Computer understanding and generalization of symbolic mathematical calculations: a case study in physics problem solving

An artificial intelligence system that learns by observing its users perform symbolic mathematical problem solving is presented. This fully-implemented system is being evaluated as a problem solver in the domain of classical physics. Using its mathematical and physical knowledge, the system determines why a human-provided solution to a specific problem suffices to solve the problem, and then extends the solution technique to more general situations, thereby improving its own problem-solving performance. This research illustrates a need for symbolic mathematics systems to produce explanations of their problem-solving steps, as these explanations guide learning. Although physics problem solving is currently being investigated, the results obtained are relevant to other mathematically-based domains. This work also has implications for intelligent computer-aided instruction in domains of this type.