IDEAS home Printed from https://ideas.repec.org/p/hub/wpecon/200851.html
   My bibliography  Save this paper

The Isis problem as a probe of flexible expertise and views of proof

Author

Listed:
  • Greer, Brian

    (Portland State University)

  • De Bock, Dirk

    () (Hogeschool-Universiteit Brussel (HUB), Belgium
    Katholieke Universiteit Leuven, Belgium)

  • Van Dooren, Wim

    (Katholieke Universiteit Leuven, Belgium)

Abstract

The Isis problem, which has a link with the Isis cult of ancient Egypt, asks: “Find which rectangles with sides of integral length (in some unit) have area and perimeter (numerically) equal, and prove the result.” Since the solution requires minimal technical mathematics, the problem is accessible to a wide range of students. Further, it is notable for the variety of proofs (empirically grounded, algebraic, geometrical) using different forms of argument, and their associated representations, and it provides an instrument for probing students’ ideas about proof, and the interplay between routine and adaptive expertise. A group of 39 Flemish pre-service mathematics teachers was confronted with the Isis problem. More specifically, we first asked them to solve the problem and to look for more than one solution. Second, we invited them to study five given contrasting proofs and to rank these proofs from best to worst. The results highlight a preference of many students for algebraic proofs as well as their rejection of experimentation. The potential of the problem as a teaching tool is outlined.

Suggested Citation

  • Greer, Brian & De Bock, Dirk & Van Dooren, Wim, 2008. "The Isis problem as a probe of flexible expertise and views of proof," Working Papers 2008/51, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
  • Handle: RePEc:hub:wpecon:200851
    as

    Download full text from publisher

    File URL: http://lirias.hubrussel.be/handle/123456789/2278
    Download Restriction: no

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hub:wpecon:200851. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sabine Janssens). General contact details of provider: http://edirc.repec.org/data/emhubbe.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.