There is little room for doubt about that cognitive diagnosis has received much attention recently. Computerized adaptive testing (CAT) is adaptive, fair, and efficient, which is suitable to large-scale examination. Traditional cognitive diagnostic test needs quite large number of items, the efficient and tailored CAT could be a remedy for it, so the CAT with cognitive diagnosis (CD-CAT) is prospective. It is more beneficial to the students who live in the developing area without rich source of teaching, and distance education is adopted there. CD is still in its infancy (Leighton at el.2007), and some flaws exist, one of which is that the rows/columns could form a Boolean lattice in Tatsuoka’s Q-matrix theory. Formal Concept Analysis (FCA) is proved to be a useful tool for cognitive science. Based on Rule Space Model (RSM) and the Attribute Hierarchy Method (AHM), FCA is applied into CD-CAT and concept lattices are served as the models of CD. The algorithms of constructing Qr matrice and concept lattices for CAT, and the theory and methods of diagnosing examinees and offering the best remedial measure to examinees are discussed in detail. The technology of item bank construction, item selection strategies in CD-CAT and estimation method are considered to design a systemic CD-CAT, which diagnoses examinees on-line and offers remedial measure for examinees in time. The result of Monte Carlo study shows that examinees’ knowledge states are well diagnosed and the precision in examinees’ abilities estimation is satisfied.
On colorings of the Boolean lattice avoiding a rainbow copy of a poset
