Teachers may be attracted to the use of a game in a learning activity under the presumption that students will find the game experience to be more “fun” than typical classroom activities. The use of a game in a learning activity should help students attain important learning outcomes and engage them in mathematical reasoning and sense making. While most of the research attention has been devoted to digital learning games, multiplayer tabletop mathematics learning games afford unique opportunities (and challenges) to engage students in meaningful mathematical activity and discourse.
Engle and Conant’s (2002) construct of productive disciplinary engagement is used to frame the notion of learner engagement with mathematical ideas during gameplay. The expectancy-value theory of achievement motivation applied to the mathematics learning game context suggested a motivational construct called subjective gameplay-value that captures multiple reasons behind a student’s willingness to play a learning game, including both enjoyment and learning value.
Two sets of principles are proposed, based on these theoretical frameworks and the game-based learning literature: 1) design principles to guide creation of games that engage students with important mathematical ideas while also motivating them to play, and 2) implementation principles to help teachers make effective use of multiplayer tabletop mathematics learning games as classroom learning activities and to facilitate mathematical discourse.
The function representations card game Curves Ahead! was created using the design principles, and then playtested as part of a design experiment to refine the game. Embedded in the game are mathematical tasks requiring students to connect and interpret multiple representations of functions. Early playtests suggested which game features were impacting subjective gameplay-value. After iterative refinements and modifications, the resulting game was playtested with differential calculus students to assess perceptions of its subjective gameplay-value.
The calculus board game Assembly Lines was also created using the design principles. Embedded in the game are tasks requiring graphical interpretation of derivatives, antiderivatives, and the Fundamental Theorem of Calculus. Game sessions with calculus students were conducted using the implementation principles. Video recordings of the sessions were analyzed to investigate how calculus students were productively engaging with mathematical ideas. The results suggested that all students were engaged in mathematical reasoning and sense making during gameplay, and most students were making “intellectual progress.” The sessions also revealed potentially positive and negative impacts of participant interactions that have implications for teacher facilitation during gameplay.