Refraction is an online puzzle game for teaching fractions developed by the Center for Game Science at the University of Washington. In the game, the player builds a network of devices that split and recombine lasers (dividing and adding their fractional power levels) in order to power disabled spaceships and save the animals inside. Along with the mathematical challenge of each level, the player must use devices to bend lasers around obstacles and to form the right beams from the right directions. Puzzles generally have many solutions, but all of them involve the target concepts. The integration of mathematical and spatial reasoning into every puzzle yields an engaging experience even for those who are competent with the game’s target fraction concepts: equal partitioning, addition, multiplication, mixed numbers, improper fractions, and common denominators.
The public version of Refraction employs a single static level progression for all players. Analysis of telemetry indicates that there are significant opportunities to improve the quality of the game and its teaching effectiveness by providing each player with a custom-designed level that takes into account their play style and knowledge of mathematical and spatial problem solving techniques. In collaboration with the Center for Games and Playable Media, Refraction now possesses a suite of powerful design automation tools that aim to provide a designer-in-the-box for use in a deeply generative and adaptive sequel to the original game. The mission generation tool translates mathematical requirements on a level into a set of high-level steps a player should complete in a puzzle. The grid-embedding tool takes a mission and determines a way to place it into the game’s 10x10 grid in a way that respect the game’s mechanics, knowledge of the player’s skill, and aesthetic style constraints. Finally, the solver tool takes a pre-existing puzzle and decides whether there are solutions to it that can be formed under certain constraints on player style. Assembling all three design automation tools together, we have a fully-automated prototype system that can devise levels that are easy for one type of player and hard for another, all the while respecting any requirements placed on the puzzle by a separate online progression management system.
This material is based upon work supported by the National Science Foundation under Grant No. 1048385. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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UCSC: Adam Smith
UW: Erik Andersen, Yun-En Liu, Eric Butler, and the Refraction Team
Early level generation prototype