PME-NA

Which Process are we Encapsulating? Rethinking APOS to Introduce a Multi-Tiered Framework for Function

• In Event: Theory in Learning Algebra and Function

Description

In mathematics education research, conceptualizing functions as both dynamic processes and static objects underpins major theoretical frameworks, including APOS (Action, Process, Object, Schema). This brief theoretical report re-examines APOS theory in the context of the function concept to introduce a two-tiered genetic decomposition. Specifically, we propose a local tier—corresponding to a single ordered pair—and a global tier—corresponding to the entire set of ordered pairs. This work has the potential to support more nuanced analyses of how students understand functions.

Authors

• Alison Mirin, University of Arizona

• Jodi Frost, Indiana State University