and embracing failure might not be present. Improv then becomes particularly relevant in math education, not necessarily from the content point of view, but from the communication and the metacognitive perspective. With improv, we can embrace both the student and the teacher as human beings, interacting together while doing mathematics. For this reason, I strongly believe that Improv brings many aspects that are particularly needed in the mathematics classroom.
Taking It Further
These activities are really just the tip of the iceberg regarding math improv. There are many other wonderful improv games that promote perception, communication, mindfulness, cooperation, and compassion — important skills to promote not only among students but also with teachers.
There are also many books and internet repositories focusing on improv. A very good resource is the Improv Encyclopedia. A list of additional recommended reading for learning more about improv is given at the end of this article.
Games generally make for engaging MTC activities and promote fruitful discussions. Improv provides a structured framework to engage with students and to handle unexpected situations, going beyond ice-breaker activities and games to give a more holistic approach to the teaching and learning experience.
Teaching is improvised, and it is much better when we have the tools to intentionally handle and enjoy the improvisation.
About the Author
Originally from Guatemala, Pedro Morales-Almazán is currently a Teaching Professor in the Mathematics Department at the University of California, Santa Cruz. He also directs the Santa Cruz Math Teachers’ Circle. He says, “I discovered mathematics when participating in math competitions in high school. Since then, I have been attracted to the puzzles and brain teasers that mathematics provides.” His teaching interests are related to inquiry-based learning, the use of technology for adaptive teaching, and improving student engagement. His research focuses on applications of Zeta Functions in Number Theory and Quantum Field Theory. Find him on Twitter @p3d40 and on Medium (in Spanish).
Recommended Reading on Improv
George, M. (2012). How Mathematics Teaching Can Be Like Improv Theater. MathAMATYC Educator, 3(2), 21–23.Morales-Almazan, P. (2021). Improv practices in Mathematics active teaching. PRIMUS, 1–16.Sawyer, K. (2019). The creative classroom: Innovative teaching for 21st-century learners. Teachers College Press.Young, A. (2013). Improvisation in the mathematics classroom. PRIMUS, 23(5), 467–476.
