Kirby Urner posted Jun 18, 2013 10:15 PM (GSC's remarks interspersed): > > 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 did not understand his reference to "K-calculus" > out of the blue. I > looked it up, but no light was shed thereby. > > http://mathforum.org/kb/message.jspa?messageID=9138177 > > http://arxiv.org/abs/physics/0201002 > I note that Clyde Greeno has provided some information about what his reference to "K-Calculus"means. The explanation does not (if I've correctly understood it) provide a response to the question I had asked: >> why haven't the 'math progressives' done something >> (however small) about increasing that percentage? [of >> college students in STEM-specific higher ed >> programmes]? > 'K-Calculus' (which I've not yet examined) may well provide part of the answer. It cannot serve as an 'action plan' to resolve [or even to progress in any significant way on] the issue(s) identified. It may well provide some 'general hints' as to how we may move for progress (but these hints would be, I believe, extremely general). > > > > > 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 > ). > > > > > By "Algebra City" I meant Baghdad, ancient (not that > ancient) site of the > Wisdom School and Al Khwarizmi, a math whiz (wiz) > from whose name we get Al > Gorithm (yes sounds like Al Gore -- didn't AG > transact with Al Jazeera > after all?). > > And what did we get from Baghdad then? From Algebra > City? Al Jabber of course. > > And if you think "jibber jabber" or "abacadabra" > that's right. You should > also think of cryptography and keeping secrets, an > ancient purpose for > which the terms "function" and "inverse function" > (encrypt / decrypt) have > relevance. You'd be smart to build lots about crypto > into algebra class > and some curricula do that, others don't. Steer > towards the ones that do > is what I'm suggesting. > > If you're a student living in the United States of > [North] America and you > notice your high school's curriculum has no mention > of Euclid's Method for > finding the GCD, feel free to write to the Governor > of your state, which > office will know to route it to the Core Standards > people who have been > using the governorships as a network to create new > standards for your > nation. > You want your nation to be at least mildly > competent right? > Canadian? Well then, you probably already know > Euclid's Method as > Canadians tend to be twice as smart as their brethren > to the south > No. I'm Indian, not Canadian. We do have very grave issues with ALL of our education systems (including math education) - none of which we are even beginning to resolve!
(Though it is not actually relevant, I believe you're mistaken in your contention that "Canadians tend to be twice as smart as their brethren to the south". I would believe that your impression to this effect actually must derive from some appropriate modification of what I've identified as 'the underlying issue in India' - see below: people in charge in the US are probably quite as blind to the crucial issue that is to use effectively whatever resources are in fact available: none of those resources - whether of finance; people; our means of 'handling issues' - are being effectively applied to the issues at hand. In most cases, we possess litle if any real understanding of the issues that are actually important/ relevant at any time).
The smallest part of the problems with our (Indian) education systems is that funds are rather scarce. [Of course, it is my contention that we do allocate relatively too little funds to education - but that is another matter].
In any case, most of the funds allocated are poorly/wrongly spent on unimaginative (and poorly designed) programs - when, in fact, we already have right at hand ALL the knowledge and understanding to improve (very significantly indeed) our entire education systems at all levels, of all kinds (with little requirements of 'extra funding').
Thus, the underlying issue appears to be that 'people in charge' are entirely willing to go about doing the very things that have already been demonstrated not to work. Some radical 'change in mindset' appears to be what's needed - which no amount of Euclid's Method will help to bring about. The underlying issue thus appears to be: "To bring about an adequate change in mindset in the people who currently control education". (After several years of striving to change the mindsets of 'the people in charge;, I have more or less given up on that. I am now trying to get to the actual people who're so poorly served by our education system - students; parents; teachers. Some minor signs of success are seen). > > -- I read in a study somewhere (Moore?). > I'm not acquainted with "Moore's study". > > Anyway, learn Euclid's Method yourself first. Can > you find a good > cartoon? It doesn't involve "factor trees" or "prime > factors" but does > involve division and taking note of the remainder. > It's a doorway into > "recursion" but needn't be given that treatment. > > There's also an "extended" Euclid's Method (EEM) > that's been used to solve > Diophantine Equations and to help with RSA, another > algorithm, named for > three crypto whizzes: Rivest, Shamir, Adleman. > See above. (I agree that Euclid's Method [extended or otherwise] does need to be effectively taught - which is not the case in our existing systems. But [I believe] it's not Euclid's Method that will provide an answer to the dilemma I confront).
Thanks for the references in your endnotes, which will obviously take me some time to absorb adequately. (I have glanced at some of them - they do not seem to address what I believe I have correctly identified above as the 'underlying issue[s]').