Michael Paul Goldenberg's blog post is mainly about Polya's heuristic methods of problem solving and of approaching mathematics as mathematicians do. He mentions in his blog post that these similar-minded thinkers from Hungary had helped added these heuristic methods to their elementary schools. He does say that "Mathematics and Plausible Reasoning" is mainly geared towards a more advanced audience but that the ideas of problem solving and the attitudes of approaching mathematics as contained in this two-volume book can apply to any math class. That is, the ideas are illustrated in this book with more advanced examples, but the principles are similar.
In short, Michael's argument is that Polya intended for his methods of approaching mathematics as problem solving are appropriate for any math class at any level but that his opponents deny that claim.
I did look again at the link I had provided, and the writer of the e-mail that Wayne Bishop quotes does mention Polya's book "Mathematics and Plausible Reasoning." I think I missed it the first time because it was not in quotation marks or in some other font to indicate that it is the title of a written work. But could the writer of the e-mail have misunderstood that someone else was referring to Polya's methods in general or Polya's book "How to Solve It"? I can't tell because we don't see what that writer is responding to. My experience with Wayne Bishop lines up well with what Michael says in his post. I would like to track down this post sometime, a post on math-teach in which I remember him telling me that he's happy to see a student who can work all the standard exercises in a textbook. And it doesn't matter to him if that student cannot solve any math problems that are new to him or her.
On 6/4/2010 at 9:18 pm, Martin C. Tangora wrote:
> 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 > > -- > > Martin C. Tangora > tangora (at) uic.edu