I had previously responded (Jun 4, 2014 2:31 AM, http://mathforum.org/kb/message.jspa?messageID=9478350) to Joe N.'s post dt. Jun 4, 2014 12:48 AM (http://mathforum.org/kb/message.jspa?messageID=9478284 pasted for reference below my signature), but my response seems to have gone 'elsewhere', so to speak - into a discussion of Piketty's views of Capitalism and its woes. Therefore, I try to address, more carefully to the extent I'm able to, Joe N.'s views pasted right here: > > (Joe N.): :I'm not really advancing the proposition to > only > teach knowledge that will be used. I was mainly > trying to point out that (1) stated or implicit goals > (according to whomever) for the educational "system" > largely contain their own distortions and > contradictions, and (2) learning that can be used > tends to be more robust. As simple as that is, it > does seem to be often ignored. > The 'goals of ANY system' will always be as perceived by someone or another - and surely they will be subject to the contradictions and distortions of the 'perceiver'. This fact is not in question at all. Well, we humans do seem to have developed language spoken and written to help us communicate in such circumstances. I note that other animals do not seem to have our ability to 'write thoughts down', so that should provide us some benefit. I also note that we can now learn to communicate in 'prose + structural graphics' (p+sg) that can, to an extent, help us surmount at least a few of the contradictions and distortions in question.
The issue is: Given the above circumstances, how may we proceed to live our lives? Well, I respond simply that one does the best one can, using available abilities and ideas (subject of course to all manner of contradictions and distortions). My claim is:
Given at least the basic effort on the part of those in the dialogue to be 'reasonably honest' about things being discussed, we can generally get 'somewhere'.
I agree also that "learning that can be used tends to be more robust", as you claim. I observe, however, that Lou Talman has rightly pointed out that we cannot really tell how 'useful' available knowledge is likely to be until it is 'used' (ideas to such effect).
I observe that such is indeed our existential situation, and we do need to go ahead accepting our circumstance whatever it may be and to seek to do the best we can with it. (Given, of course, that we try to be 'reasonably honest' about things. When one of the participants in a dialogue is 'systematically untruthful', the dialogue is likely to go nowhere fast, or just 'round and 'round the mulberry bush, so to speak - or even backwards!! In this context, you may recall some of the dialogues I've had here with Robert Hansen where this issue of honesty in dialogue has come into question).
GSC +++++ Joe N.'s dt. Jun 4, 2014 12:48 AM (http://mathforum.org/kb/message.jspa?messageID=9478284): > I'm not really advancing the proposition to only > teach knowledge that will be used. I was mainly > trying to point out that (1) stated or implicit goals > (according to whomever) for the educational "system" > largely contain their own distortions and > contradictions, and (2) learning that can be used > tends to be more robust. As simple as that is, it > does seem to be often ignored. > > On the main point of your original posting, I haven't > yet read Mark Saul's rebuttal to Liping Ma, but I do > tend to sympathize with her viewpoint. I'm not one to > disagree with teaching arithmetic to all children. > > Cheers, > Joe N