Robert Hansen (RH) posted Aug 25, 2014 7:SC08 PM (http://mathforum.org/kb/message.jspa?messageID=9574795) - GSC's remarks interspesed: > > On Aug 25, 2014, at 3:00 AM, GS Chandy > <firstname.lastname@example.org> wrote: > > > (GSC):It is possible that Elizabeth R. Slavitt of Khan > >Academy might have 'mis-spoken' a wee bit. What she > >probably meant was something like the following: > > ++++++ > > Exposing students to abstract concepts such as > >congruence, symmetry and the like through hands-on > >geometric transformations, such as rotating or > reflecting a given shape (and so on) "MAY CONTRIBUTE > TO" their *effective* understanding of said abstract > concepts. > > ++++++ > > (RH): No. We checked. The pictures are everywhere, in > place > of abstract reasoning and actual understanding. Even > on the exams. They are not using pictures as math > teachers have for eons, as part of the journey. They > are, as they have been for 40 years, trying to create > a semblance of the journey, and they will always fail > with a semblance of the journey. > Well, I'll accept that as your opinion.
As to whether your opinion is valid, I'd like to have some further confirmation from reliable sources, preferably from the horse's mouth as to what the horse might have wanted to mean. > > Teaching is about teaching things, not understanding > things. > Here I accept your tautology, but strongly disagree that you have actually understood anything worthwhile about the process (or, for that matter, its "IMPLICATIONS"). Yes, I know that you have claimed that you (and other 'experts') know everything there is to know about "IMPLICATIONS", but you demonstrate in every post of yours that you do not.
At its core, teaching has to be about helping the student to learn. Your entire argument here demonstrates that you do need to learn something, namely, the answer to the question:
"What is teaching?".
In an earlier message, I've suggested that a teacher ALWAYS requires a learner. A teacher who attempts to teach without a learner is behaving like the person pouring water into a container that isn't there: somewhat foolishly.
It can be demonstrated that 'teaching' is part of the 'learning + teaching dyad' - and it constitutes, necessarily, the secondary position in the dyad. 'Teaching', if attempted in itself and by itself is a somewhat narcissistic activity. You might with benefit recall the legend of Narcissus. > > Learning is about understanding things. Most > of the (pedagogical) issues today with the abysmal > performance in our schools is because they stopped > teaching things. There is nothing for the student to > understand. > See above.