Abstract The prevalence of e-learning systems and on-line courses has made educational material widely accessible to students of varying abilities and backgrounds. There is thus a growing need to accommodate for individual differences in e-learning systems. This paper presents an algorithm called EduRank for personalizing educational content to students that combines a collaborative filtering algorithm with voting methods. EduRank constructs a difficulty ranking for each student by aggregating the rankings of similar students using different aspects of their performance on common questions. These aspects include grades, number of retries, and time spent solving questions. It infers a difficulty ranking directly over the questions for each student, rather than ordering them according to the student’s predicted score. The EduRank algorithm was tested on two data sets containing thousands of students and a million records. It was able to outperform the state-of-the-art ranking approaches as well as a domain expert. EduRank was used by students in a classroom activity, where a prior model was incorporated to predict the difficulty rankings of students with no prior history in the system. It was shown to lead students to solve more difficult questions than an ordering by a domain expert, without reducing their performance.
Modeling students' knowledge is a fundamental part of intelligent tutoring systems. One of the most popular methods for estimating students' knowledge is Corbett and Anderson's [6] Bayesian Knowledge Tracing model. The model uses four parameters per skill, fit using student performance data, to relate performance to learning. Beck [1] showed that existing methods for determining these parameters are prone to the Identifiability Problem:the same performance data can be fit equally well by different parameters, with different implications on system behavior. Beck offered a solution based on Dirichlet Priors [1], but, we show this solution is vulnerable to a different problem, Model Degeneracy, where parameter values violate the model's conceptual meaning (such as a student being more likely to get a correct answer if he she does not know a skill than if he she does).We offer a new method for instantiating Bayesian Knowledge Tracing, using machine learning to make contextual estimations of the probability that a student has guessed or slipped. This method is no more prone to problems with Identifiability than Beck's solution, has less Model Degeneracy than competing approaches, and fits student performance data better than prior methods. Thus, it allows for more accurate and reliable student modeling in ITSs that use knowledge tracing. This paper describes an effort to model students' changing knowledge state during skill acquisition. Students in this research are learning to write short programs with the ACT Programming Tutor (APT). APT is constructed around a production rule cognitive model of programming knowledge, called theideal student model. This model allows the tutor to solve exercises along with the student and provide assistance as necessary. As the student works, the tutor also maintains an estimate of the probability that the student has learned each of the rules in the ideal model, in a process calledknowledge tracing. The tutor presents an individualized sequence of exercises to the student based on these probability estimates until the student has ‘mastered’ each rule. The programming tutor, cognitive model and learning and performance assumptions are described. A series of studies is reviewed that examine the empirical validity of knowledge tracing and has led to modifications in the process. Currently the model is quite successful in predicting test performance. Further modifications in the modeling process are discussed that may improve performance levels. Knowledge Tracing (BKT) is a common way of determining student knowledge of skills in adaptive educational systems and cognitive tutors. The basic BKT is a Hidden Markov Model (HMM) that models student knowledge based on five parameters: prior, learn rate, forget, guess, and slip. Expectation Maximization (EM) is often used to learn these parameters from training data. However, EM is a time-consuming process, and is prone to converging to erroneous, implausible local optima depending on the initial values of the BKT parameters. In this paper we address these two problems by using spectral learning to learn a Predictive State Representation (PSR) that represents the BKT HMM. We then use a heuristic to extract the BKT parameters from the learned PSR using basic matrix operations. The spectral learning method is based on an approximate factorization of the estimated covariance of windows from students' sequences of correct and incorrect responses; it is fast, local-optimum-free, and statistically consistent. In the past few years, spectral techniques have been used on real-world problems involving latent variables in dynamical systems, computer vision, and natural language processing. Our results suggest that the parameters learned by the spectral algorithm can replace the parameters learned by EM; the results of our study show that the spectral algorithm can improve knowledge tracing parameter- fitting time significantly while maintaining the same prediction accuracy, or help to improve accuracy while still keeping parameter-fitting time equivalent to EM.