Eliciting the coordination of preservice secondary mathematics teachers’ definitions and concept images of function

ABSTRACT

Given the vast experiences pre-service mathematics teachers (PSMTs) have with functions, one may assume that they have existing personal definitions and concept images. The purpose of this paper is to build an understanding of the variety of images that one might associate with a definition of function that includes ‘for each input there is one output’ and how these images are coordinated with the definition to determine whether an object is a function or not. Two cases are presented to describe PSMTs who were working from the same personal definition of function, yet used that definition differently within a task designed around the function concept. The task itself was novel in that it is presented in a non-algebraic context, namely a vending machine. As such, PSMTs were required to coordinate their personal definition and images within the novel context. Attending to PSMTs’ concept images revealed that though they were working from the same personal definition, images they drew upon to determine whether or not an object is a function were varied.

KEYWORDS:

• Function
• technology
• preservice teachers

Acknowledgements

Support for this work was partially supported by the National Science Foundation under grant DUE 1820998 awarded to Middle Tennessee State University and grant DUE 1821054 awarded to University of North Carolina at Charlotte. Any opinions, findings, and conclusions or recommendations expressed herein are those of the principal investigators and do not necessarily reflect the views of the National Science Foundation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Division of Undergraduate Education [grant numbers DUE 1820998 awarded to Middle Tennessee State University, DUE 1821054 awarded to University of North Carolina].