Students’ naïve ideas as a source of reflection in mathematics teacher education

We present results from a study using tasks aimed at accessing, discussing and developing prospective teachers’ knowledge when interpreting and giving sense to students’ non-standard productions. The final aim of developing (prospective) teachers’ knowledge is pursued by reflecting on their own knowledge on situations that are considered as strong detonators for a promotion in such knowledge and understanding. These tasks were worked in our lectures and were audio and video recorded. In that sense, we are interested to inquire into how teachers develop their awareness to possible different ways of dealing with a mathematical content by discussing naive students ideas, and on how the impact of discussing possible different conceptions may lead to new understanding and knowledge. Here we will present some results of the study by discussing a fragment of these video-recorded discussions from a course in Italy, using an inquiry in practice perspective. Such discussion lead to argue that work grounded on discussing students’ naive ideas/non-standard reasoning represents a core aspect for the mathematics teachers’ education field – in terms of all the elements involved (considering educators also as learners).