Intellectual expertise is knowledge and ability that a person has that allows them to solve extremely complex problems. It is important to understand how people become experts so that we can improve educational strategies, and help learners achieve their full academic potential. Unfortunately, the process of acquiring intellectual expertise is not well understood. The goal of this research is to build and test a computational theory of this process. My approach is to train artificial neural networks (ANNs) as a model of expert human learning. ANNs address many of the difficulties found in trying to study expertise in humans; they have already been successful in modeling other types of human learning. In completed work, I have built a first version of the model and used it to confirm two hypotheses: (1) An artificial neural network can be used as a model to investigate how people learn under different training scenarios. (2) Different methods for delivering the training material result in different final performance, and best performance is achieved by incrementally increasing the complexity of the material. I am currently testing a third hypothesis: Different delivery methods result in different internal conceptual representations and conceptual development, which in turn is responsible for the different performance. The results suggest that psychological learning theory should be considered when designing instructional strategies. My research has shown that, in contrast with symbolic models of cognition, connectionist models are able to model the human learning process, and provide practical insights into how people should be trained.