Machine teaching has traditionally been constrained by the assumption of a fixed learner's model. In this paper, we challenge this notion by proposing a novel black-box Markov learner model, drawing inspiration from decision psychology and neuroscience where learners are often viewed as black boxes with adaptable parameters. We model the learner's dynamics as a Markov decision process (MDP) with unknown parameters, encompassing a wide range of learner types studied in machine teaching literature. This approach reduces teaching complexity to finding an optimal policy for the underlying MDP. Building on this, we introduce an algorithm for teaching in this black-box setting and provide an analysis of teaching costs under different scenarios. We further establish a connection between our model and two types of learners in psychology and neuroscience, the epiphany learner and the non-epiphany learner, linking them with discounted and non-discounted black-box Markov learners respectively. This alignment offers a psychologically and neuroscientifically grounded perspective to our work. Supported by numerical study results, this paper delivers a significant contribution to machine teaching, introducing a robust, versatile learner model with a rigorous theoretical foundation.