A Structured Framework for Using Games to Teach Mathematics and Science in K-12 Classrooms.

Introduction The notion of using games to engage children in learning activities is not new. Instinctively, kids create games to help them make sense of the world around them. Mostly, they play rules-based sports games, where they interact according to specified rules of engagement that determine the behavior of players and the results of their interactions. Beyond these rules-based games, children also participate in "pretend games," where they mimic the behavior of adults and explore the implications of rules and the roles in society. There is no doubt that one way to generate children's interest in mathematics and science is through their favorite activities or games (Markey, Power, 8 Booker, 2003). In their classic book, Von Neuman and Morgenstern (1994) provided a framework for looking at games and showed how games may be categorized by the constraints put on the various players. Von Newman and Morgenstern showed that rules-based games rely on actions and reactions of players, while unstructured games (like "storekeeper") require that players contribute to the game no less than they take away. Whatever the particular rules, children use games to frame their beliefs about competition, as well as how to relate to other players and, most importantly, how to be successful. To a great extent, the classroom environment can be compared to a game. First, there are rules to define acceptable conduct for participants (teachers, students, and others) and outcomes, which determine successful and unsuccessful behavior. Traditionally, these outcomes were restricted to students (pass, fail, A, B, C, etc.), but recently outcomes are directed at teachers and school administrators, who are now accountable for student achievement in the form of legislation such as the Virginia Standards of Learning, where school designations are issued (accredited, accredited with warning, or needs improvement). Outlook on Game Theory If the association to games is valid, and the classroom environment is the setting for a high stakes game, what are the implications for the players? What is the penalty for not understanding the game properly? How can we leverage finding out what we know about games to help children learn more successfully? This idea of using games to improve the outcomes and performance of people is not new. Economists and mathematicians have contributed much to "game theory" as a structured approach for understanding business interactions (Brozik 8 Zapalska, 1999, Santos, 2002). Briefly, game theory can be divided into three broad categories: economic, combinational, and computational (Garcia et al, 2003), where interactions in the classroom fall into the first category. The latter involve finite two-person games that involve complete information games and their sums (combinatorial games) and games that require computation to create a worthy opponent. While there is pedagogy to be applied in both situations, our interest is in the former category (economic games), which mirror classroom interactions. Just like business, the classroom is a competitive environment, where teaching pedagogy may follow cooperative or non-cooperative frameworks for student interactions. In science and engineering majors at the college level, Seymour and Hewitt (1994) have argued that the learning environment is so individualistic and competitive that a "weed-out" mentality mirrors a ritualistic "masculine rite of passage" or "heroic journey" that works against the healthy representation of women in these fields. While the preceding point pertains to higher education, the same principles may be extended to K-12, since both involve risk factors and the drive toward achievement. The overarching connection between the learning environment and the business world is that they are not just about winning and losing. Both differ from war games and sports in this critical characteristic. In the classroom, as in business, winning is not predicated on someone else losing. …