The lack of standards to objectively assess the quality of teaching opened a new path of research. Teaching involves a lot of different tasks and activities that should be explored, so, consequently, when talking about quality of teaching, it makes sense to look at teaching as a process and to assess its maturity. This contribution briefly looks at existing approaches, and introduces the idea of a teaching maturity model (TeaM) for school and university teachers. Such a framework, even though it proves helpful from a measurement perspective, might not be acceptable by teachers, so this paper presents the results of a study for testing the TeaM model in respect to its usability and acceptability with informatics lecturers at the Alpen-Adria-Universität Klagenfurt. The results show the interest of our teachers in the model, but also some of the impediments that have to be dealt with when applying the model on a larger scale.