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TEL Seminar: Cluster IV “Formal Methods and Theories” Sergey Sosnovsky ‣ Requires some knowledge of probability theory, machine ‣ ‣ learning, statistics This is the core of adaptive systems’ intelligence Well defined approaches ‣ List of Topics: ‣ ‣ ‣ ‣ ‣ ‣ Item Response Theory Knowledge Tracing Performance Factor Analysis Bayesian Networks for Adaptive e-Learning Educational Data Mining Evaluation of e-Learning Systems ‣ The core technology behind adaptive testing ‣ Is used in such standardized tests as GRE, GMAT, TOEFL ‣ Allows to assess the ability of a test taker with better ‣ ‣ precision and fewer questions (than classic test theory) The math apparatus was developed in the 1950-1960s, but it became popular only in the 1980s Allows to estimate not only the ability of a student, but also the parameters of the questions ‣ Sigmoid curve: Saarbrücken, 08.10.2010 Seite/Page 7 ‣ ‣ ‣ ‣ ‣ Bayesian Knowledge Tracing: developed by Corbet 1995 (and Atkinson in 1972 ;-) Probabilistic model for modeling student’s knowledge Helps to estimate the probability of skills acquisition by a student solving problems based on the history of attempts Advanced the fields of student modeling and educational data mining Markov chain: ‣ Recent (2009) addition to the toolbox of probabilistic ‣ ‣ ‣ student modeling techniques Based on two other models: Learning Factor Analysis and the simplest of IRT models: Rasch model Helps to resolve some of the problems of earlier models (e.g. multiple evidence from a single event) Seems to outperform classic KT ‣ ‣ ‣ A Bayesian network is a probabilistic graphical model that represents a set of random variables and their conditional dependences via a directed acyclic graph. Allows to estimate the probabilities of unobservable parameters from the observable events Has been successfully applied in many ITSs: ‣ For modeling students ‣ For representing complex exercises ‣ ‣ Massive collections of data Trend towards data-driven intelligence ‣ Discovery if hidden patterns and hidden features ‣ Identification of malfunctioning system components, pieces of content, etc. ‣ Detection of critical patterns of students behavior ‣ Detection of important characteristics that define a category og users ‣ etc… Comparison of different models, components, systems Aggregation of log-data to present it in a meaningful way ‣ ‣ Saarbrücken, 08.10.2010 Seite/Page 7 ‣ ‣ ‣ Virtually no paper these days can miss the evaluation part Evaluation is the way to test your hypotheses Kinds of evaluation: ‣ Layered vs. Holistic ‣ Controlled vs. Longitudinal ‣ Test-based vs. Questionnaire-based vs. Observation-based ‣ Statistical tests ‣ Between-subject vs. Within-subject ‣…