The Mathematics Education Seminar Series presents

"Process-Object Frameworks and Mediating Metaphors"

Aaron Weinberg, Ithaca College

Monday, December 19th, 2-3pm in Science Center Room 507

Abstract: Have you ever wondered why some students have a difficult time with even the most basic notions of calculus? One explanation involves Action-Process-Object-Schema (APOS) theory. This theory might say that some of the lowest level students might view functions only as "processes." That is, a function is the process by which an input gets turned into an output. Their difficulty in calculus might be that they are unable to think of functions as "objects." We require students to think of functions as objects when we ask them to manipulate them by integrating or differentiating. After all, how do you differentiate a process? It has been hypothesized that the ability to recognize this duality between "objects" and "processes" is essential for success in math. We will introduce these ideas and present an overview of how researchers have used them to think about student learning. While these process-object frameworks are useful, they can conflict with theories of learning and we will discuss how reconceptualizing "processes" and "objects" as mediating metaphors can address some of these concerns.