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 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 Basic Math, for example, approximately 15--25 questions
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
For a more selective bibliography, see the following section.