In Intelligent Tutoring System (ITS), tracing the student's knowledge state during learning has been studied for several decades in order to provide more supportive learning instructions. In this paper, we propose a novel model for knowledge tracing that i) captures students' learning ability and dynamically assigns students into distinct groups with similar ability at regular time intervals, and ii) combines this information with a Recurrent Neural Network architecture known as Deep Knowledge Tracing. Experimental results confirm that the proposed model is significantly better at predicting student performance than well known state-of-the-art techniques for student modelling.
IRT assumes the student knowledge state is static and represented by her proficiency when completing an assessment during an exam @cite_6 @cite_14 @cite_15 @cite_21 . IRT models a single skill and assumes the test items are . It assigns student @math with a static proficiency @math . Each item @math has its own difficulty @math . The main idea of IRT is estimating a probability that student @math answers item @math correctly by using student's ability and item's difficulty. The widely used one-parameter version of IRT, known as the Rasch model, is @size 9 @mathfonts Recently, Wilson @cite_6 proposed an IRT model that outperforms state-of-the-art knowledge tracing models. In which, maximum a posteriori (MAP) estimates of @math and @math are computed using the Newton-Raphson method.
@cite_15 @cite_14 @cite_21 @cite_6
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Estimating student proficiency is an important task for computer based learning systems. We compare a family of IRT-based proficiency estimation methods to Deep Knowledge Tracing (DKT), a recently proposed recurrent neural network model with promising initial results. We evaluate how well each model predicts a student's future response given previous responses using two publicly available and one proprietary data set. We find that IRT-based methods consistently matched or outperformed DKT across all data sets at the finest level of content granularity that was tractable for them to be trained on. A hierarchical extension of IRT that captured item grouping structure performed best overall. When data sets included non-trivial autocorrelations in student response patterns, a temporal extension of IRT improved performance over standard IRT while the RNN-based method did not. We conclude that IRT-based models provide a simpler, better-performing alternative to existing RNN-based models of student interaction data while also affording more interpretability and guarantees due to their formulation as Bayesian probabilistic models. Traditionally, the assessment and learning science commu-nities rely on different paradigms to model student performance. The assessment community uses Item Response Theory which allows modeling different student abilities and problem difficulties, while the learning science community uses Knowledge Tracing, which captures skill acquisition. These two paradigms are complementary - IRT cannot be used to model student learning, while Knowledge Tracing assumes all students and problems are the same. Recently, two highly related models based on a principled synthesis of IRT and Knowledge Tracing were introduced. However, these two models were evaluated on different data sets, using different evaluation metrics and with different ways of splitting the data into training and testing sets. In this paper we reconcile the models' results by presenting a unified view of the two models, and by evaluating the models under a common evaluation metric. We find that both models are equivalent and only differ in their training procedure. Our results show that the combined IRT and Knowledge Tracing models offer the best of assessment and learning sciences - high prediction accuracy like the IRT model, and the ability to model student learning like Knowledge Tracing. We apply collaborative filtering (CF) to dichotomously scored student response data (right, wrong, or no interaction), finding optimal parameters for each student and item based on cross-validated prediction accuracy. The approach is naturally suited to comparing different models, both unidimensional and multidimensional in ability, including a widely used subset of Item Response Theory (IRT) models which obtain as specific instances of the CF: the one-parameter logistic (Rasch) model, Birnbaum’s 2PL model, and Reckase’s multidimensional generalization M2PL. We find that IRT models perform well relative to generalized alternatives, and thus this method offers a fast and stable alternate approach to IRT parameter estimation. Using both real and simulated data we examine cases where oneor two-dimensional IRT models prevail and are not improved by increasing the number of features. Model selection is based on prediction accuracy of the CF, though it is shown to be consistent with factor analysis. In multidimensional cases the item parameterizations can be used in conjunction with cluster analysis to identify groups of items which measure different ability dimensions. 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.