Knowledge tracing---where a machine models the knowledge of a student as they interact with coursework---is a well established problem in computer supported education. Though effectively modeling student knowledge would have high educational impact, the task has many inherent challenges. In this paper we explore the utility of using Recurrent Neural Networks (RNNs) to model student learning. The RNN family of models have important advantages over previous methods in that they do not require the explicit encoding of human domain knowledge, and can capture more complex representations of student knowledge. Using neural networks results in substantial improvements in prediction performance on a range of knowledge tracing datasets. Moreover the learned model can be used for intelligent curriculum design and allows straightforward interpretation and discovery of structure in student tasks. These results suggest a promising new line of research for knowledge tracing and an exemplary application task for RNNs.
Recent work has explored combining Item Response Theory (IRT) models with switched nonlinear Kalman filters @cite_11 , as well as with Knowledge Tracing @cite_5 @cite_12 . Though these approaches are promising, at present they are both more restricted in functional form and more expensive (due to inference of latent variables) than the method we present here.
@cite_5 @cite_12 @cite_11
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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 propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education.