Let the game begin! Baldermath

Learning and fun through game-guided role play

Gwen Jones is an assistant professor of education at Bridgewater University in Bridgewater Virginia. She shares her experience using “Baldermath”, a practice space developed by the Teaching Systems Lab at MIT and a math teacher and blogger Michael Pershan.

Let the game begin!

“We’re all going to be members of a 4th grade math class”, I announce to the undergraduate students in my assessment and learning course. While I passed out the packet with details about the game, I explain that this game requires that they take turns role playing a fourth grade math teacher (judge), and students (contestants) in a 4th grade math class working to solve a series of math problems. The students appear excited and eager to begin.

Why play games?

As a Teacher Educator, I am always looking for ways to increase engagement in my courses. I had recently started working with undergraduates at Bridgewater College, and I inherited a course that was taught in a traditional way (text books and lectures). I met the game designers from the MIT Teaching Systems Lab (TSL) at a Digital Media and Learning conference. They invited me to work with them to test a variety of games.

I chose to try out Baldermath in this assessment class because of the opportunity it affords students to “practice” talking about mathematical thinking in a fun, low-stakes setting of a role playing game. Baldermath is a “bluff-the-judge” game about looking at student mathematical thinking. Students in my class took turns playing the three roles within the game; the teacher, the actual struggling student, and regular 4th grade math students who may or may not be struggling.

Playing Baldermath

The game started with the whole class looking at an example of fourth grade math solution provided on the Baldermath desmos site, and shown below. As the students looked at the math example I asked them to share any thoughts they had about it.

Several students volunteered they noticed several misconceptions about parts of a whole. This discussion lasted about five minutes and provided a nice warm up and preview of the types of math examples they would encounter in the actual game.

Next, I formed the class of twenty students into four groups of five and we began to play. The classroom has three large screens and a smartboard to project the problem for each round. This was helpful in keeping all four groups together and moving through the game smoothly. As I formed the groups, I told them they would each take one turn as the teacher. Each group would decide who would role play the teacher for that round. After establishing who the teacher was, and having that person leave the room, the remaining group members then rolled the die to determine the “actual” student, and the remaining students would play the “bluffers”. The actual students were given a paper with a work example that was copied as closely as they could into their own handwriting. The remaining students were the “bluffers” and had to generate their own mathematical response to the problem as if they were a fourth grader.

The first round took about 9 minutes, which was a bit longer than the next four rounds because we were establishing the flow of the game. During each round the “teachers” from each group left the classroom and were provided with a copy of the problem to review in a separate classroom. The “students” had about 3 or 4 minutes to either copy or generate a math problem. As the facilitator, I checked in with each of the groups to be sure they were ready before inviting the teachers back into the room. After the first round, the students settled into the idea of the game, each of the rounds took about five minutes. It was surprisingly synchronized and went more smoothly than I originally anticipated it would.

As I observed the interactions and actions of my students, I was surprised by the level of enthusiasm and how they took up the roles of elementary learners. I observed my students trying to get the attention of the “teacher” and yelling, “oooh, ooh”, “Call on me first! I’ve got the answer!” There was laughter, there was fun, there was authentic interest — the “teachers” were leaning over to get a closer look at the math problems, while the “students” were describing their work in 4th grade terms, and explaining their thinking. From my perspective, it appeared that they really did spend the full hour and a half talking and thinking like 4th grade math students! They were focused on the task and had a high level of energy throughout the class. As the activity ended I heard several of the students say to each other: “That was fun.”

What did students learn about Mathematical thinking as a result of playing Baldermath?

Students completed a short reflection responding to the prompt “What did you learn about student mathematical thinking as a result of playing Baldermath? Eight respondents commented they were surprised at the variety of student approaches to the same problem, and also surprised at the variety of ways they represented their ideas such as drawings or written explanations. One student explained; “Students think of math differently. Some draw pictures, some use mathematical processes, and others use words to explain and rationalize what they’re thinking.” Four others wrote that the game helped them gain new insights and understanding about student perspectives, and the importance of listening to students explain their thinking to gain a more complete idea of where the student is struggling. One student wrote “It is interesting to see student perspective and see how a variety of students would answer the same question and how there are so many different thought processes.”

Which role was most helpful in learning about student math thinking and why?

Fourteen of the twenty students thought the role of the student was most valuable and most wrote that taking on the student really pushed them to try to think like a fourth grader. For example, one student wrote; “ I was able to actually comprehend how a student’s brain works and how they choose to show and express their work.” Those who found the role of the teacher most helpful focused on the teacher listening and gaining valuable knowledge about how students approach math. For example, one student commented that “I think being the teacher was a beneficial learning experience because it allowed you to hear all of the student’s explanations and how they believed you should get the answer.”

End of the Semester Reflection

Several months later during the final week of classes, I asked students to sit in small groups and reflect about what they thought was valuable in the Baldermath activity. :

• It was fun to get into the mindset of the students, and attempt to solve math the way they solve it.
• The game was a good way to learn how to elicit learner knowledge.
• The game was fun, there was lots of laughter.
• The students were able to see the process the students went through to get their answer.
• The students liked looking at the variety of work from the students and how each one solved the problem to get the answer.

What I would do differently

In the future I plan to do a better job of framing the experience before the game. I plan to have students read and view a series of articles and videos that will provide them with information on best practices for examining student mathematical thinking and misconceptions, and best practices in talking about math with elementary students. I would also use two class sessions instead of one, and take time to pause after two game rounds for a class discussion focused on how to address the specific misconception(s) presented in Baldermath. Finally, I would also spend more time debriefing this experience and facilitating a whole class discussion about the importance of focusing on student thinking and developing skills in talking about math concepts.

Final Thoughts

As I facilitated Baldermath and reviewed the written reflections, students clearly valued the experience and were drawn into the game in powerful ways that led them to new insights about student mathematical thinking and the importance of talking with students about their thinking. The National Council for Teachers of Mathematics Standards for K-12 practice place a strong emphasis on meaningful discourse. This ability to engage students in productive mathematical discussions is viewed as an essential skill in the K-12 Standards for Mathematical Practice. Likewise, the research on noticing student mathematical thinking points to the importance of providing opportunities for early practice teachers to learn to attend or notice the thinking patterns of student problem solving strategies, and to make correct interpretations. Teacher preparation programs struggle to provide opportunities to practice and develop these important discourse and noticing skills. In my experience, Baldermath provides a powerful experience in understanding student mathematical thinking, and builds discourse skills in noticing learner mathematical misconceptions.