CONCEPTUAL FRAMEWORK FOR DESIGNING MATH COMPUTER GAMES: ELEMENTARY GAME THEORY DIMENSIONS FOR EDUCATORS

Dmitri Droujkov, Chris Hazard, Maria Droujkova

Phenix Solutions, North Carolina State University, Natural Mathddroujkov@phenixsolutions.com, cjhazard@hazardoussoftware.com, maria@naturalmath.com

Our study addresses the research problem of constructing an interdisciplinary conceptual framework for analyzing math games through a series of design decisions. While we focus on computer games, many of the principles apply to physical space games. Definitions of decisions come from game theory research and gaming studies (Gee, 2007; Myerson, 1997). The gameplay consequences of each decision are analyzed based on existing games viewed through the lens of these definitions. The mathematics education consequences of each decision are then analyzed based on the pedagogy embodied in the gameplay, and viewed through the lens of learning theories (Piaget, 1970; Pirie & Kieren, 1994; Vygotskii & Kozulin, 1986). A series of parallels between gaming concepts and pedagogical notions helps mathematics educators make sense of game theory concepts, and apply these concepts to teaching. The resulting structure makes it clear that some types of math games are overused, and other promising types are rarely employed by mathematics education game developers.

The decisions, as well as their mathematics and math education parallels, are made along these dimensions that provide dichotomies, gradients or levels:

Abstraction dichotomy: narrative-based vs. abstract; situated vs. formalized Revelation gradient: full disclosure to hidden information; open-book to closed-book Strategic gradient: strategic to typed; problem-solving to exercises Resource levels: bounded rationality gameplay or not; level or stage learning theories Agency and autonomy gradient: high to none; open-ended to closed-ended tasks Planning levels: interactions, tasks, tactics, strategies; order of math tasks Depth gradient: expert to superficial knowledge; deep learning to expository learning Goal gradient: sandbox play to clear goals; conceptual learning to procedural fluency

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and literacy (1st ed.). New York, NY: Peter Lang Publishing.Myerson, R. (1997). Game theory: Analysis of conflict. Cambridge, MA: Harvard University

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it and how can we represent it? Educational Studies in Mathematics, 26, 165-190.Vygotskii, L., & Kozulin, A. (1986). Thought and language. Cambridge, MA: MIT Press.