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To help facilitate play and learning, game-based educational activities often feature a computational agent as a co-player. Personalizing this agent's behavior to the student player is an active area of research, and prior work has demonstrated the benefits of personalized educational interaction across a variety of domains. A critical research challenge for personalized educational agents is real-time student modeling. Most student models are designed for and trained on only a single task, which limits the variety, flexibility, and efficiency of student player model learning. In this paper we present a research project applying transfer learning methods to student player models over different educational tasks, studying the effects of an algorithmic "multi-task personalization" approach on the accuracy and data efficiency of student model learning. We describe a unified robotic game system for studying multi-task personalization over two different educational games, each emphasizing early language and literacy skills such as rhyming and spelling. We present a flexible Gaussian Process-based approach for rapidly learning student models from interactive play in each game, and a method for transferring each game's learned student model to the other via a novel instance-weighting protocol based on task similarity. We present results from a simulation-based investigation of the impact of multi-task personalization, establishing the core viability and benefits of transferrable student models and outlining new questions for future in-person research.