STUDENTS’ NON STANDARD REASONING – A MEDIATOR FOR REFLECTION IN MATHEMATICS TEACHER EDUCATION

In mathematics teacher education there are only few approaches using mistakes and non standard reasoning as learning opportunities (Tulis, 2013), while, from our prospective, one of the core aspects of teaching practice should concern teachers’ knowledge and ability to give sense to students’ production. Such knowledge would allow teachers to develop and implement ways to support students to build knowledge starting from their own reasoning, even when such reasoning differs from the ones expected by the teacher (Ribeiro et al., 2013). Aiming at accessing and developing such knowledge and ability, we have been developing tasks for teachers training that ask them first to solve problems and, afterwards, to give sense to students’ productions answering such problems. These tasks were used, at the moment, both as a tool to observe and deepen prospective teachers’ mathematical knowledge for teaching (MKT) (Ball et al., 2008) mobilized by this prompt, as well as to support, in our lectures, the development of prospective teachers’ MKT. Using such tasks in our lectures we, as educators, live a transformative experience from participating into a co-learning community with our students (prospective primary teachers). Part of these lectures were video recorded and we will discuss a fragment of these video-recorded discussions (in a context using fractions) with an “inquiry in practice” perspective (Goodchild et al., 2013). In particular, we will discuss and reflect upon some prospective teachers’ mathematical epiphanies and some of the mathematical issues arising from their unforeseen observations. Moreover we will discuss also some of our own believes (and knowledge build) arising from the later observation of the discussion and our interaction during it. Finally we will argue that this kind of work grounded on discussing non standard students’ reasoning could represent a core aspects for mathematics teachers education field, meant as co-learning community.