Starting from questions about what is privileged in mathematics teacher education, we conducted a systematic review of research on practicum. One element was to in-terrogate the notion of the desired mathematics (student) teacher reflected in existing research. Selecting peer reviewed, empirically based articles for 2001-2017 resulted in the inclusion of 51 articles. Our findings suggest the desired teacher implied in papers to have content knowledge, MKT/PCK, positive beliefs and attitudes, and the ability to reflect on teaching. Teachers who can exercise reasoned judgement were more frequently valued than teachers who can implement specific practices.