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Re: Geometry #21
Posted:
Aug 19, 2011 11:57 PM



I agree about the isosceles trapezoid ... The point I was making is that different states consider a parallelogram and trapezoid ... and I was concerned about future tests that will go across state lines ... we should all agree on a definition ...Grace Wilkie
On Thu, Aug 18, 2011 at 9:30 PM, Jonathan <jd2718@gmail.com> wrote:
> 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******************************************************************* >>> >>> >>> >> >



