Origin and motivation

Knowledge space theory (abbreviated as KST) originated with a paper by Doignon and Falmagne (1985). This work was motivated by the shortcomings of the psychometric approach to the assessment of competence. The psychometric models are based on the notion that competence can be measured, which the two authors thought was at least debatable. Moreover, a typical application of a psychometric model in the form of a standardized test results in placing an individual in one of a few dozen ordered categories, which is far too coarse a classification to be useful. In the case of the SAT, for example, the result of the test is a number between 200 and 800 with only multiples of 10 being possible scores.

In the cited paper, Doignon and Falmagne proposed a fundamentally different theory. The paper was followed by many others, written by them and other researchers (see the bibliographical notes in Section 5.13).

The basic idea is that an assessment in a scholarly subject should uncover the individual's “knowledge state,” that is, the exact set of concepts mastered by the individual. Here, “concept” means a type of problem that the individual has learned to master, such as, in Beginning Algebra:

or, in Basic Chemistry

In KST, a problem type is referred to as an “item.” Note that this usage differs to that in psychometric, where an item is a particular problem, such as: Solve the quadratic equation x2 - x - 12 = 0. In our case, the examples of an item are called instances.

The items or problem types form a possibly quite large set, which we call the “domain” of the body of knowledge. A knowledge state is a subset of the domain, but not any subset is a state: the knowledge states form a particular collection of subsets, which is called the “knowledge structure” or more specifically (when certain requirements are satisfied) the “knowledge space” or the “learning space.” The collection of states captures the whole structure of the domain.