Mathematics educator transformation(s) by reflecting on students’ non-standard reasoning

In this study, we present some results stemming from a research work exploring the way in which prospective teachers develop their interpretative knowledge and awareness by discussing students’ errors and non-stand- ard reasoning. For this purpose, we designed a particu- lar kind of task that was administrated and discussed in our own lectures. The discussions and re ections asso- ciated with this experience allowed us, as educators, to expand our own mathematical knowledge and aware- ness. Based on the analysis of video-recorded lessons delivered as a part of a course based in Italy, we will argue that work grounded in discussing students’ naive ideas/non-standard reasoning represents a core aspect of the mathematics teachers’ education eld, whereby educators are also viewed as learners.