LAUSR

Abstract The objective of an assessment in competence based-knowledge space theory (Cb-KST) is to infer the skills of an individual from her responses to a subset of problems. A major issue in this approach is the lack of a one-to-one correspondence between the competence states and performance states. The assessment is possible, but it cannotgo beyond an approximation. The problem becomes even more serious if Cb-KST is used for the assessment of learning, since changes caused at the competence level may not be represented by changes at the performance level. The consequence is that there could be no way for establishing whether learning has occurred or not. This impasse can be resolved for the class of conjunctive skill functions by pretending that the competence space induced by the skill function is well-graded. Under this condition an individual can make tangible progresses along the performance structure by learning one skill at a time, until full mastery is eventually reached. If the competence structure is a space satisfying certain compatibility conditions and the skill function satisfies a special property, called exclusiveness, then well-gradedness can be assured. A test of exclusiveness of a conjunctive skill function is described and exemplified.