Mathematics teachers’ interpretative knowledge of students’ errors and non-standard reasoning

In this work, we examined mathematical knowledge mobilised by mathematics teachers while interpreting students’ answers, which we denote as Interpretative Knowledge (IK). In particular, we analysed the IK of prospective mathematics teachers (PTs), who were students of a Mathematics Education course for the Master’s Degree in Mathematics. In order to study the possible development of the IK of these students, we explored their interpretations of secondary students’ productions and compared those given before, during, and after a collective discussion about these productions. Our findings reveal considerable differences in PTs’ knowledge and interpretations provided during the three activities, confirming that these and similar activities can be useful in training mathematics teachers in order to develop their IK.