Digital game-players devote a large amount of their time to discovering rules hidden in the code and discoverable through empirical study, experiments, and developing or rediscovering the mathematical formulae governing the code. They do this through their own independent play as they test areas, gear and abilities, through data mining using…

The assessment of knowledge and learning progress in the context of game-based learning requires novel, noninvasive, and embedded approaches. In the present paper, we introduce a mathematical framework which relates the (problem solution) behavior of a learner in the game context to the learner's available and lacking competencies. We argue that a…