In this paper, we describe the integration and evaluation of an existing generic Bayesian student model (GBSM) into an existing computerized testing system within the Mathematics Education Project (PmatE -Projecto Matemática Ensino) of the University of Aveiro. This generic Bayesian student model was previously evaluated with simulated students, but a real application was still missing. In the work presented here, we have used the GBSM to define Bayesian Student Models (BSMs) for a concrete domain: first degree equations. In order to test the diagnosis capabilities of such BSMs, an evaluation with 152 students has been performed. Each of the 152 students took both a computerized test within PMatE and a written exam, both of them designed to measure students knowledge in 12 concepts related to first degree equations. The written exam was graded by three experts. Then two BSMs were developed, one for the computer test and another one for the written exam. These BSMs were used to to obtain estimations of student's knowledge on the same 12 concepts, and the inter-rater agreement among the different measures was computed. Results show a high degree of agreement among the scores given by the experts and also among the diagnosis provided by the BSM in the written exam and the experts average, but a low degree of agreement among the diagnosis provided by the BSM in the computer test and expert's average.

In this paper we give a description of all subsemigroups of the bicyclic monoid B. We show that there are essentially five different types of subsemigroups. One of them is the degenerate case, and the remaining four split in two groups of two, linked by the obvious anti-isomorphism of B. Each subsemigroup is characterized by a certain collection of parameters. Using our description, we determine the regular, simple and bisimple subsemigroups of B. Finally we describe algorithms for obtaining the parameters from the generating set.

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