This discussion focuses upon potential implications of research conducted on preservice teachers' understanding of introductory topics from elementary number theory. Comments interlace three levels of consideration and recapitulate what is striking as some of the most interesting and important findings raised in the presentations, and flesh out some of the theoretical presuppositions underlying these findings. The potential of these findings with respect to practical classroom applications is also discussed. Finally, consideration is given as to why these kinds of phenomena are observed, what may be responsible for their emergence, and what might be done differently in elementary mathematics teacher education. (Contains 14 references.) (Author/ASK)