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Re: PARCC Definition of Trapezoid
Posted:
May 2, 2013 7:18 PM



We have had this discussion before on the list serve (more than once, in fact, and before the common core was anywhere in sight) and my understanding from other people who taught internationally was that other countries DO in fact sometimes use the inclusive definition of trapezoid.....
So is it a matter of right or wrong? I'm not sure.....it certainly brings up the interesting point that in an axiomatic system when building a proof it is important to know what your foundational definitions are. It seems to me common core analysis type questions are the perfect place to have this discussion with a geometry class. Students should be made well aware of this international debate when common core geometry is taught and be encouraged to engage in the debate...maybe a research project or an actual debate featuring one definition vs. the other. Experts could weigh in on youtube or something and students can make an informed judgement as to which definition they agree with and can then write an argument as to why they agree.
Obviously there is the question of whether or not students are going to be penalized for using one definition over the other, but in the end they will probably have to be taught that although there may be alternate acceptable definitions, and although they may disagree, they must use whatever basis of thought they are being asked to use for this particular test just as you may be sometimes asked in your job to use a particular format or system that you don't necessarily think is the best one. In theory, all students should be able to reason and think in this manner (and certainly may have been had the common core been allowed to be phased in from kindergarten on up). In reality, I certainly realize that many many students are not ready for this kind of thinking....but I think this kind of thinking and discussion is exactly what geometry education needs. Get students fired up about something!
Elizabeth Waite AMTNYS Coordinator of Reps
Original Message From: Ved Shravah <VSHRAVAH@MAIL.NYSED.GOV To: nyshsmath <nyshsmath@mathforum.org> Sent: Thu, May 2, 2013 10:44 am Subject: Re: PARCC Definition of Trapezoid
I am very surprised at this discussion. It is not up to some Math Professors in the U.S. to change the definition of Trapezoid. I have taught Mathematics for over 40 years and I have taught in different Countries and every where they have used the same definition for trapezoid that it has only one pair of parallel sides. Trapezoid is a very unique geometrical figure and is not a parallelogram. Mathematics is an international language and by changing the definition of trapezoid, it will be only the U.S. having a different definition of trapezoid and the rest of the world will follow a different definition. Ved Shravah Mathematics Associate Office of State Assessment New York State Department of Education 89 Washington Avenue, Albany, New York vshravah@mail.nysed.gov 5184081743
>>> Elise Teitelbaum <eet314@gmail.com> 5/1/2013 6:12 PM >>>
I have been teaching for almost 40 years and I too have seen one definition used in some text books while the other definition is used in others.
Do the test writers monitor this forum? (They should.) Are they aware of this problem? (They ought to be.) Are they aware enough to be sure that this issue does not cause one group of students using one definition to lose precious points on their test? (I sure hope so.) Am I confident that they will be careful about this? (NOPE!!)
How can we ensure that this will not be a problem on these all important upcoming exams?
On Wed, May 1, 2013 at 6:00 PM, Roberta M. Eisenberg <bobbi610@me.com> wrote:
I started teaching in 1962, and the honors geometry class used a textbook that had that def. The regular geom. class had the usual def. It was confusing teaching both classes and remembering which def. to use in each class.
Bobbi Eisenberg
On May 1, 2013, at 5:36 PM, Robert Bieringer wrote:
The differences in the fundamental definition of a trapezoid, I believe date back to Zalman Usiskin at the University of Chicago. The work by Dr. Usiskin led to the University School Mathematics Project [USMP] during the late 1960s into the 1970s and the "at least two parallel sides" definition, came out of those series of books. A reference I found just today, gives support to the point:
http://casmusings.wordpress.com/2012/04/01/definingtrapezoids/
Mr. Robert C. Bieringer Director of Mathematics K12 Bay Shore UFSD Bay Shore, New York 11706
ownernyshsmath@mathforum.org wrote: 
To: "nyshsmath@mathforum.org" <nyshsmath@mathforum.org> From: Gene Jordan Sent by: ownernyshsmath@mathforum.org Date: 05/01/2013 03:11PM Subject: RE: PARCC Definition of Trapezoid
Before we dive into the "inclusive" vs. "exclusive" trapezoid wars. I'm not sure anyone will be all right or all wrong on this, it sounds more like two wellgrounded options.
After hearing a great presentation by Brian Cohen at Rye Brook AMTNYS fall conference I wanted to run this by others for input:
I think PARCC has higher level math supporting the inclusive side. However, our PK5 teachers have textbooks (even CCSS aligned) that still use the exclusive rule. Even though text books aren't authoritative, they are widely used and matches what is being taught. Browsing through the latest textbook samples I have, Glencoe (2013) uses exclusive definition and one of Pearson's uses inclusive and others are vague.
I thought this was on Algebra or geometry regents before with the inclusive definition?
I also think there was a group working on CCLS glossary, not affiliated with State Ed anyone heard anything about this?
~Gene Jordan
Original Message From: ownernyshsmath@mathforum.org [mailto:ownernyshsmath@mathforum.org] On Behalf Of Tammy Woodard Sent: Wednesday, May 01, 2013 1:43 PM To: nyshsmath@mathforum.org Subject: RE: PARCC Definition of Trapezoid
This definition holds when it comes to finding area of a parallelogram, in which you use the trapezoid formula. No matter what area formula, parallelogram or trapezoid, you would get the same answer.
Tammy M. Woodard Mathematics Teacher Scarlet Team EDMS Elmira Express Indoor Varsity Assistant Track & Field Coach Elmira Express Girls JV Lacrosse Head Coach NYLAP Instructor  Texas Instruments Ernie Davis Middle School 610 Lake Street Elmira, NY 14901 (607) 7353400 twoodard@elmiracityschools.com ________________________________________ From: ownernyshsmath@mathforum.org [ownernyshsmath@mathforum.org] on behalf of Elliott Bird [Elliott.Bird@liu.edu] Sent: Wednesday, May 01, 2013 12:47 PM To: nyshsmath@mathforum.org Subject: RE: PARCC Definition of Trapezoid
I think it's valuable that you saw this. I hope others will become aware as well. The definition you saw in the 2005 glossary is an old one, and New York State has stayed with it at least up until that time.
However, many states and countries and publishers have been using the new definition (at least two parallel sides) for a long time. The newer definition is more consistent with other mathematical definitions like that of isosceles triangleat least two congruent sides. Then an equilateral triangle is also isosceles. Similarly, with the newer definition of trapezoid, every parallelogram is also a trapezoid.
Elliott Bird Consultant in Mathematics Education Professor of Mathematics, Emeritus L.I.U. ________________________________________ From: ownernyshsmath@mathforum.org [ownernyshsmath@mathforum.org] on behalf of Holly Thomas [hollythomas@mail.ircsd.org] Sent: Wednesday, May 01, 2013 12:05 PM To: nyshsmath@mathforum.org Subject: PARCC Definition of Trapezoid
I've been reviewing recently released PARCC documents and was confused that PARCC is defining a trapezoid as having "at least one pair of parallel sides". However, the most recent definition I can find issued by NYS is in the 2005 Standards math glossary, in which a trapezoid is defined as having exactly one pair of parallel sides. Since this will impact instruction from Grade 3 on, I'm curious is anyone else is aware of this issue, or any discussions surrounding it.
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