What aspects can characterize the specialized knowledge of a mathematics teacher educator?

This paper presents an exploratory qualitative study which was carried out by means of questionnaires for identifying some knowledge claimed by Mathematics Teacher Educators (MTEs) as important to be, or to become, a “good teacher educator”. The study focused the analysis on some teacher educators’ answers about MTE’s specialised knowledge. Mathematics Teachers’ Specialised Knowledge model (the so-called MTSK model) helped us to identify specific dimensions and domains of teacher educators’ specialised knowledge, identified in some mathematics teacher educators’ answers. From this information, by analysing similarities and differences and prevalent ideas, we raise hypotheses about some features that teacher educators believe as a part of MTE’s specialised knowledge. Finally, we propose an adaptation of the MTSK model that can describe the teacher educator’s specialised knowledge (Mathematics Teacher Educators’ Specialised Knowledge model - MTESK model) by capturing and including in the model the main issues obtained in the study