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Developing Mathematical Reasoning using Attribute Games

By Anne Larson Quinn, Ph.D., Associate Professor, Edinboro University, Quinna@edinboro.edu
Frederick Weening, Ph.D., Assistant Professor, Edinboro University, Fweening@edinboro.edu
Robert M. Koca, Jr., Ph.D.

Reproduced with permission from the Mathematics Teacher, copyright 1999 by the NCTM.

The game of SET® has proven to be a very popular game at our college mathematics club meetings. Since we've started playing, the membership has grown every month. In fact, one of our members brought her six year old son to a meeting, and he now looks forward to playing SET® with us every month. As a result of playing the game in our club and thinking about the results, we created and solved a variety of mathematical questions. For example, we wondered about possible strategies for winning and conjectured about phenomena that happened when playing. These questions involve a wide variety of traditional mathematical topics, such as the multiplication principle, combinations and permutations, divisibility, modular arithmetic, and mathematical proof.

In addition to encouraging the posing and solving of these problems in our math club, we took the game and our questions into our classrooms to see what reasoning could be encouraged. We tested our original questions on several groups of junior high and high school students and on several hundred freshmen and sophomore college students who were not mathematics majors.

The purpose of this article is to show how games such as SET® can be used to develop mathematical reasoning by describing student investigative work that has resulted from playing the game. After giving a description of the game, we will pose and answer some of the questions that were solved by members of our club and by students ranging in academic level from ninth grade to college. We will also describe what teachers can do to facilitate the development of reasoning using this game. Although this article discusses problems that were generated from the game of SET®, any game that uses attributes can be used to stimulate logical thinking.

Click on the attachment below to read the full paper.

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