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

vshravah@mail.nysed.gov

518-408-1743

>>> 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.

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 theUniversity 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:Mr. Robert C. BieringerDirector of Mathematics K-12Bay Shore UFSD******************************************************************* * To unsubscribe from this mailing list, email the message * "unsubscribe nyshsmath" to majordomo@mathforum.org * * Read prior posts and download attachments from the web archives at * http://mathforum.org/kb/forum.jspa?forumIDg1 *******************************************************************To: "nyshsmath@mathforum.org" <nyshsmath@mathforum.org>

From: Gene Jordan

Sent by: owner-nyshsmath@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 well-grounded 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 PK-5 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: owner-nyshsmath@mathforum.org [mailto:owner-nyshsmath@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) 735-3400

twoodard@elmiracityschools.com

________________________________________

From: owner-nyshsmath@mathforum.org [owner-nyshsmath@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 triangle--at 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: owner-nyshsmath@mathforum.org [owner-nyshsmath@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.

Holly Thomas

Math Coach

Indian River Central School District

Philadelphia, NY

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