This article describes a vision of student use of dynamically connected representations as they investigate mathematical ideas. Although this article is intended to generate discussion about the potential of dynamically connected representations, we situate the discussion within actual descriptions of its use with students in a newly designed pre-service teacher preparation program. A hand-held computer algebra system that allows various mathematical representations to be linked and then manipulated resulting in all representations changing simultaneously provides a new vehicle for exploring a sequence of iterated function values under composition. Effects of initial seed value, function parameters, and function characteristics are investigated for the sequence a[subscript n] = f(a[subscript n-1]). The authors discuss student approaches for the specific investigation and the potential for classroom instruction. The role of technology within the discourse community is also addressed. (Contains 9 figures.)