Video Games for Math: A Case For "Kid Culture"
By Lawrence Shirley, Department of Mathematics
Towson State University. Towson, Maryland

Nintendo and other video games have gained a reputation (or notoriety) of occupying so much of children's time that their schoolwork may suffer. However, rather than fighting this invasion, I suggest that we exploit video games for mathematics education, drawing values from the thinking processes learned and used in playing the games. Recently, the Nintendo company made grants to research projects in education, so it appears the company is reaching out to education. Why don't we respond by seeing the educational value of video games?
There are several types of video games and hence different types of cognitive skills involved and different ways they could be used in mathematics. One of the older types is target shooting games, such as "Duck Hunt," which is even included in a popular basic package of the Nintendo control set. Of course, these kind of games depend a lot on hand-eye coordination and timing, but the player also gains practical experience with trajectories and speed-time relationships. Maze games, often with villains in the maze to chase you, date back to "Pac-Man" in the 1970s and remain popular today. An important skill in this type of game is to build a mental map of the maze and its dangers, leading to geometrical and topological thinking experience. A third type, often including a maze, is a quest game, such as "Castlevania," where the player has an assignment of saving the princess or finding the pot of gold after struggling through many obstacles. Like the mazes, these involve map building and topology, but also require developing strategies to fight the dangers and difficulties in the way. Other games involve sports activities, simulations of driving cars or flying planes, and other skills of varying relationships to mathematics.

Mathematical Values

Video games offer many different values to mathematics education. The most easy to see are in geometry. Game players need to develop a good sense of space and topological relationships. Teachers could use this by having children do projects of drawing maps of the paths they follow in maze and quest games, including special "warp zone" paths that jump from one region of the game's world to another. Planning and strategic thinking skills are a part of many games from chess to Mastermind and also are prominent in many video games. One must plan a course of action, gather necessary materials, and follow a smooth sequence of tactics to win the victory. This is also crucial to mathematical problem solving-Polya's second step is to plan a strategy for solution. Children can discuss the values of sequencing, and link this to seriation, the commutative law, the order of arithmetic operations, and flow-charting. Finding patterns is another mathematical skill of many video games--fitting pieces of a puzzle together, recognizing relationships--just as in finding mathematical patterns areas ranging from transformational geometry to abstract algebra to functional analysis.
It is easy to see how video game skills fit into the NCTM Standards. Problem solving is essential to success both in winning a video game and learning mathematics. Spatial sense and pattern finding are key ingredients of both. By encouraging children to talk about video game strategies and draw diagrams of game worlds, the teacher is strengthening mathematical communication. Of course by reaching out to "kid culture," the mathematics teacher is showing connections between mathematics and its applications in daily life. For best use of video games for mathematics, a teacher would need to become familiar with several of the popular games with an eye to where they fit into the curriculum. This may vary considerably from game to game and between different grade levels. However, as a sample we shall take a brief look at two popular Nintendo games, the Super Mario Brothers series and Tetris.
All of the Mario Brothers games involve traveling through various "levels" of several "worlds" in a quest activity. Each level of each world has its own environment with a series of obstacles and monsters blocking the way. One can avoid or fight the monsters, often collecting weapons along the way to throw at the monsters or to make the Mario figure larger or more powerful for jumping, running or even flying. To avoid having to go through all the worlds, there are several "warp zones" which are special hidden paths that allow jumping to advanced worlds instantaneously. The player must become familiar with the alternative paths, the locations of special tools, weapons, bonus coins, etc.
When kids talk about Mario games, the conversation often goes to secrets one has found that can be helpful to others in getting farther into the game without "dying." This is where mathematical thinking can be helpful and where a teacher could plug the game into the curriculum. The teacher could ask the students to draw maps of the various "worlds," marking the various paths, dangers, and bonuses along the way. Students would need a sense of order and sequence, a topological feel and spatial sense for the vertices of the paths, and an idea of scaling to transform the worlds from the monitor to paper. Other work could include discussion of the values of speeding through the worlds quickly versus stopping to collect the bonuses and tools in a more deliberate manner. While not directly linked to mathematical curricular topics, the game is an extended exercise in problem solving and strategic thinking.
My favorite of the game I've seen, especially from a mathematical vantage, is "Tetris." This is a game of packing geometrical shapes as efficiently and compactly as possible. The screen shows tetrominoes (shapes made of four squares arranged in various patterns so they always touch edge-to-edge) falling slowly from the top, eventually landing in ever-filling layers of squares. As the shapes fall, the player can move them from side-to-side and can rotate them a full 360 degrees, to try to make them fit into the rows at the bottom. However, it is necessary to work quickly to get the shapes positioned properly before they reach the bottom, for once they touch the piles of squares, they stick and cannot be further moved. If a solid line of squares is filled it is automatically cleaned away, keeping the pile from building too high; but as gaps develop the incomplete lines of squares stay and the pile grows toward the top. When it builds so high that the new pieces touch the pile immediately, the game is ended. Scoring comes from the number of lines successfully completed.
The packing task itself gives much experience in spatial sense and a feel for the relationship of the tetromino shapes. Transformational geometry is also experienced in the rotation and sliding operations applied to the falling shapes. Since some of the tetromonies are symsnetric and others are not, the play also recognizes these differences in how the shapes can and cannot be packed. More generally, the use of the tetrominoes provides a nice introduction to general polyominoes (including the famous puzzles of pentamonies), and indirectly to nets, tangrams, and the properties of other geometrical shapes.
Incidentally, the choice of which tetromino will fall is done randomly and a tally of the numbers of each piece is shown on the screen. This, of course, could be used as an example in statistics or probability topics. Also, graphs and averages of scores in a Tetris competition are further mathematical applications of the game. These represent only a beginning. The teacher should try out the games and use creativity to see their applications to math (or other) topics.

Epilogue

Ethnomathematics, like anthropology, sometimes has a flavor of the exotic about it. However, anthropologists now argue that their field really should be the study of human culture--all human culture, not just those previously assumed to be somehow "primitive." In African universities, such studies of culture are often deemed "sociology" to avoid any negative connotations of "anthropology." In the same way, ethnomathematics, by its original meaning, attempts to broaden the meaning of academic mathematics to look for mathematics in any and all cultures. That broad definition need not be limited to foreign or third world cultures. Right under our noses, our children have their own culture. Rather than dismiss it, we need to seek out "kid culture" and demonstrate that it too is mathematics.