"Off Your Duff" Math (exercises)

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"Off Your Duff" Math (exercises)

Kirby Urner-5
Marketing STEM subjects, and consequent careers, brings us
up against stereotypes.  Those electing to stay with
mathematics sometimes presuppose that others drifted away
because math was "too hard".  

That's sometimes true, however many complain of just the
opposite, that math is "too soft" when it comes to
maintaining physical fitness, and at a young age, that
may be a high priority.  Even oldsters have been known to
deliberately climb stairs when an escalator is available.

If opting for technical skills means grooming oneself for
life in a cubicle, at a workstation, in a lab coat, this
may induce qualms, lose potential recruits.  And yet so
many careers that require mathematical skills do come
with physical challenges.  

Sailing or rowing a small watercraft from point A to
point B on the open ocean is one obvious example, an
extreme sport in this day and age.  The math involves not
only navigation, but knowing one's calorie needs,
stocking sufficient provisions.

On the other hand, rowing across the Atlantic and Pacific,
ala Roz Savage, does involve a lot of "duff time" (is
both sedentary *and* a work out), and not everyone is cut
out for such marathon exercise.  So the challenge, among
curriculum designers, is to come up with exercises that
do involve leaving one's chair, even leaving the
classroom, but are not so "out there" in terms of physical
demands that most students will not complete them.

http://mybizmo.blogspot.com/2009/10/roz-savage.html

My blog post of today, one of many on this topic, focuses
on the specific challenges of the urban landscape.  As
soon as one invokes images of GPS / GIS, using geography
as a theme, the scenery tends to magically transform into
someplace idyllic, perhaps in Alaska.  How did we get
here?  No one says.  In point of fact, if we want to loan
out school GPS devices to geo-caching teams, we should
think in terms of the city bus and train systems.  Walking
is not out of the question (on the contrary), nor bicycle
riding (though relatively unsafe in many USA cities with
no bike lanes / routes / bridges etc. -- on the other
hand, some don't have sidewalks either).

"""
Introducing bus and subway maps from around the world as
topologically correct, yet highly simplified (schematic)
is a standard data visualization segment. The next step,
of actually riding the bus and train systems, in search
of some treasure, is where this becomes a sport.
"""

http://controlroom.blogspot.com/2010/03/for-credit-curriculum-games.html

One might suppose this is all far afield and of little
relevance to Podunk High in the middle of Middle America.
That may be true.  This could be tried in London or
Vilnius or someplace first.  However, in looking over
the priorities of many funders, there's a common theme,
along with worry about the exodus from technological
subjects, and that's the rise in childhood obesity, with
all the accompanying complications.  Addressing both of
these problems with common programming is a somewhat
attractive prospect, especially since it matches what
the students themselves are saying they'd like.

The Hollywood stereotypes associated with "mathematician"
sometimes just get in the way.  Would someone learning
welding ever be likely to succeed in the math world?  
Why not?  Perhaps she's constructing a rhombic tria-
contahedron for the State Fair, also knows how to
sheer sheep, tune a piano, program a drum machine.  Is
this a future engineer then?  The point of this mental
exercise is to challenge stereotypes and not settle too
easily for the screenwriter conventions they sell us soap
with on TV.  Don't believe everything you see on a purely
fictional show like NUMB3RS.

Learning mathematical concepts while doing manual, energy
spending activities is an idea I'm transplanting from
Lincoln, Nebraska, where Dr. Bob Fuller has already
pioneered what I've called First Person Physics.  This is
more than just riding roller coasters to experience
vector force diagrams.  It's more like pre-med, taking
the physics of one's own body into account.  Even if we
don't actually get to scuba (and maybe we do), we learn
about Boyle's Law in that context, maybe Avogadro's as
well.  We're getting briefings similar to what Navy
divers get, while learning the math at the same time.

http://physics.unl.edu/~rpeg/First_Person_Physics/index.html

Mathematicians reading all this may balk at the seeming
absence of "proving" or "axioms and theorems" from the
above.  Busing and training around town with a GPS device,
doing chemistry problems along the way (BBQ at the final
destination, vegan options available (and more popular in
some venues)), may sound like a lot of fun, and maybe a
good recruiting device for other departments, but what
about "real math" (as in "purely Platonic")?

I'm not suggesting we neglect any of this heritage, am
merely contextualizing with these framing "language games
for credit".  One of your puzzles may be to prove
something, supply a missing step, identify the missing
theorem.  That you had to take the bus to get to the
puzzle place is just additional topology, added by
sponsors (funders) who think competence in getting
around your own city is a worthy curriculum objective.

Where is such programming being tried?  You'd want the
adult designers to give it a dry run, work out the kinks.
With First Person Physics, we didn't get all that far,
although the idea has continued to propagate.  Portland,
Oregon has several pilots one might consider prototypical.
However, I'd consider the whole genre of "off your duff"
math to be timely and competitive.  

The boys scouts and girl scouts have had some good ideas,
including a merit badge system, but we need to reinvent,
not just coast on 1900s templates.  Let's think about
relational database technology, Google Earth, XML...
boosting the academic content to some world class level.
Geography and astronomy should not be allowed to go
fallow, even if light pollution obliterates the stars.
Use Celestia and Stellarium (both free offerings).  Keep
telling the epic of humanity's gradually coming to
realize that it shares one big ball.  Looking at all these
bus and subway maps might actually come in useful in that
context.  And lets not forget about Unicode and those
hexadecimal numbers.

http://mathforum.org/kb/thread.jspa?forumID=206&threadID=2033943

If wishing to fund the schools directly, then I might
suggest tying in with the new Computational Thinking
course, which is still flexible enough in theory to
accommodate at least a few of these reforms.  If the
number of offerings along this "digital math track"
proliferates, while maintaining close ties with home
economics and health, then we might start seeing some
positive physical effects in our student body, sooner
rather than later.  Learning how to follow a recipe may
be mathematical, involves fractions, weights and measures.

http://mathforum.org/kb/thread.jspa?threadID=2047973&tstart=15

However, in these initial stages, what's important is to
add more computer technology to the math curriculum
without the implied message that computation is always a
sedentary activity.  On the contrary, as Wolfram and
others have clearly indicated, energy processes,
including violent ones such as earthquakes, may be
considered computational in nature.  Keith Devlin reminds
us that animal behavior is likewise mathematics made real.

Using one's body and using one's mind need not be
mutually exclusive activities -- that's a message we
wish to convey.

Kirby