Herman Rubin wrote: > > In article <[EMAIL PROTECTED]>, R. Martin <[EMAIL PROTECTED]> wrote: > >Herman Rubin wrote: > > >> In article <[EMAIL PROTECTED]>, R. Martin <[EMAIL PROTECTED]> wrote: > >> >Richard Ulrich wrote: > > >> >> On Sun, 16 May 2004 13:25:07 GMT, Art Kendall <[EMAIL PROTECTED]> > >> >> wrote: > > .................. > > >> >> Further: I have to wonder, Are today's kids really smarter in ways > >> >> that matter? I suspect that they are. Now, how do you measure it? > > >> >Anecdotal evidence, which may or may not be applicable to the > >> >question, and comes from a non-random sample and has other known > >> >uncontrolled variables: I know that some of my younger relatives > >> >know more about some academic subjects than I did at their ages. > >> >I had what I feel was a decent education for the time (1960s and > >> >1970s), and in certain subjects I'm sure I had an outstanding > >> >education. > > >> The educational system has made SOME improvements since > >> Sputnik, but also some declines. > > >> My younger relatives have been often two (sometimes > >> >more) years ahead of where I was at their ages. Different school > >> >systems, yes, different times, definitely, and my relatives probably > >> >don't represent anything like a cross section of the population. > >> >At young ages I attributed it to "Sesame Street", etc. When they're > >> >doing things like full blown calculus in high school, I'm not sure > >> >what the sources of the differences are. > > >I have not followed this thread with perfect attention, so forgive > >me if I misunderstand any of the points you're making. > > >> Are you sure they are ahead? > > >I'm reasonably sure they are in many respects. > > >> They may be in memorization > >> of facts and methods of computation, but understanding in > >> the schools has not improved much. > > >Certainly a 20 month old being able to line up 20 toys and > >count them does not imply the child has Fermat's facility for > >number theory, as it certainly is largely memorization, but IIRC > >I was learning to count on my fingers when I was in kindergarden > > The process of counting (not memorizing the names, but > realizing that it is a process) is an important concept > of the integers; it is not the only one. This is not > what is stressed, and may not even be taught. It is > mistakenly assumed that someone who can do arithmetic > understands the concepts.
I agree, but at least part of the process is purely memorizing the names. It is quite amazing to me, on a certain level, that the mind can grasp the concept of a one-to-one correspondence of abstract numbers to objects, and then the idea (which appears to come later in childhood development) that this correspondence can go on ad infinitum. > > >(OK, so I'm not Gauss :-), although I did figure out division > >on my own a few years later), so I still think the achievement > >level of younger people says something worth noting. > > Did I ever say otherwise? But can one expect them to > learn the precise concepts by themselves? This is > VERY unlikely; however, someone can be taught concepts > fairly easily if there is not too much interference by > having "learned" how to "do it" without any idea of what > it means. From Aristotle's writings, he clearly had a > totally mistaken idea of lines and "real numbers". Well, he had quite a few mistaken ideas. Of course, most of us still do. I once heard a commencement speaker say, "I have good news and bad news. The good news is that half of everything you've been taught is wrong. The bad news is we can't tell you which half." :-) rest snipped Cheers, Russell -- There are lies, damned lies, and quotes from literary icons. The opinions expressed are mine personally and do not reflect any position of the U.S. Government or NOAA. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
