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Re: MLCS Webinar on April 24: Registration Open
Posted:
Apr 9, 2012 2:26 AM
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???!!!###
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
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.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>
>>> Sent: Thursday, April 05, 2012 11:17 AM
>>> To: "Linda Zientek" <lrzientek@yahoo.com>; "AMATYC DMC"
>>> <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
>>>> website: www.malei.org
>>>>
>>>> --------------------------------------------------
>>>> From: "Linda Zientek" <lrzientek@yahoo.com>
>>>> Sent: Thursday, April 05, 2012 9:55 AM
>>>> To: "AMATYC DMC" <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
>>>>
>>> ****************************************************************************
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>>> * 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
>>
>>
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