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.
Our work relates to several areas of research in student modeling. Several approaches within the educational data mining community have used computational methods for sequencing students' learning items. Pardos and Heffernan @cite_39 infer order over questions by predicting students' skill levels over action pairs using Bayesian knowledge tracing. They show the efficacy of this approach on a test-set comprising random sequences of three questions as well as simulated data. This approach explicitly considers each possible order sequence and does not scale to handling a large number of sequences, as in the student ranking problem we consider in this paper.
@cite_39
2129373702 1597703949 160448112 2339576062
Researchers who make tutoring systems would like to know which sequences of educational content lead to the most effective learning by their students. The majority of data collected in many ITS systems consist of answers to a group of questions of a given skill often presented in a random sequence. Following work that identifies which items produce the most learning we propose a Bayesian method using similar permutation analysis techniques to determine if item learning is context sensitive and if so which orderings of questions produce the most learning. We confine our analysis to random sequences with three questions. The method identifies question ordering rules such as, question A should go before B, which are statistically reliably beneficial to learning. Real tutor data from five random sequence problem sets were analyzed. Statistically reliable orderings of questions were found in two of the five real data problem sets. A simulation consisting of 140 experiments was run to validate the method's accuracy and test its reliability. The method succeeded in finding 43 of the underlying item order effects with a 6 false positive rate using a p value threshold of <= 0.05. Using this method, ITS researchers can gain valuable knowledge about their problem sets and feasibly let the ITS automatically identify item order effects and optimize student learning by restricting assigned sequences to those prescribed as most beneficial to learning. 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. Student modeling is an important component of ITS research because it can help guide the behavior of a running tutor and help researchers understand how students learn. Due to its predictive accuracy, interpretability and ability to infer student knowledge, Corbett & Anderson’s Bayesian Knowledge Tracing is one of the most popular student models. However, researchers have discovered problems with some of the most popular methods of fitting it. These problems include: multiple sets of highly dissimilar parameters predicting the data equally well (identifiability), local minima, degenerate parameters, and computational cost during fitting. Some researchers have proposed new fitting procedures to combat these problems, but are more complex and not completely successful at eliminating the problems they set out to prevent. We instead fit parameters by estimating the mostly likely point that each student learned the skill, developing a new method that avoids the above problems while achieving similar predictive accuracy. Despite the prevalence of e-learning systems in schools, most of today's systems do not personalize educational data to the individual needs of each student. This paper proposes a new algorithm for sequencing questions to students that is empirically shown to lead to better performance and engagement in real schools when compared to a baseline approach. It is based on using knowledge tracing to model students' skill acquisition over time, and to select questions that advance the student's learning within the range of the student's capabilities, as determined by the model. The algorithm is based on a Bayesian Knowledge Tracing (BKT) model that incorporates partial credit scores, reasoning about multiple attempts to solve problems, and integrating item difficulty. This model is shown to outperform other BKT models that do not reason about (or reason about some but not all) of these features. The model was incorporated into a sequencing algorithm and deployed in two classes in different schools where it was compared to a baseline sequencing algorithm that was designed by pedagogical experts. In both classes, students using the BKT sequencing approach solved more difficult questions and attributed higher performance than did students who used the expert-based approach. Students were also more engaged using the BKT approach, as determined by their interaction time and number of log-ins to the system, as well as their reported opinion. We expect our approach to inform the design of better methods for sequencing and personalizing educational content to students that will meet their individual learning needs.