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

TL;DR

This study tackles the problem of detecting careless errors in digital learning by addressing the limitations of the contextual slip model, which struggles with multi-skill items. It introduces the Beyond-Knowledge Feature Carelessness (BKFC) model, which uses Performance Factor Analysis (PFA) to estimate knowledge and leverages 17 behavioral features to detect carelessness, even when questions involve multiple skills. The BKFC approach yields a normally distributed carelessness signal and shows a negative association with post-test performance, contrasting with the positive associations observed for carelessness detected by BKT-based and ML contextual slip models; BKFC also shows different patterns with engagement measures. The findings underscore the broader challenge of operationalizing carelessness and suggest BKFC as a complementary tool for detecting careless behavior in more complex item formats, with implications for targeted interventions and future integration with advanced knowledge-tracing methods.

Abstract

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 (PFA) 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.

Figures (2)

• Figure 1: Problem-solving and self-explanation step in Decimal Point
• Figure 2: Distribution of carelessness across the three models: BKT contextual slip (left), ML contextual slip (middle), BKFC (right).