[TheForge] Re: Another Long rambley YAK

[Mike Spencer]

(Quoting Andy at length because I'll wreck it if I edit it...)

>    The manner in which mathematical concepts are related to a pupil
>    often makes the difference between success and failure.  The
>    highly dry and technical expressions pursuant to the "purely
>    scientific" icon is usually fit for only the most mathematically
>    inclined students, and even not for them in some cases.  Relating
>    a math concept to something in the real world to which the pupil
>    can map to is one of the greatest and most effective means of
>    cementing that concept correctly in their minds.  There is no
>    single "right" way to teach such things.

No truer words have been spoken about teaching math.  I've said words
to that effect to many people [1] and almost nobody gets it.  Math is
math is what the teacher said.  Feh.

A lot of mathematicians believe, "If You Can Visualize It, It Isn't
Math."  At least one recent proof in topology (which I don't even
halfway understand) was done with computer graphics, proving this
abstract thing could exist by drawing a picture of it.  Those IYCVIIIM
guys were really PO'd.

>    the best place to see them.  Nikola Tesla is arguably the
>    greatest technical genius thus far in human history.

In the era when everybody including Edison knew for a fact that AC
motors were obviously impossible, Tesla *visualized* the AC motor in a
reverie during a walk in the park, went home and built one that worked
on the first try.

I had a math prof once who would respond to, "I don't understand that"
by repeating exactly what she'd said before, but pressing harder on
the chalk as she wrote on the board.  If the student persisted in not
getting it, she would end up *GRINDING* the chalk into dots under each
bit of the blackboard equations.  She was incapable of seeing how the
student might be seeing it and reframing her explanation.

A couple of years later I dropped out of school and got a job as the
janitor in that building.  Every night I had to scrape the puckers of
chalk of the blackboard under things that her students hadn't
understood.  She was still doing it.

- Mike

[1] http://www.nslug.ns.ca/pipermail/nslug/2003-October/002590.html

-- 
Michael Spencer                  Nova Scotia, Canada       .~. 
                                                           /V\ 
mspencer@tallships.ca                                     /( )\
http://home.tallships.ca/mspencer/                        ^^-^^

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