The Mathematical Discourse Teaching Simulator (MDTSim) is a web-based multi-modal chat tool designed to provide mathematics teachers with opportunities to develop high-leverage teaching practices. Users of the tool adopt the role of a teacher and interact with a virtual student by exchanging written text, visualizations, graphs, or other virtual manipulatives. At the end of the conversation, the tool provides automated formative feedback. The tool supports a wide range of use cases, with customizable scenarios and virtual students played by human actors or AI-chatbots.