Mathematics learning within the context of videogames is an increasingly important area of study that has not yet fulfilled its promise of powerfully contextualized and transformative learning. This research served to begin pushing the boundaries of the field by relying upon cutting edge mathematics education research on fractions and the best practices of game design through the development of "Rolly's Adventure", a videogame about multiplication of fractions with five specific characteristics: 1) consistent and useful feedback; 2) high enough levels of difficulty and ambiguity that players experience frequent failure; 3) non-standard mathematical representations and interactions; 4) mathematical notation introduced late; and 5) the legitimate possibility of alternative conceptual paths for successful progression. These five features were found to support mathematical play, as participants engaged in cycles of hypotheses and failure through generalizing acts during the game. The participants continued to generalize after the game, and were able to relate the gameplay experience to more traditional fractions problems. This document provides a full literature review of videogames and learning, fractions learning, and the synthesis of those two fields, and concludes with two journal articles about mathematical play and learning. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]