Vygotsky's notions of Zone of Proximal Development and Dynamic Assessment emphasize the importance of personalized learning that adapts to the needs and abilities of the learners and enables more efficient learning. In this work we introduce a novel adaptive learning engine called E-gostky that builds on these concepts to personalize the learning path within an e-learning system. E-gostky uses machine learning techniques to select the next content item that will challenge the student but will not be overwhelming, keeping students in their Zone of Proximal Development. To evaluate the system, we conducted an experiment where hundreds of students from several different elementary schools used our engine to learn fractions for five months. Our results show that using E-gostky can significantly reduce the time required to reach similar mastery. Specifically, in our experiment, it took students who were using the adaptive learning engine @math less time to reach a similar level of mastery as of those who didn't. Moreover, students made greater efforts to find the correct answer rather than guessing and class teachers reported that even students with learning disabilities showed higher engagement.
The problem of sequencing educational content attracted many researchers, especially in the educational data mining community @cite_3 . For example, Pardon and Heffernan @cite_34 inferred order over exercises presented to students by predicting their skill levels using Bayesian Knowledge Tracing (BKT) @cite_23 . They showed the efficacy of their approach on simulated data as well as on a test set comprising random sequences of three exercises. Ben- @cite_19 proposed a BKT based sequencing algorithm that uses knowledge tracing to model students' skill acquisition over time and sequences exercises based on their mastery level and predicted performance. The setting of this work is similar to the setting we study here, however, they use different method for sequencing which does not take the ZPD into account. @cite_10 @cite_7 introduced several sequencing algorithms. The first, EduRank, an algorithm that combines collaborative filtering with social choice theory to produce personalized learning sequences for students. The latter, MAPLE, an algorithm that combines difficulty ranking with Multi Armed Bandits. @cite_26 used experts' knowledge to bootstrap a Multi-Armed Bandit approach with models that rely on empirical estimation of the learning progress.
@cite_26 @cite_7 @cite_3 @cite_19 @cite_23 @cite_34 @cite_10
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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. 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. 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. We present an approach to Intelligent Tutoring Systems which adaptively personalizes sequences of learning activities to maximize skills acquired by students, taking into account the limited time and motivational resources. At a given point in time, the system proposes to the students the activity which makes them progress faster. We introduce two algorithms that rely on the empirical estimation of the learning progress, RiARiT that uses information about the difficulty of each exercise and ZPDES that uses much less knowledge about the problem. The system is based on the combination of three approaches. First, it leverages recent models of intrinsically motivated learning by transposing them to active teaching, relying on empirical estimation of learning progress provided by specific activities to particular students. Second, it uses state-of-the-art Multi-Arm Bandit (MAB) techniques to efficiently manage the exploration exploitation challenge of this optimization process. Third, it leverages expert knowledge to constrain and bootstrap initial exploration of the MAB, while requiring only coarse guidance information of the expert and allowing the system to deal with didactic gaps in its knowledge. The system is evaluated in a scenario where 7-8 year old schoolchildren learn how to decompose numbers while manipulating money. Systematic experiments are presented with simulated students, followed by results of a user study across a population of 400 school children.