PME-NA

Closeness, Dynamic Motion, and Static Entity: Reimagining the Genetic Decomposition of Limit

• In Event: Thinking and Learning of Calculus Concepts

Description

Building new knowledge from prior knowledge is the pinnacle process of knowledge construction within the field of mathematics. Mathematics teachers have been tasked with creating and implementing learning experiences mimicking this process to position students as authors of their own mathematical understanding. In Calculus, developing a conception of limit is crucial to developing future conceptions in Calculus. My theoretical research report lives at the intersection of APOS theory, Pseudo-conceptions, and curriculum enactment with the goal of theorizing how students develop their conception of limit in the classroom. From current literature, I describe three constructs of limit understanding: closeness, dynamic motion, and static entity. These constructs are leveraged theorize the potentiality for students to develop a pseudo-conceptual understanding of limit that could inhibit future understandings of differentiation and integration.

Author

• Derrick M Keister, Penn State University & SCH Academy