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Re: MLCS Webinar on April 24: Registration Open
Posted:
Apr 9, 2012 3:59 PM
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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 2-year, 4-year, and 5-year college
graduates be able to reason and process with a wide variety of
real-number 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
> real-scalar 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 n-dimensional space, each proportion identifies with (n-1)
> functions. For example (from HS geometry), the "Pythagorean"
> proportion m*(3,4,5) [=(m3,m4,m5)] defines the first-place-controller
> function, x->y, where y= ((4/3)x, (5/3)x)) ... having (x,y)
> function-points (x, ((4/3)x, (5/3)x)). Likewise, m*(3,4,5) has a
> 2nd-place-conroller 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 <mailto:wmackey@uark.edu>
> *Sent:* Sunday, April 08, 2012 8:37 PM
> *To:* Guy Brandenburg <mailto:gfbrandenburg@yahoo.com>
> *Cc:* Ed Laughbaum <mailto:elaughba@math.ohio-state.edu> ; Clyde
> Greeno <mailto:greeno@mathematicsinstitute.org> ; Clyde Greeno
> <mailto:clydegreeno@cox.net> ; <mathedcc@mathforum.org>
> <mailto:mathedcc@mathforum.org%3E>
> *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
> <mailto: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.ohio-state.edu
>> <mailto:elaughba@math.ohio-state.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
>> <mailto:clydegreeno@cox.net>>
>> >>> Sent: Thursday, April 05, 2012 11:17 AM
>> >>> To: "Linda Zientek" <lrzientek@yahoo.com
>> <mailto:lrzientek@yahoo.com>>; "AMATYC DMC"
>> >>> <amatyc-dmc@googlegroups.com <mailto:amatyc-dmc@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 non-STEM 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 K-basicAlgebra mathematics ... so
>> >>>> that they can make school mathematics fully commonsensible to
>> >>>> children. Most college students are "pre-service" parents ... and
>> >>>> most of the rest are "in-service" parents. The vast majority
>> >>>> arrive at college with little mathematical comprehension of K-8
>> >>>> mathematics ... and colleges typically have not provided it (even
>> >>>> to pre-service/in-service 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 K-8 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: 918-836-6284
>> >>>> e-mail: greeno@malei.org <mailto:greeno@malei.org>
>> >>>> website: www.malei.org <http://www.malei.org>
>> >>>>
>> >>>> --------------------------------------------------
>> >>>> From: "Linda Zientek" <lrzientek@yahoo.com
>> <mailto:lrzientek@yahoo.com>>
>> >>>> Sent: Thursday, April 05, 2012 9:55 AM
>> >>>> To: "AMATYC DMC" <amatyc-dmc@googlegroups.com
>> <mailto:amatyc-dmc@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
>> <mailto:mathedcc@mathforum.org> *
>> >>> * To unsubscribe, email the message "unsubscribe mathedcc" to
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>> >>> * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 *
>> >>>
>> ****************************************************************************
>> >>
>> >> --
>> >> Edward Laughbaum www.math.osu.edu/~laughbaum.6/
>> <http://www.math.osu.edu/%7Elaughbaum.6/>
>> >> The Ohio State University
>> >> 231 West 18th Avenue
>> >> Columbus, OH 43210
>> >>
>> >>
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>> >>
>>
>
>
--
Edward Laughbaum www.math.osu.edu/~laughbaum.6/
The Ohio State University
231 West 18th Avenue
Columbus, OH 43210
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