How we teach: mathematics teachers talk about what they do

The How we Teach seminar series has included seminars presented by both mathematicians and mathematics educators focusing on their teaching of mathematics to mathematics or engineering students. Video-recordings of 10 of the seminars have been analysed to discern a teaching discourse and characterise a community of practice in teaching. Further, we suggest that opportunities to talk about how we teach not only reveal the discourse, but make us aware of issues in teaching; they alert us to what we know and importantly what we do not know. Mathematicians and mathematics educators together address issues related to the learning of our students and how best effective learning can be achieved. Questioning of practices and processes in teaching, leads to possibilities for new forms of practice and development of an inquiry community in teaching.