Further my last (at http://mathforum.org/kb/message.jspa?messageID=9138520), I have read the New York Times Opinionator article, and found it to be quite insightful, though I do have some (minor) reservations. (I note that I know nothing about the work of the US philosoper Wilfrid Sellars [though I do intend to do some reading up on this]. My comments here thus neglect the authors' discussion on Sellars' work).
One of my reservations: I largely concur with Clyde Greeno's objection that the musings of the authors rather fail (though in my opinion, they do not "badly fail", as Mr Greeno claims) to resolve the issues within the 'math wars'). I believe that the authors would have succeeded in moving considerably towards some parts of a 'resolution' if they had used the seminal contributions to systems science of the late John N. Warfield - and the developments therefrom, in particular the impact of the relationship "CONTRIBUTES TO" (and its 'negative', "HINDERS") on our understanding of systems, including 'thought systems'.
Clyde Greeno rightly observes that a far too small percentage of students 'survive' school math to enter STEM-specific higher education programs. My question: why haven't the 'math progressives' done something (however small) about increasing that percentage?
I've not yet read "Wars in American mathematical education" by Andre' Toom (recommended by Domenico Rosa).
One is delighted to observe that Professor Wayne Bishop gives the article broad approval as "not bad".
Kirby Urner's objection that the article 'over-implifies' quite a bit is (more or less) justified - but I also believe that such over-simplification is inevitable given that the authors are discussing quite complex issues in 'pure prose'. Had they used the 'prose + structural graphics' (p+sg) that I recommend for the effective discussion of complex issues, I believe this objection would have had less force.
Kirby Urner: > We were also doing Venn Diagrams a lot back then. Do > people want to tell me which "algorithms" they mean > when we talk about union and intersection, set > difference? I don't think most non-STEM-informed > imaginations extend to the set object, nor the > multidimensional array object when thinking of > algorithms (nor where algorithms come from: Algebra > City).
I observe that KU's comments above would have considerable import for an argument between Joe Niederberger and Robert Hansen (which, I believe, largely developed from misunderstanding of the issues by Robert Hansen). [See thread "New tutor here", headed by http://mathforum.org/kb/message.jspa?messageID=9134056 ).
Given all of the above, there is a fair bit that is of value in the article, and it would be appropriate (I believe) to develop a few 'system models' from the elements within it. (Those models may help address some part of Clyde Greeno's objection noted above).
(Perhaps I shall do that in due course - with apologies to Robert Hansen [and his cohorts and consorts] who probably have serious reservations about 'systems modeling'. I only observe that 'systems modeling' is emphatically NOT 'CPM scheduling' on which Mr Hansen has unfortunately got himself seriously hung up.
GSC > Joe Niederberger posted Jun 17, 2013 7:58 PM: > > Everyone here should read it - > > > > > http://opinionator.blogs.nytimes.com/2013/06/16/the-fa > > ulty-logic-of-the-math-wars/?hp > > > Thanks for the link - shall read it soonest possible. > I observe that I had always enjoyed the > e 'Opinionator' pieces in the NYT - but have not seen > them for some time. > > GSC