Periods of relatively stable, rule‐like behavior alternated with short transition periods characterize cognitive development on reasoning tasks like the balance scale task. Each transition gives rise to an improvement in behavior, until a phase is reached in which performance is flawless or improvement is not worthwhile given the necessary extra effort. Several computational models have been developed to capture the developmental phenomena associated with the balance scale task. These models, which originate from different computational traditions, explain the main phenomena of (...) development. Recently, empirical phenomena have been reported that these models cannot easily accommodate. We propose a computational model that is implemented in ACT‐R and that is based on the evaluation of success of applied knowledge, combined with a mechanism to construct newknowledge by searching for differences between the left‐ and right‐hand sides of presented balance scale problems. This model accounts for the main empirical phenomena as well as for the recently reported empirical phenomena such as learning without feedback. (shrink)

Most models of response time (RT) in elementary cognitive tasks implicitly assume that the speed-accuracy trade-off is continuous: When payoffs or instructions gradually increase the level of speed stress, people are assumed to gradually sacrifice response accuracy in exchange for gradual increases in response speed. This trade-off presumably operates over the entire range from accurate but slow responding to fast but chance-level responding (i.e., guessing). In this article, we challenge the assumption of continuity and propose a phase transition model for (...) RTs and accuracy. Analogous to the fast guess model (Ollman, 1966), our model postulates two modes of processing: a guess mode and a stimulus-controlled mode. From catastrophe theory, we derive two important predictions that allow us to test our model against the fast guess model and against the popular class of sequential sampling models. The first prediction—hysteresis in the transitions between guessing and stimulus-controlled behavior—was confirmed in an experiment that gradually changed the reward for speed versus accuracy. The second prediction—bimodal RT distributions—was confirmed in an experiment that required participants to respond in a way that is intermediate between guessing and accurate responding. (shrink)