Coloring games are combinatorial games where the players alternate painting uncolored vertices of a graph one of k > 0 colors. Each different ruleset specifies that game's coloring constraints. This paper investigates six impartial rulesets (five new), derived from previously-studied graph coloring schemes, including proper map coloring, oriented coloring, 2-distance coloring, weak coloring, and sequential coloring. For each, we study the outcome classes for special cases and general computational complexity. In some cases we pay special attention to the Grundy function.
Model-tracing tutors (MTTs) have proven effective for the tutoring of welldefined tasks, but the pedagogical interventions they produce are limited and usually require the inclusion of pedagogical content, such as text message templates, in the model of the task. The capability to generate pedagogical content would be beneficial to MTT frameworks, as it would lessen the task-specific efforts and could lead to the capability of providing more sophisticated pedagogical interventions. In this paper, we show how Astus, as an MTT framework, strive to attain a higher level of automation when generating pedagogical interventions compared to other MTT frameworks such as TDK and CTAT's MTTs. This is achieved by designing a knowledge representation approach in which each type of knowledge unit has a clearly defined semantic on which the MTT's pedagogical module can rely on. We explain how this knowledge representation approach is implemented as a knowledge-based system in ASTUS and show how it allows the development of MTTs that can automatically generate the pedagogical content required to provide next-step hints and negative feedback on errors. Multiple small-scale experiments were conducted with computer science undergraduate students in order to obtain a preliminary assessment of the effectiveness of Astus's pedagogical interventions.
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