# Games That Promote Mathematical Thinking

A few years ago, I went to a conference where I was able to listen to Keith Devlin, a noted mathematician from Stanford, talk about using technology, particularly computer games, to help students think mathematically. He made the case that the symbols we use to represent mathematics, like numerals, operation signs, etc. create a barrier for students and that computer technology has the ability to help students access the mathematical thinking before they know the symbolic representation.

In a review of over a thousand online math games, he and his team found only a small handful that did this. Most fell into two other categories:

1) you practice math you know in order to get the reward of playing another round of the game; or

2) you practice the math you know as part of the game.

In either case, these games were about practicing using the symbols that represent mathematics. What does it look like, then, to have a game in which students develop an understanding of the math as part of the game without having to know the symbols of the math? These symbols would not hold meaning for the student anyway because they don’t have a well-constructed concept for what the symbols mean

Over the last month, we have discussed activities in which students think about multiplication without using the symbols of multiplication. This includes the label “multiplication” (words are symbols also) or the symbol “x.” Students worked with groups of equal sizes in a variety of contexts, but how do we turn these activities into games? This was what we tried to do with our most recent activity.

Games have a goal, a set of rules, and might involve some competition. The success of the game is self-regulated. You don’t need to tell me I won at chess or checkers. This is defined by the rules. Also, participation in the game should be focused on the development of mathematical thinking, not only practicing the math a student already knows.

The game we came up with is 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 to the emperor three things: the number of sections they made, the number of squares long for each section, and how many squares long the entire part of the wall was. They did this without looking at the drawing of the wall they had made. Then they could look at the wall they drew, counting the squares that make the wall, and check the answer they gave for how long the wall was to get a bonus from the emperor for having a correct report.

In our first week of doing the game, we just focused on students learning the game. We found that just learning the rules of the game and creating an engaging narrative have to be in place before students can actually play the game and think mathematically. When student made the sections of the wall they alternated color pens and drew a straight line to represent the section of wall. As we continue with our game, I will continue with another blog post to describe the successes and failures of trying to help students access mathematical thinking through a game.