This paper addresses dilemmas in the practices of six teachers from the perspective of alternate paradigms of knowledge growth, particularly constructivism. The dilemmas focus on the relationships between theory and practice in the growth of knowledge in learning and teaching mathematics. The data for this study are drawn from a four-year classroom-based study of six teachers who chose an investigative approach to their teaching of mathematics at the secondary level. Highlighted in this paper are three worlds or discourses: (1) the academic world of contrasting theoretical positions aiming to inform the educational context; (2) the practical world of students' everyday lives, classroom relationships, and teaching decisions; and (3) the research world which tries to act as a bridge between the other discourses. The paper concludes with a brief discussion of negotiation as a dialogic mode which creates discourse from which individuals make their own sense and communicate with others. Contains 39 references. (DDR)