Evaluations of professor performance are based on the assumption that students learn more from highly qualified professors and the fact that students observe professor performance in the classroom. However, many studies question the methodologies used for such measurements, in general, because the averages of categorical responses make little statistical sense. In this paper, we propose Bayesian multi-faceted item response theory models to measure teaching performance. The basic model takes into account effects associated with the severity of the students responding to the survey, and the courses that are evaluated. The basic model proposed in this work is applied to a data set obtained from a survey of perception of professor performance conducted by Science Faculty of the Universidad Nacional de Colombia to its students. professor scores that are obtained as model outputs are real numerical values that can be used to calculate common statistics in professor evaluation. In this case, the statistics are mathematically consistent. Some of them are shown to illustrate the usefulness of the model.