Thursday, September 6, 2012

The Magic Number Cube Consensus Game

I always tell colleagues that the best things I learned about teaching I learned on Twitter. Recently, I tried out a an activity that was new to my classroom: The Subversive Lab Grouping Game. This activity inspired me to continue with the 'subversive' teaching through games on day two. This activity is one I have done in previous years, but it's been a few and now I have repurposed it based on my success with Frank Noschese's lab grouping game. This is called the Magic Number Cube, and it is a team-building activity that I picked up in the physics modeling workshop I took a few years ago. It's an activity that has students collaborating to think through a goal-less problem in order to learn numerous lessons about my class, including the process of arriving at consensus.

My colleague Don Pata and I have discussed in the past the factors which we find to lead most to student success in our modeling classrooms. It turns out that the classrooms with greatest student success are the classes where the students have the best ability to work together to arrive at consensus. In the modeling methodology of teaching science, teachers lead students through the modeling cycle. The modeling cycle requires students to develop mental models based on observations that can explain or predict patterns and relationships in physical situations. Students share their observations and data from experiments with each other through guided classroom discussions and must arrive at consensus based on the evidence to develop a model. Models are then deployed on novel situations and to solve new problems.

Without forming consensus, students leave holes in their understanding and questions unanswered about their observations or physical situations we've investigated as a class. This makes the development of a model unstable, and thus the deployment of an unstable model leads to unreliable problem-solving and understanding. This is the reason why forming consensus as a class is so important for students to hone as a skill in the classroom. That's why we go to the lengths to train students in the process of learning in this manner before letting them loose on the content in this way. If they are not well-prepared to learn in this setting of a modeling classroom, then it won't be as great a learning opportunity for them as it could be--and we want the best for our students--so, we have to get them the best opportunities.

The opening days of my class are spent on team-building, growing the classroom climate that fosters successful teamwork, and generating consensus friendly discussion. As I mentioned, the first day activity was a lab-grouping game, which was quite successful to communicate several messages to students about focusing on process and working as a team. The second day activity, the Magic Number Cube, continues in this same theme but with a slightly different focus in its message.

Here's how the activity works:

  • Students work in groups of four
  • A six-sided cube made out of cardboard and covered in blank printer paper (about the size of a basketball) sits on the floor 
  • On five sides of the cube are written the numbers 1-5, just like a die
  • Students can observe the cube on all sides, up close, or from far away
  • The cube cannot be touched, moved, or flipped over
  • Students must determine what is on the bottom face of the cube, and what reasoning helped them arrive at their determination
  • Students then create a whiteboard with their group that displays what they think is on the bottom face of the cube and explains their reasoning
Once students have constructed their whiteboards, they will present their ideas to their classmates and discuss everyone's reasoning. This is a process that makes thinking visible to other students. After discussing the ideas of each group and giving students the opportunity to question one another's reasoning, we ask students to vote as a class on one idea that they can accept. We do this with a 'show of thumbs' where:
  1. Thumbs Up = agree with the idea and reasoning
  2. Thumbs Down = disagree with the idea and reasoning
  3. Thumbs Sideways = could accept the idea but perhaps differ in reasoning
After an initial vote, we see where the class stands, give students a chance to ask additional questions, change their minds based on any newly shared information, and then revote. When the class arrives at consensus, they erase their whiteboards. 

The importance of arriving at consensus is discussed with students; the process they just went through to arrive at consensus is made transparent by naming/describing the steps; and the activity is debriefed by students. 

Students are really eager to find out what is on the bottom face of the cube, but it must be stressed to students that this activity is done to show how learning will look/feel in this class:
  • It can be frustrating not to know everything, sometimes; however, uncertainty helps us grow in our understanding
  • It is not about answers, it's about how you arrive at answers and solve problems
  • When we focus on answers, and not process, it leads to a fixed mindset
  • Fixed mindedness promotes worry about grades, being smart, and leads to self-limitations
  • Our class encourages growth mindset, where students can work to surpass their current knowledge and ability through teamwork, critical thinking, and practice
  • The process we used in this activity to arrive at consensus will be our most important learning tool
This activity is a very low-risk opportunity for classes to practice all the skills necessary to doing the model development cycle, whiteboarding, and arriving at class consensus. It was originally used as a get-to-know-you team-building activity when I first saw it; however, I wanted it to be more than just that. It has proven to be a thought-provoking activity to promote discussion and questioning in students as well as demonstrate model development and arriving at consensus.

One of the most insightful parts of this activity, and perhaps a subversive outcome, is observing the variety of ideas that students share about what might be on the bottom face. Student-thinking and lines of reasoning are two fascinating elements of education, and this activity illustrates those very well. 

All too often, school is reduced down to answers. The focus on answers starts early in elementary school and 'programs' student thinking, which leads to a fixed mindset as students get older. The limitations of a fixed mindset are perhaps at the root of many of the challenges students experience in school, but this can all be overcome if the focus is shifted from answers to process, the mindset can become a mind shift. Students can begin to move toward a growth mindset and realize that their potential is up to them. Ultimately, isn't this a message we want students to take away from school and use in their future? 


  1. Love it! Is the 6th side blank and you just want to see what the kids will come up with and how they'll justify their conclusions, or is there an answer that you (for obvious reasons) didn't put in the blog? I ask because I'm definitely going to be making one this weekend.

  2. I guess I would respond with a question: What do YOU think is on the bottom face, and what reasoning makes you think so?

  3. Hi Gary

    A great activity and I like the approach. A couple of questions:

    If I can see 5 out of 6 numbers, does assumption come into the response?
    How long do you allow for the exercise?
    What are your thoughts on using abstract items on the visible walls such as a picture of a dog, a river, some lines, a number, etc?

    I am keen to find a good consensus building activity to use in my own teaching practices.

    Best regards

  4. That’s interesting and what makes it interesting is habit is a unique game of all I haven’t seen such of it before or a group of office mates playing such a game together. This is fun.

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  7. Thank you so much for sharing! I coach a division 1 Odyssey of the Mind Team, and am working with them to develop their teamwork skills. While searching for consensus building exercises, I've happened upon your post. In Odyssey, we are more concerned with creative problem solving and teamwork than arriving at 'the right answer.' So excited to bring this to the team. They'll talk for days! Many thanks for sharing.

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  10. we are more concerned with creative problem solving and teamwork than arriving at 'the right answer.' So excited to bring this to the team. They'll talk for days! Many thanks for sharing mp4hentai


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