
Re: MLCS Webinar on April 24: Registration Open
Posted:
Apr 9, 2012 5:02 PM



Ed,
Your, "I am not certain what you mean that it is not a matter of opinion" No issue: If "proportion reasoning" is a special case of "function reasoning", it follows that "function reasoning" is more useful than "proportion reasoning"... all opinions notwithstanding.
"... not teach functional reasoning..." Not at all what I meant. My own recommendation: teach the broader kind ... to impart the big picture ASAP ... to the extent that it is pertinent and can be fully commonsensible ... with emphasis on whatever special kinds warrant attention ... linearity, powers, exponentials, waves, etc. But too much detail, too early, forces haste, superficiality, alienation and withdrawal ... which is the prevalent mode.
Cheers. Clyde
From: Ed Laughbaum Sent: Monday, April 09, 2012 2:59 PM Cc: mathedcc@mathforum.org Subject: Re: MLCS Webinar on April 24: Registration Open
Clyde,
Sorry I write in a manner that is confusing. I find writing a listserv post not demanding of too much time, and therefore I may not think through what I have said or what I want to say. It can then seem like "stream of consciousness" writing.
Ignoring your first three paragraphs, I would focus on my intention that (linear) proportional reasoning is a special case of (linear) functional reasoning. I am not certain what you mean that it is not a matter of opinion. Unless it is your way of saying that "why would you teach (linear) proportional reasoning when it is just a special case of linear functional reasoning, and thus one would teach linear functional reasoning?" Can we/should we stop there and not teach functional reasoning (with the implications that 2year, 4year, and 5year college graduates be able to reason and process with a wide variety of realnumber function types)?
Regards,
Ed ====================================== On 4/9/2012 2:26 AM, Clyde Greeno wrote: ???!!!###
I can't make much sense of " ... focusing on proportional reasoning ... or whether we should be focusing on function...." Are we saying we better be focusing on functions *instead of* on proportionality? Or are we saying that we better expand our focus so that (often myopic) "proportional reasoning" should be attended as a special aspect of "function reasoning".
Mathematically, I take "proportion" to mean the set of all realscalar multiples of any tuple of quantities or of numbers ... each of those tuples being a "ratio" within that proportion. In the case of tuples being ordered pairs, proportions are simply the mx functions ...[often called the y=kx "direct variation" functions, with (slope) k being its "constant of proportionality".]
In ndimensional space, each proportion identifies with (n1) functions. For example (from HS geometry), the "Pythagorean" proportion m*(3,4,5) [=(m3,m4,m5)] defines the firstplacecontroller function, x>y, where y= ((4/3)x, (5/3)x)) ... having (x,y) functionpoints (x, ((4/3)x, (5/3)x)). Likewise, m*(3,4,5) has a 2ndplaceconroller function and a 3rd place controller function
Since it appears that "proportional reasoning" is just a special case of "function reasoning", it is logically certain that "functional reasoning" is at least as useful as "proportional reasoning." That much is not at all a matter of opinion.
So, I find the dialog to be quite confusing.
Cordially, Clyde
From: wmackey Sent: Sunday, April 08, 2012 8:37 PM To: Guy Brandenburg Cc: Ed Laughbaum ; Clyde Greeno ; Clyde Greeno ; <mathedcc@mathforum.org> Subject: Re: MLCS Webinar on April 24: Registration Open
I agree that functions are much more useful in everyday life.
wayne
Quoting Guy Brandenburg <gfbrandenburg@yahoo.com>:
> Electric bills aren't necessarily exactly proportional to the kwh > used. And does 16 cents really matter anyway? > > Guy > > On Apr 5, 2012, at 1:27 PM, Ed Laughbaum > <elaughba@math.ohiostate.edu> wrote: > >> Hi Clyde, >> >> A couple things... >> >> I am glad I could give you a segue to one of your issues that needs >> discussion  from a posting earlier today. Greenspan & Shanker >> used the example of teaching the concept of a tax using a pizza and >> M & M's used to teach addition as an emotional (or personal) >> contextual situation. This is what I had in mind, but certainly >> agree with your position. >> >> Relative to this post, I have observed that I often see the >> mathematical literacy proponents argue for proportional reasoning as >> a mainstay outcome. This in turn, reminded me (recall through neural >> associations) of an informal survey I took on several colleagues who >> were not in any of the STEM fields but all had a bachelors degree >> through a PhD. In the following "problem" everyone used >> proportional reasoning. >> >> If you use 1205 kWh of electricity and your bill is $130, how much >> is your monthly bill if you use 1225 kWh? Everyone got $132.16 for >> the answer when it is $132. >> >> What I wonder is, if focusing on proportional reasoning will solve >> this very simple problem (of thinking relationships are >> proportional), or whether we should be focusing on function. Or >> something else? Of course, my opinion is on function, but it is an >> opinion. >> >> Regards, >> >> Ed >> =========================================== >> On 4/5/2012 12:27 PM, Clyde Greeno wrote: >>> >>> >>> >>>  >>> From: "Clyde Greeno" <clydegreeno@cox.net> >>> Sent: Thursday, April 05, 2012 11:17 AM >>> To: "Linda Zientek" <lrzientek@yahoo.com>; "AMATYC DMC" >>> <amatycdmc@googlegroups.com> >>> Subject: Re: MLCS Webinar on April 24: Registration Open >>> >>>> >>>> Webinar description, as posted: >>>> "Mathematical Literacy for College Students (MLCS) is a new course >>>> that is part of an AMATYC initiative called New Life for >>>> Developmental Math as well as the Carnegie Quantway project. It >>>> is an innovative way to redesign the developmental curriculum, >>>> providing pathways for the nonSTEM student. The course uses >>>> integrated, contextual lessons to develop conceptual understanding >>>> and technology to improve mastery of skills. In one semester, a >>>> student placing into beginning algebra will gain the mathematical >>>> maturity to be successful in statistics, liberal arts math, or >>>> intermediate algebra. Reading, writing, critical thinking, and >>>> problem solving are key components to reaching that goal. Webinar >>>> participants will learn much more about the course as well as >>>> receive ideas for course development including a sample course >>>> outline and a sample lesson. " >>>> ================= >>>> Excerpt about "Position paper": >>>> " ... the appropriate preparation that all students should receive >>>> in developmental math courses. "?? >>>> ================ >>>> >>>> As yet, I have seen no indication that "Mathematical Literacy for >>>> College Students" ... or any other "reformed" course ... has >>>> addressed the need for empowering American adults with strong >>>> *conceptual understanding* of KbasicAlgebra mathematics ... so >>>> that they can make school mathematics fully commonsensible to >>>> children. Most college students are "preservice" parents ... and >>>> most of the rest are "inservice" parents. The vast majority >>>> arrive at college with little mathematical comprehension of K8 >>>> mathematics ... and colleges typically have not provided it (even >>>> to preservice/inservice teachers) ... which explains why the >>>> schools do/can not do so. >>>> >>>> How can we speak of "mathematical literacy" of adults who cannot >>>> make personal common sense of K8 mathematics? >>>> >>>> Hopefully, >>>> >>>> >>>> Clyde Greeno, >>>> Academic Director and >>>> Clinical Professor of Mathematics Instruction >>>> The American Institute for the Improvement >>>> of Mathematics Learning and Instruction >>>> P.O. Box 54845 >>>> Tulsa, OK 74155 >>>> Tel: 9188366284 >>>> email: greeno@malei.org >>>> website: www.malei.org >>>> >>>>  >>>> From: "Linda Zientek" <lrzientek@yahoo.com> >>>> Sent: Thursday, April 05, 2012 9:55 AM >>>> To: "AMATYC DMC" <amatycdmc@googlegroups.com> >>>> Subject: MLCS Webinar on April 24: Registration Open >>>> >>>>> Registration for Kathleen Almy's webinar is open. This is an AMATYC >>>>> DMC sponsored webinar. >>>>> >>>>> New Pathways for Developmental Math: A Look into Mathematical Literacy >>>>> for College Students >>>>> Tuesday April 24 at 3 EST/2 CST >>>>> >>>>> For more information, visit the DMC website: >>>>> https://sites.google.com/site/amatycdmc/ >>>>> >>>>> Thanks, >>>>> Linda Zientek >>>>> DMC Chair >>>> >>> **************************************************************************** >>> * To post to the list: email mathedcc@mathforum.org * >>> * To unsubscribe, email the message "unsubscribe mathedcc" to >>> majordomo@mathforum.org * >>> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 * >>> **************************************************************************** >> >>  >> Edward Laughbaum www.math.osu.edu/~laughbaum.6/ >> The Ohio State University >> 231 West 18th Avenue >> Columbus, OH 43210 >> >> >> TODAY(Beta) . Powered by Yahoo! >> 'American Idol' men amaze judges >> Privacy Policy >> >>
 Edward Laughbaum www.math.osu.edu/~laughbaum.6/ The Ohio State University 231 West 18th Avenue Columbus, OH 43210

