Computational Science is an emerging interdisciplinary field that integrates computing, mathematical modeling and visualization to solve problems in physical, natural, behavioral and social sciences as well as problems in finance and engineering. It is at the intersection of mathematics, computer science and science, and provides an important approach for advancing the development of scientific knowledge at an undergraduate level. Use of this tool requires identifying a meaningful issue or question, introducing the topic in a standard fashion (qualitatively and/or through use of analytical equations, etc.), and then moving beyond a standard classroom treatment through use of an appropriate numerical method that allows students to enrich their learning experience. In this talk I will present two volcanological examples to illustrate the range of ways in which Computational Science methodologies can be brought to bear in the classroomthe first suitable for introductory level students and the other derived from materials prepared for use with a more advanced course.