[1] Knowledge spaces were introduced in 1985 by Jean-Paul Doignon and Jean-Claude Falmagne,[2] and remain in extensive use in the education theory.
Common tests, such as the SAT and ACT, compress a student's knowledge into a very small range of ordinal ranks, in the process effacing the conceptual dependencies between questions.
Consequently, the tests cannot distinguish between true understanding and guesses, nor can they identify a student's particular weaknesses, only the general proportion of skills mastered.
Each feasible state of knowledge about S is then a subset of Q; the set of all such feasible states is K. The precise term for the information (Q, K) depends on the extent to which K satisfies certain axioms: If S∈K, then there exists x∈S such that S\{x}∈KThe more contentful axioms associated with quasi-ordinal and well-graded knowledge spaces each imply that the knowledge space forms a well-understood (and heavily studied) mathematical structure: In either case, the mathematical structure implies that set inclusion defines partial order on K, interpretable as an educational prerequirement: if a(⪯)b in this partial order, then a must be learned before b.
There exist several querying algorithms that allow one or several experts to construct a knowledge space by answering a sequence of simple questions.