Defining Mastery: Knowledge Tracing Versus N- Consecutive Correct Responses

Knowledge tracing (KT) is well known for its ability to predict student knowledge. However, some intelligent tutoring systems use a threshold of consecutive correct responses (N-CCR) to determine student mastery, and therefore individualize the amount of practice provided to students. The present work uses a data set provided by ASSISTments, an intelligent tutoring system, to determine the accuracy of these methods in detecting mastery. Study I explores mastery as measured by next problem correctness. While KT appears to provide a more stringent threshold for detecting mastery, N-CCR is more accurate. An incremental efficiency analysis reveals that a threshold of 3 consecutive correct responses provides adequate practice, especially for students who reach the threshold without making an error. Study II uses a randomizedcontrolled trial to explore the efficacy of various N-CCR thresholds to detect mastery, as defined by performance on a transfer question. Results indicate that higher thresholds of N-CCR lead to more accurate predictions of performance on a transfer question than lower thresholds of NCCR or KT.