# Games That Promote Mathematical Thinking, Part 2

Before Christmas our team developed a game to work with students on building the concept of equal size groups. We named the game “The Great Wall.” Students are given the task of building the Great Wall of China for the emperor. They are directed to build sections of the wall, each a certain number of squares long and then report three things to the emperor: the number of sections they made, the number of squares long for each section, and the total number of squares long the entire part of the wall was. They made their report without looking at the drawing of the wall they had previously made. This requires the student to imagine the wall and begin to build the ideas associated with multiplication. Afterward, they could look at the wall they drew, count the squares that made the wall, and check the answer they gave for the total length to get a bonus from the emperor for having a correct report.

As we tried the game with the students, we saw some interesting things. One was that students had a more difficult time counting the squares to make the sections of the wall than we expected. This was problematic when we had them check their answers. In one case, a student figured out the correct number of blocks used to make x number of y blocks each and got confused when he counted the blocks in the drawing and ended up with a different number.

Another interesting behavior we saw was how some students would make a section of wall with, say, six blocks by counting each block at a time while other students would sweep along the blocks until it was six blocks long. The students that swept along the blocks seemed to have an easier time remembering the number of sections and the number of blocks in each section than the students who counted each block.

Through the development and use of the game as an independent activity, we found that the students took more time learning how to think about the mathematics during the game than we originally intended. If the game is designed for students to construct new mathematical ideas, then how realistic is it to have them work without a teacher monitoring? Does that mean that games in classrooms should be used only for reinforcing the mathematics students have already constructed? Or can they serve another purpose as well?

We want to engage students in activities that relate to their enjoyment of games. Doing so means creating a balance between two elements: the thinking energy spent on the game playing versus the energy spent on mathematical thinking. The best games accomplish both of these things.

I would enjoy hearing your experiences trying to make games out of mathematics. Where have you found success in gamifying mathematics?