Robert Hansen (RH) posted May 30, 2014 7:00 PM (http://mathforum.org/kb/message.jspa?messageID=9475180) - GSC's remarks interspersed and follow: > > (RH to Joe N):I know you are just funning ... > I may well be mistaken, but I don't believe Joe N. was "funning" at all. A delightful RH passage follows: > > but my point was that > mathematics is the *search* for and the *sense* for > the *logical* connections between visceral truths, > not the visceral truths themselves. I know the > Collatz conjecture is true, we all do, but a > mathematician is tormented by why is it true. > Cracking such riddles is pure mathematics and if the > requisite of art is creativity, then pure mathematics > is pure art. But one does not have to crack riddles > as tough as the Collatz conjecture to meet the > standard of creativity. One is creative whenever one > senses and finds *logical* connections that are new > and original. Not new and original to the world, just > new and original to the themselves. > As, for instance, when RH went around plastering all the walls of the halls and corridors of the offices where he was working with 30-foot PERT Charts??
THAT was for sure "new and original" to him... and the "*logical* connections" that drove him to these stupendous (and stupefying) activities have never yet been *logically connected* - even to RH himself! > >Having things > *explained*, even when the student *understands* the > explanation, is not sufficient for creativity unless > the student goes much further with this activity and > explains to themselves a bunch of other stuff. > Above is clear demonstration of the validity of my claim that RH has understood little or nothing of what constitutes "creativity" (in math or in anything else).
"Learning ANYTHING new" is an act of great creativity - and EVERY child does it successfully from the very day he/she is born. (Till the 'question-asking frame of mind' that is inherent in EVERY child is forced into dormancy by 'Dickensian' educational systems that insist on 'by-rote learning'). The attachment "How A Child Learns" seeks to describe a couple of minor aspects of the stupendous feats of *real creativity* that EVERY child routinely performs.
Piaget and Montessori demonstrated the above very clearly nearly a century ago - but we still have the 'Robert Hansens of Education' insisting on stuff like QUOTE (learning)" is not sufficient for creativity unless the student goes much further with this activity and explains to themselves a bunch of other stuff". UNQUOTE
Just what does RH think the student is doing when he/she "learns SOMETHING NEW" ???!!
THAT'S the "other stuff" exactly, Mr Hansen!
(More indication in the paragraph below that RH understands little or nothing of what he is pontificating about). > > Solving difficult problems is also not sufficient > unless the student goes much further with this activity > explains to themselves > other things. And these other things do not have to > be grand revelations. Generally they are little > things. To be considered *creative* the only > requirement is that they are *new* and *original* to > the the thinker. > Do you see any contradictions in the above, Mr Hansen?? No, I guess you don't. (More delightful stuff, below): > > To sum up. Mathematics is the *search* for and the > *sense* for the *logical* connections between > visceral truths. When all three elements are present, > search, sense, and logic, then mathematical > creativity ensues. > WOWWWW!!! That IS a 'summing up', indeed! > > Schools have never emphasized creativity in > mathematics. No doubt, there is usefulness in applied > math, but the creative math student is pretty much on > their own. This is in contrast to how the other arts > are taught. But schools used to at least teach the > subject at a level at a level high enough to inspire > creativity. Now, because of political motives, even > that is gone for the vast majority of the students.:( > By and large, we could agree with much of the above-quoted para - except that there are grave doubts on just HOW Robert Hansen may have arrived at such a 'commonsense view'.
GSC ("Still Shoveling! Not PUSHING!! Not GOADING!!!")
RH responding to Joe N.: > On May 30, 2014, at 3:28 AM, Joe Niederberger > <firstname.lastname@example.org> wrote: > Joe N.'s post that brought about RH's above exegesis): > > R Hansen: > >> The Collatz conjecture appears to be > >> true, viscerally, > > > > Intersting thought. > > > > From wherever: > > 1 > > : felt in or as if in the internal organs of the > body : deep <a visceral conviction> > > 2 > > : not intellectual : instinctive, unreasoning > <visceral drives> > > > > > > So this is how Hansen does math. Cool beans. > > > > Cheers, > > Joe N