Math Forum Discussions

Martin C. Tangora

Posts: 25
Registered: 12/4/04

Re: New Post at RME: Who Was George Polya's Intended Audience? (Or More Mathema
Posted: Jun 4, 2010 9:18 PM

Plain Text

Both J Groves and M P Goldenberg
seem to be unaware that Polya wrote "How to solve it"
for a general audience, and then wrote
"Mathematics and plausible reasoning" for a much more highly
trained audience. Thus the argument about the intended
audience is just noise because of the failure
to distinguish the two books.

Actually M & PR is two volumes, and there is
a fourth book written after HtSI and before M&PR.

It is too bad that statements like "this claim is false"
and "long overdue and clearly definitive retort"
are posted without adequate knowledge.

On 6/4/2010 8:05 PM, Jonathan Groves wrote:
> Dear All,
>
> Here is a link that Michael had sent me that shows their claim about
> Polya's book intended for math majors or graduate students and not
> K-12 math students:
>
> http://mathforum.org/kb/message.jspa?messageID=1479090&tstart=0.
>
> However, this claim is false since the introduction to Polya's book
> "How to Solve It" clearly says that Polya wrote the book for all
> teachers and students of mathematics.
>
> Section 1. Problem Solving in Mathematics.
>
> [snip]
>
> Though Johnson and Rising do not explictly mention what audience George
> Polya intended for his book "How to Solve It," it is clear that they realize
> his book was intended for all students and teachers of mathematics.
> In short, Johnson and Rising believe that problem solving is an integral part of
> EVERY math class, not just those in college with math majors or just classes for
> "mathy" kids. And they realize that George Polya would agree wholeheartedly.
>
> Section 2. The New Math Era.
>
> [snip]
>
> Jonathan Groves
>
> On 6/2/2010 at 4:40 pm, Michael Paul Goldenberg wrote:
>
>> Please read the latest post at
>> RationalMathEd.blogspot.com: "Who Was George Polya's
>> Intended Audience? (Or More Mathematically Correct
>> Lies)"
>>
>> Excerpt: One of the more difficult aspects of wars,
>> even ones where the main ammunition is words, is
>> separating lies from facts. Every side in a war has a
>> proclivity for propaganda. Inconvenient facts are
>> brushed aside. Inaccuracies, petty or gross, become
>> the coin of the realm. The Big Lie rules.
>>
>> Of course, sometimes, it is possible to sort through
>> the fog of war to arrive at what appears to be
>> incontrovertible truth. It may take years, even
>> decades, to find the facts, even when they are
>> readily available to anyone who bothers to look in
>> the right place for them. Sometimes, they've been
>> staring everyone in the face for a very long time.
>>
>> Thus, it is with no small embarrassment that I
>> present a long-overdue and clearly definitive retort
>> to one of the lies frequently promulgated a decade or
>> so ago by Professor Wayne Bishop and some of his
>> Mathematically Correct and HOLD anti-progressive
>> allies, namely that George Polya's work on heuristic
>> methods (from the Greek "???????" for "find" or
>> "discover": an adjective for experience-based
>> techniques that help in problem solving, learning and
>> discovery) was intended only for graduate students or
>> perhaps undergraduate mathematics majors, not for the
>> general student of mathematics, and certainly not for
>> high school students or younger children.
>>
>> Of course, in the Math Wars, it is of the utmost
>> importance to the counter-revolutionaries and
>> anti-progressives that nothing that broadens access
>> to mathematics be allowed to stand unchallenged or
>> unsullied. Any curriculum, pedagogy, tool, etc., that
>> is brought forward by reformers as "worth trying"
>> must be smashed. That has been the tireless task of
>> members of groups like Mathematically Correct and
>> HOLD: to undermine any and all efforts to change what
>> they view as immutable approaches to the teaching and
>> learning of mathematics.
>>
>> Read the entire post at: http://tinyurl.com/2bl5f7r

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Martin C. Tangora
tangora (at) uic.edu