Research on computational estimation and mental computation has received a considerable amount of attention from mathematics educators during the past decade. These proceedings resulted from a meeting to explore dimensions of number sense and its related fields. The participants came from three groups: mathematics educators actively pursuing research on the topic; cognitive psychologists; and other mathematics educators who have adapted methods and models from psychology. The conference was unusual in that no formal papers were presented; instead, each participant submitted suggestions for preconference reading which was to serve as background for 2 days of discussion. The discussions were focused by the following questions: (1) What is number sense? How do we assess and teach it? How is it linked to mental computation and computational estimation?; (2) What research questions regarding these issues need to be addressed? What are the theoretical foundations for this research?; and (3) What do you want to see accomplished at the conference? Part I of the proceedings consists mainly of transcripts of the responses to three questions. After the conference had concluded, each participant was asked to write a short paper to include reflections on the themes of the conference. These papers are contained in Part II of the proceedings. Appendices list references and participants. (YP)