Date: Oct 8, 1992 12:26 PM
Author: Dale Parson
Subject: Orienteering for Mathematics

I originally wrote this article for a Pennsylvania homeschoolers'
newsletter.

ORIENTEERING
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I posted the following summary of using *orienteering* for providing
a base for kids' learning mathematics back in late March. My apologies to
those who have already read it, but I know we have a lot of new
subscribers. When I found myself running through the woods last Sunday
intersecting a mental line segment that represented a dotted brown line
on a map that in turn represented a ditch, with another mental line
segment
that represented the compass-directed path I was making through the woods
(no trail), I confirmed that I have been gaining some physio-mathematical
skills in learning this sport. The intersection occured right where I
wanted it to.

A few things have changed since this post. The kids are now 6 & 3 years
old. I am running the green course (1st advanced level). They have
finished
the "Little Troll" program. The program consists of their doing a string
course or beginner course with much adult guidance (the 3 year old can
walk
more than half of a white course on his own feet now, thank goodness), and
getting a Troll sticker on a card for it. After collecting 5 stickers on
a card
you mail it off to the US Orienteering Federation (address below) & get
back a
Little Troll patch to sew on a jacket. The patches are nice, and the kids
have
now moved on to the Chipmunk program. The courses are the same, but you
start
to get some guidelines on what to cover. Map color and symbol meanings
seem to take better with our 6 year old than more geometric elements of
map reading such as direction planning. That will follow.

I've also started looking at applying fractal geometry to the twistiness
of woods features & paths through them. It'll be awhile until the kids
are doing fractals, but I sure get to have fun with it. That's one of
the things I like about doing homeschooling: I get to do reconnaissance
into neat stuff to show the kids.

Dale Parson, dale@mhcnet.att.com

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Orienteering is a sport consisting of going into the woods with a map &
compass, finding checkpoints ('controls'), and punching a 'control card'
to prove you were there. There are orienteering meets with speed
competition
if you're into that, although many practitioners compete mostly with
their own previous times. Course levels vary in difficulty, from 'string'
(our 2 year old can do this by himself, following strings carrying a
hard-drawn map, very short course) thru 'white' (beginners, all on trails,
1-1.5 miles), 'yellow' (partly off-trails, 1.5-2.5 miles, still beginner,
our
5 year old can walk one of these without pooping out) thru 'orange'
(intermediate, 2-3 miles, where I'm at, not due to distance, but because
finding the controls gets tougher) thru advanced levels (green, red, blue,
up to 5.5 miles, controls can be VERY well hidden).

It's a thinking-person's walk, & fun for those desk-sitters like myself
who can beat hard-core jocks by virtue of superior map&compass skills
(the REAL practitioners are ALL good at map&compass, so competition for
them degenerates to mostly physical prowess). Where's the educational
hook? I first started thinking about orienteering-as-math when running
across Seymour Papert's use of having kids walk & turn as an intro.
to Logo (somebody else can post about Logo if there's a question, but
basically is body-oriented geometry/computer programming that has
locally-referenced linear (go forward N steps) and rotational (turn
right Y degrees) building blocks, not global Cartesian-coordinate-
disembodied geometry (no universal frame of reference outside the body).
Logo was meant to map to kids' perceptions of their bodies-in-the-world,
& is often intro'd by having them walk out Logo programs before
approaching
the computer.

Orienteering extends Papert's simple walks. There IS a universal
reference--north is north--but setting up the map-to-where-I-am
correspondence & using that to decide next move is VERY body
oriented. It's not just an APPLICATION of math, its INHERENTLY
mathematical. One of the most fundamental mathematical concepts is
MAPPING, relating entities in one domain somehow to entities
in another. Orienteering does this right up front. Most beginners,
including 5 year olds, like to get the map, the compass, and their
eyes all agreeing on north at one time before proceeding. There
are short-cuts for speed--use the protractor built into the orienteering
compass to get off-north degrees from the map without looking at the
world, then set the compass physical sight using this reading without
aligning the map--but like most math short-cuts, beginners should
best avoid them until they are comfortable with the basic processes.

Beyond mapping, there is SCALING/RATIOS, English-to-Metric, PLANNING,
domain-specific symbol recognition, physical fitness & endurance,
geography, patience building in 5 & 37 year olds, after-walk picnics,
ecology & botany (it's in the woods or desert), & history (our last meet
was at Daniel Boone Homestead). With a 5 year old I keep the formal math
pretty light, but when augmented with protractor+ruler play to draw
shapes at home on off-days, it's a good dose of body geometry. When
we get to the Pythagorean theorem or linear projections some day,
these kids should have lots of concrete experiences from which to
build.

For those interested, get a Silva or similar style compass (under $20),
maps are usually $3-$5 per meet per map, inexpensive hobby, in eastern
PA-NJ-Delaware it's:

Delaware Valley Orienteering Association
212 Westover Drive
Cherry Hill, NJ 08034

elsewhere in US:

Ask your local parks/recreation people (in Phoenix the parks dept.
sets these up) sports equip/camping stores, or colleges. The
U.S. Orienteering Federation is at:

USOF
PO Box 1444
Forest Park, GA 30051