There has been considerable interest in constructing pen-based intelligent tutoring systems due to the natural interaction metaphor and low cognitive load afforded by pen-based interaction. We believe that pen-based intelligent tutoring systems can be further enhanced by integrating animation techniques. In this work, we explore methods for recognizing and animating sketched physics diagrams. Our methodologies enable an Intelligent Tutoring System (ITS) to understand the scenario and requirements posed by a given problem statement and to couple this knowledge with a computational model of the student's handwritten solution. These pieces of information are used to construct meaningful animations and feedback mechanisms that can highlight errors in student solutions. We have constructed a prototype ITS that can recognize mathematics and diagrams in a handwritten solution and infer implicit relationships among diagram elements, mathematics and annotations such as arrows and dotted lines. We use natural language processing to identify the domain of a given problem, and use this information to select one or more of four domain-specific physics simulators to animate the user's sketched diagram. We enable students to use their answers to guide animation behavior and also describe a novel algorithm for checking recognized student solutions. We provide examples of scenarios that can be modeled using our prototype system and discuss the strengths and weaknesses of our current prototype. Additionally, we present the findings of a user study that aimed to identify animation requirements for physics tutoring systems. We describe a taxonomy for categorizing different types of animations for physics problems and highlight how the taxonomy can be used to define requirements for 50 physics problems chosen from a university textbook. We also present a discussion of 56 handwritten solutions acquired from physics students and describe how suitable animations could be constructed for each of them.