In learning, errors are ubiquitous and inevitable. As these errors may signal otherwise latent cognitive processes, tutors--and students alike--can greatly benefit from the information they provide. In this paper, we introduce and evaluate the Systematic Error Tracing (SET) model that identifies the possible causes of systematically observed…

Unexpected outcomes can reflect noise in the environment or a change in the current rules. We should ignore noise but shift strategy after rule changes. How we learn to do this is unclear, but one possibility is that it relies on learning to learn in uncertain environments. We propose that acquisition of latent task structure during learning to…

This paper investigates how individuals' performances of a cognitive task in a high-pressure competition are affected by their peers' performances. To do so, I use novel data from the National Spelling Bee, in which students attempt to spell words correctly in a tournament setting. Across OLS and instrumental variables approaches, I…

The conflict monitoring account posits that globally high levels of conflict trigger engagement of top-down control; however, recent findings point to the mercurial nature of top-down control in high conflict contexts. The current study examined the potential moderating effect of associative learning on conflict-triggered top-down control…

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction and disjunction fallacies, averaging effects, unpacking effects, and order effects on inference. On the one hand, quantum theory is similar to other categorization and memory models of cognition in that it relies on vector…

Probability theory has long been taken as the self-evident norm against which to evaluate inductive reasoning, and classical demonstrations of violations of this norm include the conjunction error and base-rate neglect. Many of these phenomena require multiplicative probability integration, whereas people seem more inclined to linear additive…

This study examined age differences in error processing and reinforcement learning. We were interested in whether the electrophysiological correlates of error processing, the error-related negativity (ERN) and the feedback-related negativity (FRN), reflect learning-related changes in younger and older adults. To do so, we applied a probabilistic…

Judgments under uncertainty are often mediated by intuitive heuristics that are not bound by the conjunction rule of probability. Representativeness and availability heuristics can make a conjunction appear more probable than one of its constituents. Alternative interpretations of this conjunction fallacy are discussed and attempts to combat it…

A probabilistic approach is introduced to classify and diagnose erroneous rules of operation resulting from a variety of misconceptions ("bugs") in a procedural domain of arithmetic. The model is contrasted with the deterministic approach which has commonly been used in the field of artificial intelligence, and the advantage of treating the…

Several common errors reflecting difficulties in probabilistic reasoning are identified, relating to ambiguity, previous outcomes, sampling, unusual events, and estimating. Knowledge of these mistakes and interpretations may help mathematics teachers understand the thought processes of their students. (MNS)