Carelessness Detection using Performance Factor Analysis: A New Operationalization with Unexpectedly Different Relationship to Learning

--Detection of carelessness in digital learning platforms has relied on the contextual slip model, which leverages conditional probability and Bayesian Knowledge Tracing (BKT) to identify careless errors, where students make mistakes despite having the knowledge. However, this model cannot effectively assess carelessness in questions tagged with multiple skills due to the use of conditional probability. This limitation narrows the scope within which the model can be applied. Thus, we propose a novel model, the Beyond-Knowledge Feature Carelessness (BKFC) model. The model detects careless errors using performance factor analysis (PF A) and behavioral features distilled from log data, controlling for knowledge when detecting carelessness. We applied the BKFC to detect carelessness in data from middle school students playing a learning game on decimal numbers and operations. We conducted analyses comparing the careless errors detected using contextual slip to the BKFC model. Unexpectedly, careless errors identified by these two approaches did not align. We found students' post-test performance was (corresponding to past results) positively associated with the carelessness detected using the contextual slip model, while negatively associated with the carelessness detected using the BKFC model. These results highlight the complexity of carelessness and underline a broader challenge in operationalizing carelessness and careless errors. Academic discussions of carelessness in classrooms date back to the 1950s [1]. Often viewed as the result of ineffective self-regulation, carelessness is thought to occur when students commit hurried or impulsive behaviors that result in mistakes on problems that could have been answered correctly. By distinguishing mistakes made due to carelessness from those caused by other factors, such as lack of knowledge, adaptive instruction can be provided to engage or reengage students in the effective use of self-regulation during the process of problem-solving. In the last several decades, two streams of work have run in parallel to investigate carelessness and detect careless behaviors.