Performance of the adaptive algorithm in tracking the knowledge of actual children. a. Estimated knowledge space at the end of training for one subject (same format as figure 2a). This subject attained a high level of achievement in distance and complexity dimensions, but remained limited in the speed dimension. b. Regions of knowledge space where errors were corrected in the course of training. The graph shows the probability density of errors observed throughout the training period which were later corrected (i.e. at the end of training the corresponding region had an estimated probability of success > 0.95). c. Evolution of the knowledge volume for six representative children. All showed evidence of learning (compare figure 2b). d. Here we compare the evolution of knowledge for two children; measured in a narrow rectangular cube along each dimension, which allows a relatively bias free measurement of progress for that dimension in particular. Both children quickly hit an asymptote on the speed dimension, but their performance showed a double dissociation along the distance and complexity dimension. Note: The dotted curves in figures c and d are included for comparison and represent knowledge volume change over time in simulations with a fixed knowledge of 0.4 and 1 (as in figure 2b).