Today's generative AI systems are tuned to present information by default, rather than engage users in service of learning as a human tutor would. To address the wide range of potential education use cases for these systems, we reframe the challenge of injecting pedagogical behavior as one of \textit{pedagogical instruction following}, where training and evaluation examples include system-level instructions describing the specific pedagogy attributes present or desired in subsequent model turns. This framing avoids committing our models to any particular definition of pedagogy, and instead allows teachers or developers to specify desired model behavior. It also clears a path to improving Gemini models for learning -- by enabling the addition of our pedagogical data to post-training mixtures -- alongside their rapidly expanding set of capabilities. Both represent important changes from our initial tech report. We show how training with pedagogical instruction following produces a LearnLM model (available on Google AI Studio) that experts substantially prefer across a diverse set of learning scenarios, with average preference strengths of +31\% over GPT-4o, +11\% over Claude 3.5 Sonnet, and +13\% over the Gemini 1.5 Pro model on which LearnLM was based.