We have developed models of how strategies are constructed and retained as male and female high school and university students gain experience in solving online qualitative chemical analysis problems. The most common strategies that students used when solving online problem-solving simulations were first classified using self-organizing artificial neural networks. This resulted in strategy maps detailing the spectrum of problem solving strategy and highlighting the qualitative and quantitative differences among these approaches. Next, learning trajectories were developed by Hidden Markov Modeling of sequences of performances, which stochastically described student's progress in understanding chemistry. We have found that students quickly establish preferred strategic approaches and that these stabilized strategic approaches are re-used up to four months later to solve additional cases. While males and females correctly identified the same percentage of unknown compounds, the prop...