Figurative and Operative Partitioning Activity: Students' Meanings for Amounts of Change in Covarying Quantities

Researchers have emphasized the importance of characterizing students' abilities to coordinate changes in covarying quantities. In this paper, we characterize three undergraduate students' coordination of covarying quantities' amounts of change during a teaching experiment. We adopt Piagetian notions of figurative and operative thought to describe the extent their meanings for covariational relationships are constrained to or supported by theirpartitioning activity- the mental and physical actions associated with constructing accruals in quantities' magnitudes. Our analysis suggests that students' construction of amounts of change is constrained by figurative partitioning activity that requires carrying out or emulating particular actions on perceptually available material. In contrast, operative partitioning activity supports the students' transformation and (anticipated) regeneration of partitioning activity in order to conceive equivalent covariational relationships among various situations and representational systems. We conclude by discussing how documenting these distinctive meanings contributes to extant literature on covariational reasoning and, more broadly, the theorization of mathematical concept construction.