This paper reports on a research study based on data from experimental teaching. Undergraduate dance majors were invited, through real-world problem tasks that raised central conceptual issues, to invent major ideas of calculus. This study focuses on work and thinking by these students, as they sought to build key ideas, representations and compelling lines of reasoning. Speiser and Walter's psychological and logical perspectives (see Speiser, Walter, & Sullivan, 2007) provide opportunities to focus not just on the students' thinking, but perhaps most especially, through detailed examination of important choices, on their exercise of agency as learners. Close analysis of student data through these lenses triggered the development of two new analytic categories--"logic of agency" and "logic of proof." The analysis presented here treats students as active shapers of their own experience and understanding, whose choices open opportunities for continued growth and learning, not just for themselves but also for each other. (Contains 1 table and 19 figures.)