The purpose of this study was to investigate the preservice secondary mathematics teachers' development of pedagogical understanding in the teaching of modular arithmetic problems. Data sources included, written assignments, interview transcripts and filed notes. Using case study and action research approaches cases of three preservice teachers reported here as a result of focusing visual (geometric) and analytical instruction in number theory, initial cognitive dissonance, rich discussions in their learning groups, and ramifications for changes in their future teaching practices. (Contains 5 figures.)