From: Mark Korsky
Subject: barefoot math course
Date: Thu, 19 Jun 2003 18:08:35 -0400

I teach mathematics at a small private high school in Taos. Street shoes
aren't permitted in the buildings, so in warm weather many students and
most of the staff go barefoot.

Over the last year, I've been writing the text for algebra 2 and advanced
math, called "Mark's Barefoot Math Course." It's a completely original
approach to teaching high school math.  My two classes this year really
enjoyed it, and enjoyed being "guinea pigs" in this experiment at math
education.

With Peter Rupprecht's permission, I've posted photos of my students and
the "Please remove your shoes" sign on the library door in the Files
section of the SBL Yahoo! Groups site, see Barefoot Math Course
folder. These pictures will appear in the acknowledgements of the version
I'll teach from next year: "With gratitude to my first guinea pigs."

You'll notice several students in shoes, and shoes lying around in the
Second Hour picture. The students often put shoes on between classes, to
walk on the rough gravel in the courtyard. I invited anyone who wished to
join me barefoot for the photo, so several students took their shoes off
to pose.

I've made barefooting a humorous integrating theme in the text. Here are
some examples.

On logical propositions:
"It's illegal to drive barefoot in New Mexico."  This is  a logical
proposition, because either driving barefoot is legal, or it's illegal.
The statement is _false_, because there's no law against driving barefoot
in New Mexico.

On the logical conjunctions "and" and "or":
"Moonbeam is barefoot and it is Thursday."  "Moonbeam is barefoot or it is
Thursday."  Under what conditions are these statements true? False? Negate
these statements.

Logical equivalence:
"x is barefoot if and only if x is not wearing shoes or socks."

Logical fallacies:
(ad hominem) Mark is a barefoot anarchist. Therefore, what Mark says is
false. (false dilemma) If I let you in my store barefoot, then I'll have
to let people in naked. (undistributed middle) All hippies go barefoot.
Johnny Appleseed went barefoot. Therefore, Johnny Appleseed was a hippie.

Combinatorics problem:
Moonbeam has 3 matching pairs of toerings: 2 silver, 2 gold, and 2
enameled. If she only wears the rings on her middle 3 toes, and only wears
one ring on each toe, in how many different ways can she put them all on
her feet?

Proportion problem:
There are 11,275,001 citizens in the tropical anarchist commonwealth of
Harmonia. 48% of them love to go barefoot. Of these, 23% go barefoot all
the time.  How many of the citizens of Harmonia go barefoot all the time?

Pressure example:
_Pressure_ is defined as a force per unit area. For example, weight is a
force. If Moonbeam stands barefoot, the pressure her feet exert on the
ground is approximately her weight divided by the surface area of her
footprints. If she's wearing spike heels, her weight is the same, but the
pressure is much greater, because a much smaller area is in contact with
the ground.

Suppose that Moonbeam weighs 120 pounds. If her feet are 7 inches long
and 3 inches wide, then the area of her bare footprints might be roughly
10 square inches. This would result in an average pressure of 12 pounds
per square inch.

Now suppose that the area of one spike heel is 1/4 square inch. Then
when she walks in spike heels and puts all her weight on one heel, the
pressure P is given by P  = (120 pounds)/(1/4 square inch) = 480 pounds
per square inch.

This is the pressure of the spike heel on the ground. The shoe exerts
a smaller but still large pressure on the heel of her foot at the same
time. (Why is the pressure on her foot smaller?)

Mark Korsky
Taos, New Mexico