Important: A MINOR MIRACLE has recently occurred, to which I wish to draw the attention of everyone at Math-teach, as below:
Robert Hansen (RH) posted Jul 9, 2013 5:43 AM: > > I have always assumed that people that get things, > get more of the things themselves than the things > that are given to them. In other words, if you teach > me to fish, I fish. > Indeed. The next part of RH's argument is truly fascinating: > > The majority of my knowledge of > mathematics, the conclusions, the theorems, etc, I > discovered/invented/created on my own, but not in a > vacuum. Not without the starter bits and pieces given > to me along the way. And I created a many of my own > starter bits and pieces. > Now there - neatly encapsulated in the description of the way RH claims that he had himself 'learned math' - is the whole argument contradicting practically everything he has been arguing here for years about the way he'd teach math!!
That is, in fact, the WHOLE BALL GAME!
The way RH had learned math is in total contradiction to the 'teaching philosophy' he has been expounding here at Math-teach these many years.
Astonishing! Thank you, RH.
You (and others here who have been arguing here ever so assiduously over the years) might perhaps like to make yourselves aware that the above is PRECISELY what the 'One Page Management System' (OPMS) approach tries to enable EVERY learner to do. More information about the OPMS is provided in brief at the attachments to my post heading the thread "Democracy: how to achieve it?" - see http://mathforum.org/kb/thread.jspa?threadID=2419536 . > >I understand that some > people take on mathematics in a very different way, > like reading a good book. They leave it to the author > to tell the story to them. I am not one of those > people. I have always been filled with anticipation > in these subjects. > Of course.
RH should perhaps also make himself aware that 'reading a good book' *SHOULD* (if one does it right) also be as 'creative' and 'constructive'** an activity as, say, 'learning math' (in the way RH has described above). It really COULD have a great many similarities with the way that RH described he had learned math.
GSC ("Still Shoveling!") P.S.: ** THAT DREAD WORD AGAIN (namely, "constructive")!!