This article is concerned with the professional development of mathematics teachers. It starts with a need, identifies a problem, and suggests some ways of coping with the problem. The need is for teachers to develop mathematical communication and reflection skills in their practice. There is a widespread agreement that these skills are an important component of mathematics teachers' professional toolbox, as can be seen from curriculum reform documents. There is equally widespread agreement on the problem: that most teachers have not been sufficiently prepared for these skills and, furthermore, that teachers know little about how to effect improved preparation, whether in preservice or in inservice education. The authors repeatedly encountered this problem during their involvement in the inservice preparation of Danish teachers to meet the new requirements of the Danish Ministry of Education. In an attempt to solve this problem in her inservice courses, Lisser Rye Ejersbo has developed a method of adapting research ideas from the mathematics education research literature into experiential activities during the course. In this article, the authors describe how one such idea--the virtual monologue--has been transposed from a tool for researchers to a tool for teachers. They do this by means of a case study--the taxicab scenario--which is analysed from four different perspectives, or "looks". (Contains 3 footnotes.)