Coordinating vector field equations and diagrams with a serious game in introductory physics

Mathematical reasoning with algebraic and graphical representations is important for a throughout understanding of physics problems and concepts. Many problems require students to fluently move between algebraic and graphical representations. We developed a freely available serious game to challenge the representational fluency of introductory students regarding vector fields. Within the game, interactive puzzles are solved using different types of vector fields that must be configured with the correct mathematical parameters. A reward system implemented in the game prevents from using trial-and-error approaches and instead encourages the player to establish a mental connection between the graphical representation of the vector field and the (algebraic) equation before taking any action. For correct solutions, the player receives points and can unlock further levels. The graphics implemented in the game make the effects of changing the direction of a field or its magnitude visible and thus can help the learner gain a throughout understanding of vector fields. We report about the aim of the game from an educational perspective, describe potential learning scenarios and put in perspective the use of the game in the classroom.