Category learning has traditionally been studied by examining how percentage correct changes with experience (i.e., in the form of learning curves). An alternative and more powerful approach is to examine dynamical learning trajectories--that is, to examine how the parameters that describe the current state of the model change with experience. We describe results from a new experimental paradigm in which empirical-learning trajectories are directly observable. In these experiments, participants learned two categories of spatial position, and they were constrained to identify and use a linear decision bound on every trial. The dependent variables of principal interest were the slope and the intercept of the bound used on each trial. Data from two experiments supported the following conclusions. (1) Gradient descent provided a poor description of the empirical trajectories. (2) The magnitude of changes in decision strategy decreased with experience at a rate that was faster than that predicted by gradient descent. (3) Learning curves suffered from substantial identifiability problems.