ABSTRACT
At the very beginning of my research I knew in the broadest terms that I wanted to study an investigative approach to mathematics teaching. 1 It was obvious that the subjects of my research would be teachers of mathematics and their students, and that the research would take place in mathematics classrooms and their relevant surroundings. I wished to explore what such an approach might look like in practice and to attempt to characterize it from practical manifestations in classrooms, rather than from my own preconceived notions. I did not intend to study my own teaching as I was no longer a classroom teacher. I therefore wished to study other teachers, but it was not clear who they should be or what form the study should take.
