How can ALEKS uncover, by efficient questioning, the particular knowledge state of a student? While the details of ALEKS's method for achieving such a goal are technical, the guiding intuition is straightforward. At every moment of an assessment, ALEKS chooses a question to be "as informative as possible." (In ALEKS, assessments may be called "knowledge checks.") In our context, this means a question which the student has, in the system's estimate, about a 50 percent chance of getting right. The student's response (correct or false) determines a change in all the likelihood values: for instance, if the question involved manipulation of fractions, and the student's response was correct, then all the knowledge states containing this item would have their likelihood values increased. The specific way the questions are chosen and the likelihood values altered makes it possible for ALEKS to pinpoint the student's state in a relatively short time. In Business Math, for example, approximately 15--25 questions usually suffice.

Finally, it should be noted that the assessment report given to students, instructors, and administrators is a very precise summary of the student's knowledge state. If the structure is known, the outer fringe and inner fringe together completely define the student's knowledge state. Internally, the system registers the student's knowledge or non-knowledge of each item in the domain.

A more thorough but still accessible overview of Knowledge Space Theory is available on the ALEKS website: Cosyn, Doignon, Falmagne, "The Assessment of Knowledge, in Theory and Practice":

A comprehensive treatment of Knowledge Space Theory can be found in Doignon and Falmagne, Learning Spaces (Springer-Verlag, Berlin, Heidelberg, 2011).

A comprehensive scientific bibliography on Knowledge Spaces is maintained here:

For a more selective bibliography, see the following section.