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Mid-August 2002


In this Issue:

Linda Dobson on Building a Life
Not Back to School
Harmonious Multiplication
Marilyn Burns on Music and Math
NHEN Launches Membership Drive!
Playing with Math
Messing Around with Math Books
Real World Geometry
John Holt on Measurement
True Confessions of Alison McKee
Unschool Friendly Conferences


"Your efforts may, at first, seem more like scrap lumber randomly scattered
across the vast universe that is your child rather than a remarkable
structure you watch rise, floor by measurable floor. But the Eiffel Tower
didn't appear overnight, and the most beautiful cathedrals of the world took
decades to complete.

It helps to think of yourself not as "teacher" the way you remember it, but
like the supplier whose purpose is merely making sure the builder - your
child - can get his hands on the necessary materials when he needs them. Be
happy when you make any sale, however modest. The true architect will use the
materials in his own way, in his own time.

Schools force a child into using his limited resources today. "Build a bird
house," they demand, "so that we may count how many sticks you've collected."

At home there's no need for immediate "proof". Be patient. Don't measure. Who
can say what exquisite masterpiece your child will shape and build from the
scraps tomorrow - or ten years from now? The more he collects, the greater
the structure he's capable of building. And when that structure is life
itself, don't settle for a bird house today. Trust you'll find a castle

Simply provide the materials."

from The Art of Education
Linda Dobson


Not Back to School

In late summer, when it sometimes seems that the entire universe is obsessed
with Back to School hoopla, new and even not-so-new unschoolers often find
themselves filled with doubts. Many parents feel confident in their ability
to help their children understand almost anything, except math. "But how will
they learn math?" is one of the most common questions posed to unschoolers on
email lists, message boards, and in face to face conversations with the
curious and the hopeful.

This issue is a musing about math - how kids learn skills and how they don't,
what helps, what hinders. Having fun with math. Learning to see and share the
math in everyday life.

I've included several longer book excerpts from favorite authors. I hope they
supply you with food for thought, and that you'll seek out the books to read
further after you've finished pondering this newsletter. I've also included
some recent conversations on math from the Unschooling-dotcom email list.
Want to read more? Come join the conversation at


Harmonious Multiplication

From a conversation on the Unschooling-dotcom email list:

"... the bit about multiplication was just a side note to the division being
repeated subtraction. Most kids undoubtedly don't see multiplication as a
quick way to do repeated addition either. Multiplication as far school
learning is concerned is just more magical mumbo jumbo like division. "

"My kids know how it really works, and how to do it in their heads, but I'm
pretty sure if they saw some typical 6th grade math textbook with pages of
"problems" in the regular school format they wouldn't know what it was or
what a person might be expected to do with it. If someone spoke the same math
question in English ("How many fifteens are in 300?") they could figure it

I liken that to being able to sing and harmonize and to make up songs but not
to understand a bit of musical notation." Sandra

"And - SHEESH - imagine teaching musical notation to a kid who hasn't ever
heard music?

Schools teach math to kids who have no equivalent of having "heard music".
They have no relevant context." --pamS

To subscribe to the Unschooling-dotcom email list send a blank email to:
[email protected]
Or visit the email list website at:


Marilyn Burns on Music and Math

I began taking piano lessons when I was seven or eight years old. I remember
learning to read notes and play scales and memorizing the sharps and flats
for each key. These things were basic to learning to play the piano, just as
we may think of arithmetic facts and procedures as being basic to learning

There's a big difference, however, between the way I was taught to play the
piano and the way I was taught mathematics. Before learning to play the
piano, I'd had many opportunities to hear music played on the piano. I'd seen
people play the piano - in person and in movies. I'd watched and listened to
my mother play the few songs she knew. In my very first piano lesson, I was
invited to learn to play a song. Making music was part of my learning, and
each new piece of music I tackled taught me new skills and gave me the chance
to practice what I had already learned.

Yes, I did practice scales, arpeggios, and other exercises in isolation from
playing music. But I was always clear that my goal for learning to play the
piano was to play music.

Three of my aunts came to visit regularly and showed interest in what I was
learning on the piano.

"I'd love to hear you play a song," Aunt Freda would say.

"What piece can you play for me?" Aunt Florrie would ask.

"Come, darling, play something on the piano," Aunt Gertie would coax.

And I would give a short performance, pleased by their interest and bathed in
their attention. I continued studying the piano all through high school,
which amounted to almost ten years of lessons. Never, never, in all of those
years, did Aunt Freda, Aunt Florrie, or Aunt Gertie ask me to play scales or
arpeggios. It was music they wanted and expected to hear.

So who cared about my ability to play scales, arpeggios, and other exercises?
My piano teacher did, and she had me do so for part of my one-hour lesson
each week. But the bulk of each lesson focused on the music I was learning to
play, and most of the teaching of skills - helping me with fingering, playing
difficult passages, interpreting the music - was done in the context of the
music I was studying.

What's the parallel with math? While I never lost sight that making music was
the reason for learning to play the piano, when learning math I never got
even a glimpse of anything beyond learning skills. All I experienced for the
first several years of school was a steady diet of pages of practice with
arithmetic skills, with a little bit of measurement and learning about shapes
thrown in.

I thought doing arithmetic exercises was doing math. It isn't. Doing math has
to do with thinking and reasoning about problems or situations that call for
applying mathematical ideas and skills. The skills are part of doing math, or
course, but for a purpose, not as ends in themselves. Skills should be
learned in the context of problems and situations and should not exist
isolated from the problems and situations that give them their purpose.

from Math: Facing an American Phobia
Marilyn Burns


NHEN Launches Membership Drive!

NHEN Mission Statement:
The National Home Education Network exists to encourage and facilitate the
vital grassroots work of state and local homeschooling groups and individuals
by providing information, fostering networking and promoting public relations
on a national level. Because we believe there is strength in a diverse
network of homeschoolers, we support the freedom of all individual families
to choose home education and to direct such education.

National Home Education Network
Changing the Way the World Sees Homeschooling

Since its founding in 1999, NHEN, an all-volunteer organization connecting
homeschoolers nationwide, has evolved into a respected source of information
for the homeschooling community as well as the general public. Our
award-winning website contains a wealth of firsthand information about
homeschooling, written from a variety of viewpoints. In keeping with our
mission statement, NHEN espouses no one particular political agenda or
homeschooling philosophy. Instead, we know that homeschooling parents can
read all of the material and determine for themselves what is best for their

In response to media requests, we help reporters find accurate, balanced
information about homeschooling and put them in touch with NHEN members who
have previously indicated a willingness to be interviewed. Information and
interviews provided by NHEN contacts have appeared in articles in Time, on
National Public Radio, and other national, state, and local media.

All homeschoolers are invited to participate in our network. NHEN membership
is free. By joining NHEN you will add your voice to those of thousands of
other homeschoolers who have approved our mission statement. The more
homeschoolers connect through our network, the better we will be able to help
each other in our joint efforts to improve the climate for homeschooling in
this country; numbers matter to legislators and the media.

By joining NHEN you also send a message of appreciation to the dedicated
volunteers who answer questions, provide extensive website information, work
on the newsletters and email list forums - free of charge for all.
NHEN operates only through volunteer contributions. Once you've joined, be
sure to read the NHENotes and find out how you could help! NHEN T-shirts,
fanny packs, and tote bags are also available for sale. And, as a 501C3
nonprofit organization, NHEN is happy to receive a donation of any size.

Join us and help change the way the world sees homeschooling!
National Home Education Network
P.O. Box 7844
Long Beach, California 90807


Playing with Math

From a conversation on the Unschooling-dotcom email list:

"My kids figured out multiplication by "skip counting" and goofing around
with pennies and stuff, and by me giving them a blank multiplication table
for them to fill in if they wanted to, as a puzzle. I didn't give them
terminology or time limits or reasons. It was fun for its own sake. And
they discovered the cool patterns of fives and nines and twos and threes all
on their own." Sandra

"My kids learned multiplication facts by playing games too, I guess.

A page of 100 numbers, ten rows of ten numbers in each row -- a "Hundreds
Chart" as they're usually called -- is nice to just have around <G>. Make
some copies so you have one to pull out and play with when something just
comes up.

One fun thing to do (if it isn't fun - don't do it) is to draw a simple
pattern in all the squares where the number is a multiple of two - draw an X
across the square, for example. Then - draw a different pattern, with a
different color, in all the squares where the number is a multiple of three.
Then a different one for multiples of four -- and so on. Make the patterns
simple and use different colors -- as you're doing it - it is interesting to
see how some numbers are "special" -- they start looking much more fancy than
others -- the number twelve, for example, gets the patterns for two, three,
four, AND six. It is really kind of a cool thing - and kid sometimes want to
do it over and over - with different colors and patterns. Again - this isn't
an "assignment - done to "teach" them the multiples -- it is a game.

Also - play "Buzz" --- we play in the car. If you're doing "threes" you play
like this:
First person says: 1
Second person says: 2
First person says: BUZZ
Second person says: 4
First person says: 5
Second person says: BUZZ
First person: 7
Second person: 8
First Person: BUZZ

If you have more people you'll find some interesting things -- for example,
if you have three people, doing "threes" is boring since the same person just
says BUZZ every time. That is enlightening - itself, but doesn't make for a
fun game, so the kids will figure out to avoid doing numbers that don't work
well for whatever number of people they have playing.

Then - you can make the game WAY more complicated. Do two sets of multiples
at once when you play: "BIZZ BUZZ".

Example -- 5 people playing twos are BIZZ and threes are BUZZ:
Person 1: 1
Person 2: BIZZ
Person 3: BUZZ
Person 4: BIZZ
Person 5: 5
Person 1: BIZZ BUZZ
Person 2: 7
Person 3: BIZZ
Person 4: BUZZ
Person 5: BIZZ

and so on." --pamS

"...wondering why phonics and times tables is relevant to the *unschooling*
list anyway, LOL." Rachel

"As an unschooler - I expect that my kids will learn to sound out words
(phonics) and will learn to multiply (multiplication tables). Unschooling
doesn't mean "unlearning" <G>. I don't "make them learn" and I don't plan
their learning in some systematic structured progressive bit-by-bit way. But
I do have a lot of ideas and fun and interesting possibilities always at my
fingertips -- that's how we live our lives. I treat multiplication tables as
a potentially interesting and useful thing to know or do in the same way I
treat riding a horse, clearing the dinner table, going to an opera, or
reading a book.

So - you'd have to know that, I guess, or you might think I was suggesting
sitting your kid down and telling them, "Now is multiplication time - please
fill out this chart in this way using these colored pencils." No -- we're not
doing that. In fact, I'm more likely to fool with it myself and then "let"
the kids do one too, if they ask. Or - I might say, "Here - I had this cool
idea about multiplying - wanna see it?" OR - a kid might moan and groan that
they don't know multiplication facts and it is slowing them down in some
other activity they're trying to pursue - so I might tell them that I have
some pretty fun ways in mind that can help them learn them.

It is always an offer and it is always something that they can take or leave
or expand or cut short or whatever.

I agree - a formal phonics or math program would not be appropriate to
suggest on an unschooling list. Thanks for pointing that out, Rachel, and
giving me the opportunity to clarify how I intended the multiplication stuff
to be considered - just as something fun that kids and parents might enjoy,
not as a "lesson," by any means.

You should have seen me sitting here drawing the spirolaterals the other day
-- I had a bunch of kids here and after 5 minutes they were all drawing and
coloring too. That's just for fun, not school." --pamS


Messing Around with Math Books

Here are a few titles that are personal favorites on our bookshelves.

How Math Works
Carol Vorderman
Part of the Readers Digest "Works" series. Filled with things to make and
projects to do, math as discovery, history and invention.

Math Wizardry for Kids
Margaret Kenda and Phyllis S. Williams
Puzzles, projects, games and creations. Dig in!

Factastic Book of Comparisons
Russell Ash
How big? How many? How much? A fascinating compilation of facts and
comparisons covering topics from animal speeds to the size of the universe.
Fun for browsing and pondering.

And one webpage of links to truly fascinating mathematical sites.
Go figure! The Fascinating World of Mathematics
HSC (HomeSchool Association of California) gateway to the web


Real World Geometry

"A friend of mine just made a big tent. Big. Like 18' tall in the center,
7' side poles, 22 feet long or so. Big.

He's a very meticulous guy.

I've made tents, but never that big. Still, all mine had sides out at
angles, and roofs at angles.

I figured mine out on paper, and double-checked the measurements before I cut
the cloth, and they worked out fine.

My friend said (and I let him run on without comment, because he has to leave
for three weeks of a big medieval deal tomorrow and he was stressed enough)
that had the walls been straight it would have only involved geometry, but
with angled side-walls it was trigonometry and so he asked our friend Tomas,
a research engineer involved in astronomy or some space something, to help
him with the math. So they worked it all out. And the measurements were
wrong. So he had to recut the cloth, but he finally got it worked out.

I "don't know trig," and that's for sure. It's something engineers do.
Sometimes not well, apparently! <g>

But cloth, I can do. And the angles and measurements are very mechanical.
There's an angle from the top of the wall, and it can only go so far. There
are triangles involved. They can be drawn on paper, and measured. And the
long side of the triangle is just a measurement. And the corners can be made
out of a rectangle with the diagonal of the longest length, cut and turned so
the points of the triangles are both up, and the short side is toward the

And if all else fails, and a calculation was wrong, it's easier to shorten
side-poles or get longer poles than it is to redo all those acres (okay,
dozens of yards) of canvas!!

I've built tents in English and with sketches. Not trigonometry."

Sandra Dodd, on the Unschooling-dotcom email list

To subscribe to the Unschooling-dotcom email list send a blank email to:
[email protected]
Or visit the email list website at:


John Holt on Measurement

What then should we do about making the world of numbers and math accessible,
interesting, and understandable to children?

A few good principles to keep in mind: (1) Children do not need to be
"taught" in order to learn; they will learn a great deal, and probably learn
best, without being taught. (2) Children are enormously interested in our
adult world and what we do there. (3) Children learn best when the things
they learn are embedded in a context of real life, are part of what George
Dennison, in The Lives of Children, called "the continuum of experience." (4)
Children learn best when their learning is connected with an immediate and
serious purpose.

What this means in the filed of numbers and math is simply this: the more we
can make it possible for children to see how we use numbers, and to use them
as we use them, the better.

What do we adults do with numbers? We measure things with them, a huge
variety of things in the real world around us. Why? So that we can think
better about them and make better use of them. We measure, among a host of
other reasons, to find out whether we are sick or well; to find out whether
we are doing something better than we did before; to find out which of
several ways of doing this is better; to find out how strong we have to make
things in order to make them stand up; to find out where we are, or where
we're going; to find our, if we do a certain thing, what other things are
likely to happen as a result. And so on. We don't measure things out of idle
curiosity. We measure them so that we can decide things about them and do
things with them.

Since all this is inherently interesting and important to us, it will also
interest children.

So we should introduce children to numbers by giving them or making available
to them as many measuring instruments as possible - rulers, measuring tapes
(in both feet and meters), scales, watches and stopwatches, thermometers,
metronomes, barometers, light meters, decibel meters, and so on. Whatever we
measure in our lives and work, we should try to measure so that children can
see us doing it, and we should try to make it possible for them to measure
the same things, and let them know how we are thinking about the things we
have measured.

Children are interested in themselves, their own bodies, their growth,
quickness, strength. In What Do I Do Monday? I suggested a whole range of
experiments that children might do to measure their own size, strength, and
speed, and how these things change over time and vary with different
conditions. Thus children might measure their own respiration and pulse rate,
then exercise violently for a while, then measure their breathing and pulse
rate again, then measure it at intervals to see how long it takes it to get
down to normal. Or children might do various tests of speed and strength,
running timed distances or lifting weights or doing other exercise, and what
happens when they try to do this a second time, and how their performance
varies with the amount of rest they have, and how their speed or strength,
and their recovery times, vary from week to week or from month to month.

Aside from involving numbers, all this is true science, not the passive
science of the schools where children are told about the wonderful things
that scientists have discovered, or the fake science of other schools where
children do "experiments" to find out what is already well known, or to get
answers which a teacher marks "right" or "wrong."

How Children Fail revised edition
John Holt


True Confessions of Alison McKee

.... when Christian was ten, he developed a keen interest in the nature
preserve that is at our back door. During the winter months, he would just
wander the acres. After one of these wanderings, he announced that he wanted
to do a "habitat study." Apparently, he had been scouting for a plot of land
to study for quite some time.

As on other occasions, Christian knew what he wanted to do and had devised
his own plan of study. Over the next few weeks, he made repeated trips to his
little plot of land in the park. Each time he returned from one of his
excursions, he had new and interesting things to tell us. One afternoon he
might tell me about a flock of geese that he;d seen heading north: a sure
sign of spring! A week later, he might report that the temperatures were
somewhat cooler; therefore some of the buds had ceased opening. His reports
were always interesting and involved great detail.

In my eagerness to help Christian "do a better habitat study," I began to
interfere. At my suggestion, he showed me his plot of land. It was simply a
stretch of land next to the path, and included a piece of field, some
low-lying shrubs, and a small section of woods. There was nothing
particularly remarkable about it; it just was.

I, of course, being a "teacher" began to cook up lots of ideas about how he
should do his study. I knew how such projects should be conducted! When I was
in high school, our biology teacher had assigned just such a project, and
later I had helped many of my own students put together sciences projects.
These experiences called for the application of "proper methodology" and I
was ready to see to it that Christian was well-versed in its use. Suggestions
poured forth. I didn't bother to ask Christian whether or not he wanted my

My first suggesting was that Christian measure his plot of land. Measuring, I
surmised, would lend itself to creating a scaled drawing. I knew from
experience that illustrations were and important part of any graded project
and felt that Christian needed to include one in his work. Never mind the
fact that he might come to the same conclusion on his own, or, conversely,
never feel that he should illustrate or share his work with anyone!

Christian acquiesced. Together with his sister, we took our meter stick (all
scientific measurements must be done in metric measure - another of my
"teacher" notions) and measured the plot. Without realizing it, I was already
limiting Christian's project. Not only was I setting boundaries to something
that he had seen as free of boundaries, I was also causing him to think in
terms of my limiting experiences of "school projects."

When we returned home, I asked Christian to draw a scaled map of his plot of
land. Christian saw no need for this but, like a good son, he tried. Soon his
interest was truly on the wane. Seeing this, I once more attempted to take
control in hopes of rekindling his dying interest in his habitat study.
Before I had jumped in, I had noticed that Christian had been taking
temperature readings using the thermometer outside our bedroom window. This
met his needs. He simply enjoyed noting the temperature and the date and time
of day that it was taken. Now I insisted he chart and graph his readings, and
of course, this put a damper on his interest in keeping track of temperature
at all. To counter this, I offered him a bribe - a nifty thermometer he could
clip onto his jacket. Christian seemed to understand what I didn't; that the
thermometer was not a gift, but rather an attempt to buy back his interest
and that if he accepted the thermometer, he'd be more firmly bound by my
notion of how he should conduct his project.

Although the thermometer temporarily rekindled Christian's interest in his
habitat project, by this time the damage had been done. My schooled voice had
overpowered Christian's intuitive idea of how to study his habitat, and as a
result he gave up on it. Finally, as I watched him put away his notes for the
last time, the light dawned; I remembered what John Holt had said in a Mother
Earth News interview: that rewarding a child for work that is self-rewarding
eventually kills the child's interest in doing the work at all. This was
exactly what I had done. I felt remorse when I realized that my best
intentions to help Christian had, in fact, not helped at all.

When I realized that we had effectively ruined Christian's habitat study, we
sat down for some serious discussion. If we were going to continue
unschooling, we needed to understand what had driven us to insist that
Christian change the design of his study. Our discussions eventually led us
to a truth that we were not readily acknowledging: in spite of our
convictions about the merits of unschooling, we simply didn't trust our
children and their intuitions about how best to learn.

Although we had watched our children initiate many interesting projects, any
time Christian or Georgina decided to do something that reminded us of our
school experiences, we'd feel the urge to help them "get it right." We'd
meddle just a little bit with such projects, so that neither Christian nor
Georgina would wander too far from our understanding of how things "ought" to
be studied.

"I ruin Christian's interest in his habitat study" from
Homeschooling Our Children: Unschooling Ourselves
Alison McKee


Unschool Friendly Conferences

Feeling like a fish out of water after attending a large curriculum oriented
homeschool convention? The following conferences have unschooling presenters
and participants, including many regular posters at the unschooling.com
website and email discussion list.

Diversity in Education
Keynote Speaker - Linda Dobson
September 14, 2002
Iroquois Ridge High School, Oakville, Ontario

Texas Family Learning Conference
Keynote Speakers - David Albert, Sandra Dodd
October 4 & 5, 2002
Sheraton Brookhollow in Houston, Texas

Live and Learn Unschool Conference
October 11 - 13, 2002
Columbia, SC

If you have information on other unschooling friendly conferences please
email the editor at [email protected]


Final Thought

"Computation (routine calculation) is to mathematics as spelling is to
literature. It has value in itself, but it is no substitute for the real

Patricia Kenschaft
Math Power: How to Help Your Child Love Math, Even if You Don't


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See you in September!

Deborah A Cunefare, Newsletter Editor
[email protected]

Unschooling.com is a service of Home Education Magazine
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