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Re: Khan Academy: Math instruction goes viral
Posted:
Jan 11, 2012 5:14 PM
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On Jan 11, 2012, at 3:06 PM, Dan Partelly wrote:
>>> To be even mentioned by someone I absolutely do not know >>is
>>> totally afirst to me. I am grateful to Partelly and I >>really
>>> mean it, hopefully not out of vanity.
>
> I appreciate it. If you Google "Lagrange calculus" one of your
> papers appear on the second page of results, so it's not
> extraordinary your work can be found by someone who holds a
> interest in the subject.
Google is truly amazing. But, may I ask, what was the source of your
interest?
> Besides your work and the videos I mentioned, I found through
> Google and I appreciated very much the exposition of David
> Hestenes in Clifford Algebras for physics and William Bourke's "Div
> Grad Curl are dead".
Hestenes is one of my heroes. For two reasons.
One is his insistence that the contents themselves have a role to
play. Take for instance how to solve a quadratic equation. You can
either "complete the square" of change the origin "to the vertex".
Are the two equivalent? (IMO not at all.)
The other is the description he gives of his lack of success with the
NSF and of the referees' comments and votes he got. (Page 37 of
<http://geocalc.clas.asu.edu/pdf-preAdobe8/OerstedMedalLecture.pdf>
It described very exactly my own experience with the NSF's calculus
reform round about 1990.
> One thing which is worth mentioning is that work like yours is
> useful not only to students or persons interested in learning more
> math, but to parents / anyone else who is interested in helping
> their kids/wards/relatives in math. It's a great boon to have
> access to decades of experience in teaching distilled in a book or
> some videos, this way you stand a real chance of helping the young
> ones instead of confusing them even more, or know nothing but
> "drill till you drop" approach (not that drilling is not necessary,
> it has it's place IMO). There are maybe not many parents interested
> to do this for their kids, but yeah, I know some.
That would explain at least some of the downloads. For instance, at
one point, I was getting downloads from a US military address which
left me quite puzzled. So, yes, I can see that now but I never
thought of it.
> As for the disjoint format of Khan like videos, I think it would be
> much more useful if it would basically give up "lecturing" and
> focus on interesting and hard problems, kinda like in a recitation
> session, and make this thing crystal clear. i.e, use the video not
> to learn math, but to consolidate your knowledge by trying to work
> the problems exposed, and having access to solution if you fail.
A long time ago, I tried "programmed instruction" and as I was
dissatisfied with it, I then tried "branched programming
instruction". That, though, would have required an immense amount of
work so I quickly gave up. But I think that even computerized, it
wouldn't really work because slight linguistic variations would be
likely to prevent students from recognizing a choice as being THEIR
choice and they would get lost in the branching. And that would be
the end of that inasmuch as it would cause the fatal "disconnect".
> Bye the way, I've been meaning to ask you something. A couple of
> days ago I recommended someone to read your papers on calculus and
> he asked me something. Basically on page 3
> of "A LAGRANGIAN APPROACH TO THE DIFFERENTIAL CALCULUS" , right
> before the Variance theorem you write:
>
> "........ shows that x0 is a monotonic point with variance (½,½) or
> (oe,oe) or a turning point with variance (oe,½) or (½,oe) depending
> on the parity of n and on the sign of .... "
>
> Id like to ask you what is the exact meaning of the pairs of type
> (½,½), (oe,½) ?
The text should read "... shows that x0 is a monotonic point with
variance ( /, / ) or ( \ , \ ) or a turning point with variance ( / ,
\ ) or ( \ , / )". It is not standard language but because it is
transparent. I am using it extensively in the local analysis of
functions, e.g. page 44 of
<http://www.freemathtexts.org/Standalones/RAF/RAFpdf/
RAFv5-1chapter3.pdf>
I also use (u , u) and (n , n) and for inflection points, (u , n) and
(n , u) where the letters stand here for something like half circles
with horizontal diameters. See the above on page 47 and following.
When that kind of things occurs (also in the Concavity Theorem a few
page later) it is because whatever read the file did not have the
same table of characters as whatever wrote the file. (Happens in
email too.) I should correct the files but ...
Best regards
--schremmer
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