What's in a Name? Seeking Geometry in Geometric Sequences

Mathematical terminology is sometimes created according to conventions that are not obvious to students who will use the term. When this is the case, investigating the choice of a name can reveal interesting and unforeseen connections among mathematical topics. In this study, we tasked prospective and practicing teachers to consider: What is geometric about geometric sequences? Participants embedded their explanations within a scripted dialogue between teacher- and student-characters in a mathematics classroom, provided commentary on this dialogue, and expanded on its mathematical content. Participants most often leverage the concept of a geometric mean to explain why geometric sequences are named as such. To capture this informal arguments, we built on the work of Toulmin (1958/2003) to conceptualize and develop the Toulmin-Reversed (Toulmin-R) model. [For the complete proceedings, see ED630210.]