Re: Scientific method was physical pendulums/ an opportunity

[Hugh Haskell <haskell@ODIE.NCSSM.EDU>]

Jack Uretsky wrote:

>        Yeh!  Even more blatant, I think, is that gravity problems
> are independent
> of mass.  But getting the students to do algebra, and watch the mass
> cancel out
> (or leaving only mass ratios) is an impossibility.  It makes me
> wonder about the
> big push, currently, to introduce algebra in the lower grades.  Yes,
> you can teach
> them to mouth the words (or write down symbols), but doesn't it take
> maturity to
> understand the meaning (or use the symbols to solve problems)?
>                                        Regards,
                                                Jack

I agree with your last question here, and that is why I disagree with
your implied conclusion. Understanding, especially the deep
understanding required to appreciate such things as why the mass
drops out of earthbound gravity problems, takes time. It isn't
necessarily maturity that is required (although that helps--perhaps a
necessary but not sufficient condition), but time itself. Most of us
need time along with maturity to appreciate these aspects of nature
that have been brought up here. We have all had that experience of
pure joy when we discover some apparently simple thing that we didn't
realize before (the feeling so aptly characterized elsewhere on this
list as the "Aha orgasm"). That's the maturity part. But we wouldn't
have had that experience if it hadn't been that we had been working
with these ideas for some time--in my case 40 years or so. So it is
important to start the process as soon as the students are
intellectually capable of using (but not necessarily understanding)
the processes that we want them to understand at some later time.

I contend that almost nobody understands a new idea the first time
around. It takes several exposures and often years for the mind to
process the idea to full understanding. Sometimes finding
understanding is so difficult that nobody gets it for years, even
decades. Didn't Bohr once say words to the effect that nobody
understands quantum mechanics? The earlier the students get started
on that process the better it is for those of us who labor farther
along the chain (provided, of course, that the seeds of
misunderstanding aren't planted at that early stage by a teacher
whose level of understanding has not progressed very far).

Of course, it isn't easy to determine which concepts any given
student is capable of absorbing at any given time, nor is it easy to
make certain that the teachers who are responsible for introducing
these concepts are adequately prepared to do so. But those are whole
other threads.

Hugh


Hugh Haskell
<mailto://hhaskell@mindspring.com>

Let's face it. People use a Mac because they want to, Windows because they
have to..
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