Knowledge representations are central to many cognitive processes, and how these representations change is a central issue in learning and cognitive development. Here we developed and implemented a Bayesian inferential procedure to detect and elucidate representational change in numerical estimation. The proposed procedure of an adaptive numerical experiment both infers a learner's representation and predicts the feedback that is likely to induce representational change. We provide an application of this procedure using simulated subjects and demonstrate its effectiveness in inferring representational state and inducing change.