For the past 3 weeks, Orlando Math Circle’s Girls’ Special Project group has engaged
with recreational pattern discovery through games, discussion, and sheep.
Two college volunteers designed a simple simulation game, Sheep Machine, in which
players can zap sheep with a rainbow ray gun to change the color of their wool, ad infinitum.
Players are asked to figure out the pattern that the rainbow ray gun follows. In the spirit of Mathematical modeling, members of our Girls’ Special Project Group were invited to investigate the patterns that emerge, document their process of discovery, and present a solution to the pattern in the form of an equation: “Given a sheep of color X, when zapped, it will follow this pattern.”
Sheep Machine contains very limited instruction and simple controls: a left click will zap the sheep, and a right click will reset the sheep to its original state. Initially, Linus the pink-wooled sheep and Ada the cyan-wooled sheep occupy the Sheep Machine– but with the “Create new sheep!” feature, the students can add a third sheep, Grace, whose initial color can be chosen from a bank of ten colors. The students were given the Sheep Machine game with no other instruction or hints; it was made very clear to them that they will have to figure out their own ways of classifying data and communicating their thoughts and observations with one another.
The Sheep Machine project was started in an effort to encourage students to treat math in a way that a scientist might approach a problem: Have an initial reaction. Make predictions. If there aren’t any words to describe what you see, invent a language to communicate patterns and behavior. Design and document a repeatable experiment. Collect data– make sure the data makes sense– then collect it again. Recognize and acknowledge sources of error. Defend your decisions with logic and reasoning. Verbalize your hypotheses, process, failures, successes, and
results with peers– in a way that someone with no prior knowledge can digest.
Although Sheep Machine can be a culture shock for students that have never dealt with “math that doesn’t have one obvious solution,” playing with it has allowed our students to see the value in having a variety of minds working together, sharing observations, and offering unique angles toward a solution.
