Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

The roles of visualization and symbolism in the potential and actual infinity of the limit process

Tools
- Tools
+ Tools

Kidron, Ivy and Tall, David (2014) The roles of visualization and symbolism in the potential and actual infinity of the limit process. Educational Studies in Mathematics . doi:10.1007/s10649-014-9567-x

Research output not available from this repository, contact author.
Official URL: http://dx.doi.org/10.1007/s10649-014-9567-x

Request Changes to record.

Abstract

A teaching experiment—using Mathematica to investigate the convergence of sequence of functions visually as a sequence of objects (graphs) converging onto a fixed object (the graph of the limit function)—is here used to analyze how the approach can support the dynamic blending of visual and symbolic representations that has the potential to lead to the formal definition of the concept of limit. The study is placed in a broad context that links the historical development with cognitive development and has implications in the use of technology to blend dynamic perception and symbolic operation as a natural basis for formal mathematical reasoning. The approach offered in this study stimulated explicit discussion not only of the relationship between the potential infinity of the process and the actual infinity of the limit but also of the transition from the Taylor polynomials as approximations to a desired accuracy towards the formal definition of limit. At the end of the study, a wide spectrum of conceptions remained. Some students only allowed finite computations as approximations and denied actual infinity, but for half of the students involved in the study, the infinite sum of functions was perceived as a legitimate “object” and was not perceived as a dynamic “process” that passes through a potentially infinite number of terms. For some students, the legitimate object was vague or generic, but we also observed other students developing a sense of the formal limit concept.

Item Type: Journal Article
Divisions: Faculty of Social Sciences > Centre for Education Studies (2013- )
Journal or Publication Title: Educational Studies in Mathematics
Publisher: Springer Netherlands
ISSN: 0013-1954
Official Date: August 2014
Dates:
DateEvent
August 2014Published
5 August 2014Available
DOI: 10.1007/s10649-014-9567-x
Status: Peer Reviewed
Publication Status: Published

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item
twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us