PME-NA

Using Abstraction to Characterize Students’ Development of Meanings for How Quantities Change

• In Event: Using Abstraction to Characterize Students’ Development of Meanings for How Quantities Change

Description

Recognizing directions and amounts of change in relationships between two changing quantities has been shown to support robust covariational reasoning. In this report, we leverage Piaget’s construct of reflective abstraction as a mechanism to describe how two middle school students developed such meanings for recognizing and categorizing direction and amounts of change. Using a teaching experiment methodology, we examined the students’ meanings across three connected tasks with differing contexts and resources. We show how the students engaged in three types of reflective abstraction (pseudo-empirical, reflecting, and reflected) as they developed meanings for directions and amounts of change across the sequence. We conclude with implications for researchers and practitioners around task design to support students’ reflected abstraction related to covariational reasoning and other mathematical topics.

Authors

• Allison Juliana Olshefke-Clark, University of Delaware

• Teo Paoletti, University of Delaware

• Allison L. Gantt, The College of New Jersey

• Osmond Amponsah Asiamah, University of Delaware