Team research is important in studying cognition as enactive. This paper contains four different pieces of research directed toward the evidences and artifacts of two students in Canada engaging in a sustained mathematical activity. These four portraits of mathematical cognition in action consider the conversation in which the activity occurs; the structures manifested in the beliefs of these students about mathematics; the patterns of reasoning in action; and the dynamical growth or changes in the mathematical understanding of this pair of students. These approaches and pieces of research can be observed as coemergent. An introductory paper, "Enactivism and Education, Especially Mathematics Education" is followed by four research papers: "A Portrait of Mathematical Conversation" (Lynn Gordon Calvert); "A Portrait of the Coemergence of Reasoning" (David A. Reid); "A Portrait of Beliefs in Action" (Elaine Simmt); and "A Pathway Portrait of Mathematical Understanding in Inter-Action" (Thomas E. Kieren). Appendixes contain verbal snapshots and writing samples of the two students. Contains 52 references. (MKR)