This paper will take the form of a conversation. For many years, Trevor Fullerton has been developing and researching a set of generic teacher competencies which can be applied to teaching in all areas of the curriculum. Ken Clements, on the other hand, has been sceptical that such generic competencies can be helpful insofar as mathematics teacher education is concerned. He has always considered that such competencies are unlikely to assist in the process of satisfactorily developing prospective teachers of mathematics. The two have had long discussions on whether their positions can be reconciled, and this paper will present the fruits of their deliberations.