IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

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

  • Greer, Brian

    (Portland State University)

  • De Bock, Dirk


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

  • Van Dooren, Wim

    (Katholieke Universiteit Leuven, Belgium)

Registered author(s):

    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.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Our checks indicate that this address may not be valid because: 500 Can't connect to ( [302 Found]--> If this is indeed the case, please notify (Sabine Janssens)

    Download Restriction: no

    Paper provided by Hogeschool-Universiteit Brussel, Faculteit Economie en Management in its series Working Papers with number 2008/51.

    in new window

    Length: 34 pages
    Date of creation: Oct 2008
    Date of revision:
    Handle: RePEc:hub:wpecon:200851
    Contact details of provider: Web page:

    More information through EDIRC

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    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)

    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.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.