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.
Multiple researchers have used Bayesian knowledge tracing as a way to infer students' skill acquisition (i.e., mastery level) over time given their performance levels on different question sequences @cite_25 . These researchers reason about students' prior knowledge of skills and also account for slips and guessing on test problems. The models are trained on large data sets from multiple students using machine learning algorithms that account for latent variables @cite_18 @cite_17 . We solve a different problem --- using other students' performance to personalize ranking over test-questions. In addition, these methods measure students' performance dichotomously (i.e., success or failure) whereas we reason about additional features such as students' grade and number of attempts to solve the question. We intend to infer students' skill levels to improve the ranking prediction in future work.
@cite_18 @cite_25 @cite_17
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Bayesian knowledge tracing has been used widely to model student learning. However, the name “Bayesian knowledge tracing” has been applied to two related, but distinct, models: The first is the Bayesian knowledge tracing Markov chain which predicts the student-averaged probability of a correct application of a skill. We present an analytical solution to this model and show that it is a function of three parameters and has the functional form of an exponential. The second form is the Bayesian knowledge tracing hidden Markov model which can use the individual student's performance at each opportunity to apply a skill to update the conditional probability that the student has learned that skill. We use a fixed point analysis to study solutions of this model and find a range of parameters where it has the desired behavior. *Revised version, Feb 2017 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. Knowledge Tracing is the de-facto standard for inferring student knowledge from performance data. Unfortunately, it does not allow modeling the feature-rich data that is now possible to collect in modern digital learning environments. Because of this, many ad hoc Knowledge Tracing variants have been proposed to model a specific feature of interest. For example, variants have studied the effect of students’ individual characteristics, the effect of help in a tutor, and subskills. These ad hoc models are successful for their own specific purpose, but are specified to only model a single specific feature. We present FAST (Feature Aware Student knowledge Tracing), an efficient, novel method that allows integrating general features into Knowledge Tracing. We demonstrate FAST’s flexibility with three examples of feature sets that are relevant to a wide audience. We use features in FAST to model (i) multiple subskill tracing, (ii) a temporal Item Response Model implementation, and (iii) expert knowledge. We present empirical results using data collected from an Intelligent Tutoring System. We report that using features can improve up to 25 in classification performance of the task of predicting student performance. Moreover, for fitting and inferencing, FAST can be 300 times faster than models created in BNT-SM, a toolkit that facilitates the creation of ad hoc Knowledge Tracing variants.