Game-based classroom activity is intended to leverage students' interest and motivation to play, and to provide safe contexts for supporting students' academic learning. However, a basic criticism of many games currently used in classroom settings is that they can fail to meaningfully embody academic content. A more subtle concern is that cognitive and social dynamics emerging from the structuring and enactment of poorly designed games may compromise students' affective disposition and, so, undermine their learning opportunities. Using the case of classroom games designed for mathematical learning, I propose to examine how certain structural dynamics of a learning activity such as the rules and protocol for interaction, choice of media, or criteria for success may influence student interest, engagement, and eventual learning outcomes. This theoretical article reviews cognitive, developmental, and game-related literature in order to develop a rationale for "accountable design"--an approach that considers how these dynamics may be coordinated to support both the instructional objectives of educators, as well as the individual social and developmental needs of students. (Contains 3 figures and 3 footnotes.)