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Re: Geometry #21
Posted:
Aug 18, 2011 9:30 PM



The use of the term "isosceles trapezoid" presupposes that exactly one pair of sides is parallel. But we do not expect that level of analysis from students on state tests.
In this case there was a different problem  a conversational register used in formal context, confounding the ideas of "some" and "all." They've made this sort of error in the past, as well. I believe it is even goes back to the beginning of Math A (I don't think it showed up before that).
Jonathan Halabi HS of American Studies the Bronx
On Thu, Aug 18, 2011 at 9:11 PM, Grace Wilkie <gwilkie@highlands.com> wrote:
> I remember having so many conversations about the trapezoid with a person > outside of NY ... > > There is also some disagreement on the allowed number of parallel sides in > a trapezoid. At issue is whether parallelograms<http://en.wikipedia.org/wiki/Parallelogram>, > which have two pairs of parallel sides, should be counted as trapezoids. > Some authors[2] <http://en.wikipedia.org/wiki/Trapezoid#cite_note1>define a trapezoid as a quadrilateral having > *exactly* one pair of parallel sides, thereby excluding parallelograms. > Other authors[3]<http://en.wikipedia.org/wiki/Trapezoid#cite_noteMathworld2>define a trapezoid as a quadrilateral with > *at least* one pair of parallel sides, making the parallelogram a special > type of trapezoid (along with the rhombus<http://en.wikipedia.org/wiki/Rhombus>, > the rectangle <http://en.wikipedia.org/wiki/Rectangle> and the square<http://en.wikipedia.org/wiki/Square_%28geometry%29>). > > > Where we will have a test that will be used in many states we must make > sure we are all working from the same definition ... > > Grace > > > > On Thu, Aug 18, 2011 at 7:30 PM, <elizwaite@aol.com> wrote: > >> Agreed...I see what you're saying now... >> You would have preferred the question said The quadrilateral *could be*and then the choices. >> Liz Waite >> >> >> >> Original Message >> From: Jonathan <jd2718@gmail.com> >> To: nyshsmath <nyshsmath@mathforum.org> >> Sent: Thu, Aug 18, 2011 4:45 pm >> Subject: Re: Geometry #21 >> >> There's clearly a best answer. I didn't mean to raise it as a grading >> issue. It is, rather, a quality issue. >> >> I am concerned that this is yet again a poorly written question. They've >> chosen what reads like universal language, but intended that it apply to a >> particular example. >> >> And this is in a geometry course, the primary place in secondary >> mathematics where the distinctions between "all" and "some" and between >> "always," "sometimes," and "never" are taught and reinforced. >> >> Jonathan Halabi >> HS of American Studies >> the Bronx >> >> >> On Thu, Aug 18, 2011 at 3:42 PM, <lboyce@pbcschools.org> wrote: >> >>> In the case of multiple choice questions I teach my students to choose >>> the BEST answer from the choices given. >>> >>> Loretta Boyce >>> Mathematics Teacher >>> Dana L West Jr Sr High School >>> 30 Maple Ave >>> Port Byron, NY 13140 >>> >>> >>> >>> >>> ownernyshsmath@mathforum.org wrote:  >>> >>> To: "nyshsmath@mathforum.org" <nyshsmath@mathforum.org> >>> <nyshsmath@mathforum.org> <nyshsmath@mathforum.org> >>> From: Jonathan ** >>> Sent by: ownernyshsmath@mathforum.org >>> Date: 08/18/2011 12:56PM >>> Subject: Re: Geometry #21 >>> >>> >>> It could be an isosceles trapezoid, but that's not the question as asked. >>> We really should be expecting mathematically precise language. >>> >>> Sent from my iPhone >>> >>> On Aug 18, 2011, at 12:08 PM, elizwaite@aol.com wrote: >>> >>> Right...but were you saying that out of the 4 choices none were >>> correct? >>> Liz >>> >>> >>> >>> Original Message >>> From: Jonathan <jd2718@gmail.com> >>> To: nyshsmath <nyshsmath@mathforum.org> >>> Sent: Thu, Aug 18, 2011 10:52 am >>> Subject: Re: Geometry #21 >>> >>> In a kite, neither pair of sides is parallel. >>> >>> Sent from my iPhone >>> >>> On Aug 18, 2011, at 10:32 AM, <elizwaite@aol.com>elizwaite@aol.comwrote: >>> >>> I believe isosceles trapezoid is correct. Although I do recall an >>> earlier conversation on this list from several years ago where a few people >>> defined a trapezoid as a quadrilateral with AT LEAST one pair of parallel >>> sides where most of us used EXACTLY one pair of parallel sides. This would >>> make a difference, I think. >>> Liz Waite >>> >>> >>> >>> Original Message >>> From: Jonathan < <jd2718@gmail.com>jd2718@gmail.com> >>> To: nyshsmath < <nyshsmath@mathforum.org>nyshsmath@mathforum.org> >>> Sent: Thu, Aug 18, 2011 10:24 am >>> Subject: Geometry #21 >>> >>> The diagonals of a quadrilateral are congruent but do not bisect eac >>> other. The quadrilateral is: >>> >>> Iso trapezoid >>> Parallelogram >>> Rectangle >>> Rhombus >>> >>> But none of these are necessarily correct (kite, anyone?) >>> >>> Sent from my iPhone >>> >>> On Aug 10, 2011, at 4:48 PM, Iva Jean Tennant < <tennantij@aol.com><tennantij@aol.com> >>> tennantij@aol.com> wrote: >>> >>> Hi All >>> Sorry this is a bit late, but I have been away for the last week. I hope >>> you are all enjoying some time off over the summer. >>> I know most of you have seen the news around the release of the PARCC >>> Model Content Frameworks for public comment. For those of you who have not, >>> read on. >>> · The Model Content Frameworks in Mathematics and English >>> language arts/literacy were released for public review on August 3rd, >>> after several rounds of feedback from the PARCC states. This public review >>> period is an opportunity for an even wider group of interested parties to >>> provide feedback on all parts of the frameworks, including the introductions >>> and the grade level analyses, which contain suggested areas of emphasis and >>> priority. >>> · By following the this link, >>> http://www.parcconline.org/parcccontentframeworks, you will be able to >>> review the draft Model Content Frameworks and provide your feedback through >>> an online survey. *All feedback is due to PARCC by Wednesday, August >>> 17th.* >>> During this public review period, PARCC hopes that teachers in >>> particular will provide their feedback on the draft Model Content >>> Frameworks. While teachers have helped to develop the frameworks to this >>> point, the feedback of a broader group of educators is critical. The Model >>> Content Frameworks are being shared directly with NCTM, NCSM, NCTE, AFT, and >>> NEA, as well as others, so these organizations can share them with their >>> members, as well. >>> >>> >>> · >>> >>> John Svendsen >>> Mathematics Associate >>> Office of Curriculum and Instruction >>> NYS Education Department >>> EB 320 >>> Albany, N.Y. 12234 >>> (518) 4745922 >>> (518) 4861385 (fax) >>> <jsvendse@mail.nysed.gov> <jsvendse@mail.nysed.gov><jsvendse@mail.nysed.gov><jsvendse@mail.nysed.gov><jsvendse@mail.nysed.gov> >>> jsvendse@mail.nysed.gov >>> <http://www.emsc.nysed.gov/ciai/mst/math/home.html><http://www.emsc.nysed.gov/ciai/mst/math/home.html><http://www.emsc.nysed.gov/ciai/mst/math/home.html><http://www.emsc.nysed.gov/ciai/mst/math/home.html><http://www.emsc.nysed.gov/ciai/mst/math/home.html> >>> http://www.emsc.nysed.gov/ciai/mst/math/home.html >>> <http://www.emsc.nysed.gov/ciai> <http://www.emsc.nysed.gov/ciai><http://www.emsc.nysed.gov/ciai><http://www.emsc.nysed.gov/ciai><http://www.emsc.nysed.gov/ciai> >>> www.emsc.nysed.gov/ciai >>> >>> >>> ** >>> >>> ******************************************************************* * >>> 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******************************************************************* >> >> >> >



