On 8/5/2011 6:13 AM, Ondřej Bílka wrote:
On Fri, Aug 05, 2011 at 03:43:04AM -0700, BGB wrote:
On 8/4/2011 6:19 PM, Alan Kay wrote:
Here's the link to the paper
[1]http://www.vpri.org/pdf/rn2005001_learning.pdf
inference:
it is not that basic math and physics are fundamentally so difficult to
understand...
but that many classes portray them as such a confusing and incoherent mess
of notation and gobbledygook that no one can really make sense of it...
old stale/dead rant follows:
it is like, one year, with the help of a physics book,
google+wikipedia+mathworld, and good old trial and error, I proceed to
write a (basically functional, but not particularly "good") rigid body
physics engine.
several years later, I took a physics class, with a teacher that comes off
like Q (calling everyone stupid, comparing the students with dogs, ...)
and writes out esoteric mathematical gobbledygook beyond my abilities to
make much sense of (filled with set-notation and other unrecognized
symbols and notations, some in common with first-order logic, like the
inverted A and backwards E, ..., and others unknown...).
...
granted, I have also seen in introductory programming classes just how
poorly many of the students seem to grasp some of the basics of
programming (struggling with things like variable declarations, loops,
understanding why never-called functions fail to do anything, ...), so I
guess ultimately it is kind of similar (in an almost sad way, programming
really doesn't seem like it should be all that difficult from the POV of
someone with a fair amount of experience with it).
but, at the same time, there would also be nothing good to be gained by
belittling or being condescending towards newbies...
Well I faced oposite problem that for classes people unnecesarily
complicate things by trying to make it accessible for newbies.
One of my experiences that high school physics could be three times
easier and simpler if students learned differential equations.
this was Physics 101 in college, which was supposed to be teaching
Newtonian Mechanics...
however, the topic would likely have been much simpler if presented with
algebraic notations and forward calculation, rather than a teacher going
off into gobbledygook lands and wanting everyone to write proofs...
say, one could be like, on a test:
"write out a calculation to express the velocity (V) of object X under
acceleration A at time T."
as opposed to, say, "write a proof that an object X at time T under
acceleration A will have velocity V."
as for differentials... dunno, personally I find it easier just to
imagine it as a large number of timesteps. linear systems and discrete
time-steps seem to work fairly good for computer-based simulators.
then, one can go claim that the time-step is arbitrarily small.
vectors are nice though.
for example, in the book I had, some aspects of the topic were expressed
in terms of a mess of trigonometry which wouldn't really work correctly
in 3D.
some of these topics were fairly simple/elegant-looking if expressed
with vectors.
so, linear systems and vectors, probably could do fairly well I think.
more so, linear systems and vectors would give students a model that
they could more easily use with or test on a computer.
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