Students build mathematical theory: semantic warrants in argumentation

In this paper, we explore the development of two grounded theories. One theory is mathematical and grounded in the work of university calculus students’ collaborative development of mathematical methods for finding the volume of a solid of revolution, in response to mathematical necessity in problem solving, without prior instruction on solution methods. The second theory emerges from microlinguistic analysis of students’ mathematical choices and use of warrants in substantial argumentation to communicate, clarify, and convince others of the validity of their conjectures and mathematical work. Our goal was to illuminate mathematical argumentation by collaborative groups of calculus students at a qualitative level of detail sufficient to reveal one view of how these students satisfied the creative drive for mathematical meaning, communication, and accuracy in problem solving as evidenced in one classroom over several days.