Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Education » math-teach

Topic: Inclusive and exclusive definitions... again!
Replies: 17   Last Post: Mar 29, 2010 10:12 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Allan Turton

Posts: 33
From: Australia
Registered: 3/9/06
Re: Inclusive and exclusive definitions... again!
Posted: Mar 24, 2010 6:52 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Thanks for your response Jonathan. "Oblique" anything does have great appeal to me as at least you don't have to introduce extra terminology. The "equilateral triangle as isosceles" is one I understand but then we still have the same issue as with quadrilaterals: what do we call (concisely) the non-equilateral, isosceles triangles? Seeing as though both Australia and the US have just released national curricula it'd be great if they could also specify what they mean by the terms they use, like this one from the US Grade 2 Common Core Standards:

"Recognize rectangles, rhombuses, squares and trapezoids as examples of quadrilaterals..."

While later on in Grade 3:

"Describe, analyze, compare and classify two-dimensional shapes by their properties and connect these properties to the classification of shapes into categories and subcategories (e.g., squares are "special rectangles" as well as "special rhombuses").

It's clear that there is a jumble of inclusive and exclusive definitions at work, made more difficult by my original point - there aren't enough names for the "endpoints".

An illuminating review of what definitions are actually used in textbooks is "The classification of quadrilaterals: a study of definition" by Zalman Usiskin and others. I got it just the other day and while it isn't ideal bed-time reading, it does reveal that there is much confusion between and within publications. I suspect not much will change unless some authority sets out some consistent definitions or at least guidelines for discussion with students.

Al



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.