In mathematical psychology, a knowledge space is a combinatorial structure describing the possible states of knowledge of a human learner.[1]To form a knowledge space, one models a domain of knowledge as a set of concepts, and a feasible state of knowledge as a subset of that set containing the concepts known or knowable by some individual. Typically, not all subsets are feasible, due to prerequisite relations among the concepts. The knowledge space is the family of all the feasible subsets.
Knowledge spaces were introduced in 1985 by Jean-Paul Doignon and Jean-Claude Falmagne[2] and have since been studied by many other researchers.[3][4] They also form the basis for two computerized tutoring systems, RATH (defunct now) and ALEKS.[5]
It is possible to interpret a knowledge space as a special form of a restricted latent class model.[6]
Knowledge Space Theory (KST) was motivated by the shortcomings of the psychometric approach to the assessment of competence like SAT and ACT.[7] The theory was developed with an objective of designing automated procedures which -
Assessments based on KST are adaptive and can account for possible slips or guesses. KST aims to give a detailed assessment of student's knowledge state as opposed to a numerical mark in traditional assessments. More specifically, the result of a KST based assessment tells two things -
An important subclass of knowledge spaces, the well-graded knowledge spaces or learning spaces, can be defined as satisfying two additional mathematical axioms: