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

Allison W. McCulloch; John N. Lovett; Lara Dick; Milan Sherman; Cyndi W. McCul ton; Michael Meagher

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

Allison W. McCulloch ^[1] ; Jennifer N. Lovett ^[2] ; Lara Dick ^[3] ; Milan Sherman ^[4] ; Cyndi W. McCul ton ^[6] ; Michael Meagher ^[5]
1. [1] University of North Carolina at Charlotte
  
  University of North Carolina at Charlotte
  
  Estados Unidos
2. [2] Middle Tennessee State University
  
  Middle Tennessee State University
  
  Estados Unidos
3. [3] Bucknell University
  
  Bucknell University
  
  Borough of Lewisburg, Estados Unidos
4. [4] Drake University
  
  Drake University
  
  Township of Lee, Estados Unidos
5. [5] Brooklyn College
  
  Brooklyn College
  
  Estados Unidos
6. [6] NC State University
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Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 53, Nº. 6, 2022, págs. 1387-1412
Idioma: inglés
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Resumen
- 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.