Graduate students in political science come to the discipline interested in exploring important political questions, such as "What causes war?" or "What policies promote economic growth?" However, they typically do not arrive prepared to address those questions using quantitative methods. Graduate methods instructors must provide the quantitative tools and statistical knowledge for answering these questions through data analysis. Often this is done with a heavy emphasis on lecture and textbook training, which comes with an array of Greek letters, formulae, and formal proofs, or by walking students through point-and-click statistical software without ever seriously engaging the underlying mathematical concepts. Neither approach is ideal because they both leave students lacking real understanding of core concepts. In this article, we discuss a useful alternative: Monte Carlo simulation. Simulations allow students to experience and visualize the meaning of core statistical concepts and to make comparisons between various statistical methods. We describe how simulation can illustrate these difficult concepts and improve comprehension of foundational material, even for students with minimal quantitative backgrounds.