A rapidly growing number of user and student modeling systems have employed numerical
techniques for uncertainty management. The three major paradigms are those of Bayesian …

Knowledge spaces offer a rigorous mathematical foundation for various practical systems of
knowledge assessment. An example is offered by the ALEKS system (Assessment and …

Learning spaces offer a rigorous mathematical foundation for practical systems of
educational technology. Learning spaces generalize partially ordered sets and are special …

Based on the formal concept of" knowledge structures" originally proposed by Jean-Claude
Falmagne and Jean-Paul Doignon, this book contains descriptions of methodological …

The book describes up-to-date applications and relevant theoretical results. These
applications come from various places, but the most important one, numerically speaking, is …

Abstract The applicability of Knowledge Space Theory (Falmagne and Doignon) and
Bayesian Belief Networks (Pearl) as probabilistic student models imbedded in an Intelligent …

An intelligent tutoring system for learning basic statistics, called Stat-Knowlab, is presented
and analyzed. The algorithms implemented in the system are based on the competence …

Based on the celebrated Birkhoff theorem, Doignon and Falmagne (1985) establish a one-to-
one correspondence between certain binary relations on a domain of (dichotomous) items …

The dichotomous knowledge structure theory was introduced to polytomous items, which is
proved meaningful in representing individuals' partial mastery of items. Given that different …

Skills represent the underlying cognitive abilities, which consist in methods, algorithms or
tricks etc. Skills can be used to interpret individuals' knowledge states. A skill map assigns a …