Sunday / July 21

Improv Games to Engage Students in Mathematical Discussions

In our work, we help teachers support rich, inclusive mathematical discussions among all students. For these discussions to happen, a classroom culture must be developed based on what are often new norms for mathematics class: that students should listen to each other, not just the teacher; that mistakes are OK, even welcomed, as students search for mathematical truth together. New norms take time and deliberate effort to develop.

Games In math class?

Improv games used as warms ups are an important means for developing new norms.

These are often the same games that improvisational actors use to learn their craft. Improv games have simple rules of interaction that foster spontaneity and strong collaboration among participants. They also encourage playfulness, which leads to the joy in mathematics class.

By using the games at the beginning of selected lessons, teachers have found that their nonmathematical context can be important for students who may have never before participated in discussions about mathematical truth. The games bridge between students’ everyday experiences and academic practices in a lively, engaging way that is safe for all students, regardless of their mathematical history. While games can take 5 to 10 minutes at the beginning of a class period, they will ultimately save time by jumpstarting new norms. The games need to be followed by a discussion that makes explicit the connection to these norms. Playing the games grounds that discussion in students’ own experiences, making it easier to establish a new way of behaving in mathematics class.

A game for you to try

In summary, improv games are a fun, low-risk way for all students to become familiar with norms supporting rich mathematical discussion that can engage all students. You can find hundreds of these games yourself through a quick web search. In our book, Mathematical Argumentation in Middle School—the What, Why, and How, we provide games tied to specific norms. Here is a game for you to try with your students:

Zip, Zap, Zop 

  • Players stand in a circle so that everyone can see everyone else.
  • The players throw an imaginary ball to one another within the circle, saying “zip,” “zap,” or “zop” (one with each throw, in that order, repeating the sequence until the game is over).
  • The first player starts by throwing a “zip” to someone else in the circle.
  • The catcher then becomes the thrower and throws the “zap” to someone else in the circle.
  • Players continue, in any order, until most have had a turn.

Connecting the game to norms

Consider the norms that can be established through this simple game:

When playing the game, inevitably, someone will say the wrong word, and that can prompt what is known as the “circus bow.” In the circus, when acrobats make a mistake and land in the net, they do not slink off in embarrassment. Instead, they jump off the net and make a bow with a flourish, as if they had intended the fall all along. Students can take a circus bow whenever they “mess up.” This helps reinforce dramatically that making mistakes is OK.

Players in the game must pay attention to each other to see where the “ball” is going for each turn. They need to speak loudly enough to be heard, but moreover, they need to look at each other. Looking at each other is so basic a norm that as adults we barely think about it, but students in mathematics class may be used to looking at the teacher only—except when they are getting into trouble! Looking at people as they speak helps establish an atmosphere of respect where everyone seeks to understand each other.


To help you think about how students may connect the game to these norms, here is the discussion one teacher with whom we worked had with her students after Zip, Zap, Zop.

Ms. Haddad: All right. Think about what we just did. Think about how does the game relate to having conversations in the classroom? How does that game relate to us and our classroom norms? Who would like to share a connection for us? Jadzia?

Jadzia:            It connects because when we were doing Zip, Zap, Zop, we were going back and forth, and it’s like speaking but actually is a game. And when we were doing the conjecture, argument, we are also doing the same with ideas instead of using zip, zop, or zap.

Ms. Haddad: Outstanding. So passing around the ideas just like we passed around zip, zap, and zop. Other connections, Kai?

Kai:                 We were speaking loudly enough so everyone can hear.

Ms. Haddad: Yes! Speak loudly enough so when you share your conjecture, everyone can hear and respond. Other connections from the voices we haven’t heard from? Tamiko?

Tamiko:          We didn’t always have to get it right.

Ms. Haddad: Absolutely. Can you share a little bit more about that?

Tamiko:          We could mess it up, say the words in the wrong order, and we would just start again.

Ms. Haddad: Was it okay?

Class:              Yes!

Ms. Haddad: Yes, so when we’re making our conjectures, it’s okay if we are not right the first time as long as you try. Right? Usher?

Usher:            Because like, if discussion takes time, one person’s going at a time and nobody’s talking over each other.

Ms. Haddad: Perfect. 


You may find improv games are “perfect” in your class, too.


Written by

Jennifer Knudsen has been working in mathematics education since her days as a Peace Corps volunteer in Kenya and as a teacher in in New York City Public Schools. She has focused on students’ engagement in mathematics as an equity issue throughout her career, including work on numerous curriculum and professional development projects. She directs the Bridging Professional Development project as part of her role as a senior mathematics educator at SRI International. She holds a B.A. from The Evergreen State College, where she learned to love mathematical argumentation. She lives in Austin, Texas with her husband and daughter.

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