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TEL Seminar: Cluster IV
“Formal Methods and Theories”
Sergey Sosnovsky
‣ Requires some knowledge of probability theory, machine
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learning, statistics
This is the core of adaptive systems’ intelligence
Well defined approaches
‣ List of Topics:
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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
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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
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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
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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
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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
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Massive collections of data
Trend towards data-driven intelligence
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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
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Saarbrücken, 08.10.2010
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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
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Statistical tests
‣ Between-subject vs. Within-subject
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