Jonathan Groves posted Oct 16, 2010 1:33 AM (GSC's comments interspersed): > GS Chandy, > > I agree that such lists of objectives that you have > proposed here are good > for students to pursue. Too many of my own students > in online classes > lack many of these abilities, at least in the > classroom. Their discussions > are shallow because they stick to the obvious. > I would guess that, outside > the classroom or at least the math classroom, they > can think better than > they actually do. > I'm entirely certain that practically all (if not entirely all) students do innately possess the abilities to develop all of these useful skills (if such abilities have not already been drummed out of their psyches by an insensitive educational system, by teachers insisting on 'by-rote repetition' of meaningless formulae, and the like. I've indicated at the document "How a child learns" that practically all children inherently do possess abilities to pick up very complex skills indeed, far more complex than the skills we demand of them in schools (and even colleges) - and they do indeed pick up such skills in real life - but yet so many of them fail to pick up things like multiplication, division, and the like!
I do strongly believe that what the educational system really needs to do is itself to learn how to tap into this 'innate ability to learn' that's naturally possessed by students. The Montessori system does recognize this - but relatively few schools actually do use these Montessori insights in anything after primary schools. > > As I continue to see more and more > shallow discussions, > I continue to wonder if many of the students are > really just faking their > efforts to participate. > I'd suggest that the 'faking' is far less of an issue than the fact that the educational systems have by and large forced the students to suppress their 'question-asking faculty', rendering it dormant, so to speak. I'm pretty certain that the OPMS process can and does help regenerate that faculty. Description of the OPMS process is available at the attachments to my posting dated Oct 8, 2010 10:01 AM at this thread - see http://mathforum.org/kb/message.jspa?messageID=7234262&tstart=0 . > > I will have to try tracking down more articles, but I > recall seeing some > earlier this year, one a few days ago and another one > this past spring that > suggest students' abilities to think are actually > better than what "school > testing" indicates. > I shall look forward keenly to seeing links to those articles, if you should get hold of them - they seem to be quite supportive of my stance on this issue. > > One of them is a preprint of one > chapter of a book by > Terezinha Nunes and Peter Bryant, which I had found > in a files section of > a Yahoo group on math education. Whether the book is > published or what > the title of the book is, I will have to check. > Since it is a preprint, > I will also have to check if it is acceptable to > share this document with > others. I do not believe there is a web reference > for this document; > Google searches have turned up nothing. > > This preprint is the one I had seen this past spring. > The main idea in this > document is that not only does proportional reasoning > develop without > formal education, formal education may actually > significantly hinder that > development in many students. > I do believe that the above contentions are largely correct, if the formal education is entirely 'conventional', insisting on 'by-rote parroting' without trying to inculcate students' real interest in what is to be learned. > > The other article I had seen several days ago is one > written by Ralph > A. Raimi: "Basketball Logic and the NAEP." The link > to the article > is found at > > http://www.math.rochester.edu/people/faculty/rarm/Logi > c2009.html. > > The following conclusion he reaches is quoted below: > > "I believe, therefore, that the public is being given > the wrong information, > and is led to believe things that are simply not so. > The NAEP scores affect > to tell us that children fail to understand certain > things touching on > mathematics as it is presented to us in the real > world, whereas what these > children are exhibiting ignorance of is something > quite different: the skill > to read an examination paper and to imagine the > real-world situation those > words think they are describing to him. Very often, > as happens repeatedly in > other examinations where parents protest and exam > publishers apologize, those > words don?t really do their job. But even when the > writing is plain, and good, > should we label this NAEP ?story-problem? skill > ?Mathematics?? > I don't know anything about the NAEP to comment, but I do believe Raimi's other contentions seem to be entirely valid. > > "Can we really say that half of our high school > students seriously believe > that because all basketball players are tall every > tall person is not only a > basketball player but one of our own team? Yet we do > solemnly say that. > NAEP itself says so. They have measured it." > > Jonathan Groves > Well, I've seen such non sequiturs often enough, some of them right here at this forum!