The research mathematicians in the classroom:How their practice has potential to foster student horizon

In this chapter, we explore research mathematicians’ views on their teaching and how it is related to their own mathematical research while they teach calculus to students who may become mathematics schoolteachers. We use observational and interview data of lectures and tutorials across Greece and the UK, focusing on four extending practices found as drawing on examples, connecting mathematical areas, visualising and simplifying. We explain how explicitness to students through meta-commenting on the four practices has the potential to foster students’ mathematical horizon, concluding with a discussion of the implications for mathematics teacher education