[email protected]

Let me rephrase what I wrote before about Rosie doing worksheets with her
friend - I got carried away and didn't say what I really meant in there at
all. First, Rosie WANTED to do the worksheets and play school and she was
totally HAPPY doing it. She was not disturbed in the LEAST by the fact that
she got all the math problems wrong and all the spelling words wrong except
one. She gets it that she's not learning the same stuff at the same time as
every other kid and that she knows more about some things and they know more
other things. Also - I misunderstood about the mom grading the problems, the
kids graded each other - the mom gave them the answers to do it with, I
guess. Anyway, that wasn't really relevant - it didn't bother Rosie to have
her papers graded, it was part of what they were playing - she was ENJOYING
it. No problem at all there.

My point was that if you're unschooling, you have to be aware that your kids
may get into these situations where they openly demonstrate that they clearly
don't know what other kids of their exact age are being taught and it could
be embarrassing or upsetting - to the kid or to the parents. COULD be!!!
Wasn't at all in our case.

The point I was trying to make was unschoolers come to a problem late, but
with a maturity of thought that school schedule doesn't allow. When I said
Rosie can think more clearly than the other girl - I was thinking about the
opportunity she has to think more clearly about the stuff before she learns
to "do" it. I didn't mean she just thinks more clearly, in general, about
anything and everything. Here is an example of what I was thinking about
(none too clearly, myself, given how very badly I expressed it):

When my older daughter was about 6 or 7, she had a friend (Mary) who had an
older brother who was learning his "multiplication facts" in school. He
apparently practiced, out loud, so much that Mary memorized them too. Much
was made over this by their teacher - a 1st grader knowing all her
multiplication facts - very exciting.

A few years later, I was running a little "math club" for some 4th graders
and Mary was part of it. One day I heard one of the other girls explaining to
Mary that multiplication was really just a shortcut for doing repeated
addition. This was clearly a new concept to Mary -- she'd learned to DO
multiplication so young that she hadn't been able to really think clearly
about it at that time and, since then, she'd just done it without giving it
any thought and had, apparently, never realized that multiplication was
really not a whole "new" operation, but just another way to do addition.

Contrast that to how an unschooled child I know learned multiplication. She
added and added, she would add 8+8+8+8+8+8+8 for example, two numbers at a
time. One day she announced, "Every time I want to add up seven eights, it is
always going to be 56 so I can just say that seven eights is fifty-six and
not have to do all that adding. Mom answered: "Yep. And if you want, you can
just do the same thing for lots of numbers, like four fives or three nines or
whatever you want." "WOW" says the child - that is very cool. Mom: "I can
show you how to make a table so you can do it for all the numbers from 1 to
10 or from 1 to 12 or whatever you want." So they did that and the child
memorized the multiplication facts because she was THRILLEd with the concept
of being able to do addition so quickly.

Now, this is a simple example, most people (but not all, by any means), come
to realize that multiplication is really repeated addition, pretty quickly.

However, take more difficult concepts and apply the same approach. How many
adults can quickly and easily explain why dividing one fraction by another
gives an answer that is BIGGER, not smaller. Why is 1/2 divided by 1/4 equal
to 2? Most adults will say because you get it by inverting and multiplying so
1/2 divided by 1/4 becomes 1/2 times 4/1 which is 4/2 which is 2. BUT that is
just a technique to DO it, not an explanation of the underlying concept. What
are you really doing when you divide one fraction by another?

If you teach a child: "To divide one fraction by another you invert and
multiply," and make them practice doing it over and over, then that may very
likely be as clear as their thinking ever gets about that. But if you wait
until it comes up in some interesting relevant context where they really need
to or want to divide one fraction by another and take THAT opportunity to
investigate and understand it - then the child will be able to think about it
more clearly.

The time that some kids spend doing worksheets will be time that unschooled
kids spend doing other things. The other things are not likely to be things
that would show up in testing, for example, for kids that age. As I said, 5th
graders are not getting tested on world geography, for example. This is a
choice people make - if they choose to do "school" curriculum stuff - either
a little or a lot - then I support to the maximum their "right" to do it and,
heck, I'll even admit that could be the best choice for their family and
maybe I'm making a terrible mistake not doing it too. I'm not omniscient and
can't predict the future. However, IF someone is going to unschool - then
their kids get to learn things on their own timetable and I really believe
that one of the huge benefits is that, when they DO learn things, they do it
because of their own choice/interest and that is conducive to more clear
thinking, more focus, more in-depth understanding, of what they are learning.

I hope that makes more sense. Rosie's friend is a great kid and she and her
family are great friends of ours and I certainly didn't mean to say that she
isn't just wonderfully bright and intelligent. Her family is more of an
eclectic homeschooling family, not radical unschoolers like us, and they
spend plenty of time following their children's interests and supporting
those interests. I'm just really glad that they're homeschooling and have
found a way to do it that works well for them.

My point was that radical unschoolers ought to be aware that they are
"trading off" having their kids know stuff at certain ages at least partly
because we think that they'll be able to "get it" better, if we let them wait
until they are ready and wanting to learn it (whatever it is). Of course,
some of it they'll never get to - that's another reality.

I worry about parents who want to radically unschool and, at the SAME time,
satisfy spouses or friends or relatives that their kids really are learning
just fine. It might not really seem "just fine" to them if the child doesn't
learn long division until she's 13 instead of when it is taught in schools at
about 9 years old. So - you sort of need to be clear in your own heads about
whether or not that kind of delay is okay with you and whether you feel
confident about the benefits of letting things "wait" like that. I sort of
see that as the purpose of this list, really, to help each other understand
the benefits of it, especially for people who get the "disadvantages" flung
at them by concerned spouses and others. They need to know that there are
real reasons why some of us think that it is better to not teach something
just because it is "time" according to schools.

--pamS


[Non-text portions of this message have been removed]

joanna514

I usually don't get myself through long posts, but that was a great
one pam!
I had to figure out how to multiply fractions for some costumes I was
making for my kids play, and I couldn't remember what to do. We were
at a rehearsal, so I called this 13 yo kid over and asked him if he
knew how to do it, and though he said he worked on that in school, he
couldn't remember either.
So I sat there and really though about it. I used my brain and
mentally put together the fractions into wholes and saw how many
wholes I had and figured out how much material I needed. THEN I
figured out/remembered the formula. It was strangely empowering.
Joanna


--- In AlwaysLearning@y..., PSoroosh@a... wrote:
>
>
> Let me rephrase what I wrote before about Rosie doing worksheets
with her
> friend - I got carried away and didn't say what I really meant in
there at
> all. First, Rosie WANTED to do the worksheets and play school and
she was
> totally HAPPY doing it. She was not disturbed in the LEAST by the
fact that
> she got all the math problems wrong and all the spelling words
wrong except
> one. She gets it that she's not learning the same stuff at the same
time as
> every other kid and that she knows more about some things and they
know more
> other things. Also - I misunderstood about the mom grading the
problems, the
> kids graded each other - the mom gave them the answers to do it
with, I
> guess. Anyway, that wasn't really relevant - it didn't bother Rosie
to have
> her papers graded, it was part of what they were playing - she was
ENJOYING
> it. No problem at all there.
>
> My point was that if you're unschooling, you have to be aware that
your kids
> may get into these situations where they openly demonstrate that
they clearly
> don't know what other kids of their exact age are being taught and
it could
> be embarrassing or upsetting - to the kid or to the parents. COULD
be!!!
> Wasn't at all in our case.
>
> The point I was trying to make was unschoolers come to a problem
late, but
> with a maturity of thought that school schedule doesn't allow. When
I said
> Rosie can think more clearly than the other girl - I was thinking
about the
> opportunity she has to think more clearly about the stuff before
she learns
> to "do" it. I didn't mean she just thinks more clearly, in general,
about
> anything and everything. Here is an example of what I was thinking
about
> (none too clearly, myself, given how very badly I expressed it):
>
> When my older daughter was about 6 or 7, she had a friend (Mary)
who had an
> older brother who was learning his "multiplication facts" in
school. He
> apparently practiced, out loud, so much that Mary memorized them
too. Much
> was made over this by their teacher - a 1st grader knowing all her
> multiplication facts - very exciting.
>
> A few years later, I was running a little "math club" for some 4th
graders
> and Mary was part of it. One day I heard one of the other girls
explaining to
> Mary that multiplication was really just a shortcut for doing
repeated
> addition. This was clearly a new concept to Mary -- she'd learned
to DO
> multiplication so young that she hadn't been able to really think
clearly
> about it at that time and, since then, she'd just done it without
giving it
> any thought and had, apparently, never realized that multiplication
was
> really not a whole "new" operation, but just another way to do
addition.
>
> Contrast that to how an unschooled child I know learned
multiplication. She
> added and added, she would add 8+8+8+8+8+8+8 for example, two
numbers at a
> time. One day she announced, "Every time I want to add up seven
eights, it is
> always going to be 56 so I can just say that seven eights is fifty-
six and
> not have to do all that adding. Mom answered: "Yep. And if you
want, you can
> just do the same thing for lots of numbers, like four fives or
three nines or
> whatever you want." "WOW" says the child - that is very cool.
Mom: "I can
> show you how to make a table so you can do it for all the numbers
from 1 to
> 10 or from 1 to 12 or whatever you want." So they did that and the
child
> memorized the multiplication facts because she was THRILLEd with
the concept
> of being able to do addition so quickly.
>
> Now, this is a simple example, most people (but not all, by any
means), come
> to realize that multiplication is really repeated addition, pretty
quickly.
>
> However, take more difficult concepts and apply the same approach.
How many
> adults can quickly and easily explain why dividing one fraction by
another
> gives an answer that is BIGGER, not smaller. Why is 1/2 divided by
1/4 equal
> to 2? Most adults will say because you get it by inverting and
multiplying so
> 1/2 divided by 1/4 becomes 1/2 times 4/1 which is 4/2 which is 2.
BUT that is
> just a technique to DO it, not an explanation of the underlying
concept. What
> are you really doing when you divide one fraction by another?
>
> If you teach a child: "To divide one fraction by another you invert
and
> multiply," and make them practice doing it over and over, then that
may very
> likely be as clear as their thinking ever gets about that. But if
you wait
> until it comes up in some interesting relevant context where they
really need
> to or want to divide one fraction by another and take THAT
opportunity to
> investigate and understand it - then the child will be able to
think about it
> more clearly.
>
> The time that some kids spend doing worksheets will be time that
unschooled
> kids spend doing other things. The other things are not likely to
be things
> that would show up in testing, for example, for kids that age. As I
said, 5th
> graders are not getting tested on world geography, for example.
This is a
> choice people make - if they choose to do "school" curriculum
stuff - either
> a little or a lot - then I support to the maximum their "right" to
do it and,
> heck, I'll even admit that could be the best choice for their
family and
> maybe I'm making a terrible mistake not doing it too. I'm not
omniscient and
> can't predict the future. However, IF someone is going to unschool -
then
> their kids get to learn things on their own timetable and I really
believe
> that one of the huge benefits is that, when they DO learn things,
they do it
> because of their own choice/interest and that is conducive to more
clear
> thinking, more focus, more in-depth understanding, of what they are
learning.
>
> I hope that makes more sense. Rosie's friend is a great kid and she
and her
> family are great friends of ours and I certainly didn't mean to say
that she
> isn't just wonderfully bright and intelligent. Her family is more
of an
> eclectic homeschooling family, not radical unschoolers like us, and
they
> spend plenty of time following their children's interests and
supporting
> those interests. I'm just really glad that they're homeschooling
and have
> found a way to do it that works well for them.
>
> My point was that radical unschoolers ought to be aware that they
are
> "trading off" having their kids know stuff at certain ages at least
partly
> because we think that they'll be able to "get it" better, if we let
them wait
> until they are ready and wanting to learn it (whatever it is). Of
course,
> some of it they'll never get to - that's another reality.
>
> I worry about parents who want to radically unschool and, at the
SAME time,
> satisfy spouses or friends or relatives that their kids really are
learning
> just fine. It might not really seem "just fine" to them if the
child doesn't
> learn long division until she's 13 instead of when it is taught in
schools at
> about 9 years old. So - you sort of need to be clear in your own
heads about
> whether or not that kind of delay is okay with you and whether you
feel
> confident about the benefits of letting things "wait" like that. I
sort of
> see that as the purpose of this list, really, to help each other
understand
> the benefits of it, especially for people who get
the "disadvantages" flung
> at them by concerned spouses and others. They need to know that
there are
> real reasons why some of us think that it is better to not teach
something
> just because it is "time" according to schools.
>
> --pamS
>
>
> [Non-text portions of this message have been removed]

[email protected]

In a message dated 3/20/02 10:22:01 PM, PSoroosh@... writes:

<< My point was that radical unschoolers ought to be aware that they are
"trading off" having their kids know stuff at certain ages at least partly
because we think that they'll be able to "get it" better, if we let them wait
until they are ready and wanting to learn it (whatever it is). >>

If people really care about keeping their kids "caught up" with school, the
best thing is to send them to school. (Most people forget or never
understood, though, that at least half the kids in school are not caught up
with school, but still....)

I know for a fact that some in-person friends of mine think I'm lazy which is
why my kids learn to read late. They don't see at all the MANY things my
kids know about that their kids have never even heard of or considered. And
I hear from my kids sometimes, their surprise that other kids their age or
older don't know ANYTHING about ___ (Thailand / chain mail / polar bears /
chess / whatever it might have been that came up in conversation or play and
the other kids said "What?" about).

Holly does not read fluently. But in the past few days we have had
conversations about the history of England *because* she asked about
spellings. Why two words that sounded the same looked so different. And
she's totally onto the fact that words from Greek will use "ch" to sound like
"k" and "ph" to do "f." So if she wants to spell something I can say "It's
Greek," and she says, "So 'ch,' like 'Christ'?" or something.

How many first graders learning to spell by writing each word ten times in
preparation for a spelling test on Friday are going to wonder about such
things, or care? How many teachers of first graders are going to explain
past "just memorize it"?

One of the things was Holly asking me to spell "please," and it being too
long for her to remember two rooms away. So I wrote it down. She said six
letters for one syllable was too much. I told her "thought" was worse.

We talked about ski and skate later in the car, being from Norse. That came
from discussing onomatopoeia. (I had to look up the spelling, and won't even
THINK of confusing Holly with THAT much Greek.)

Onomatopoeia came from a discussion with Marty the day before about "Whoosh"
sounding like "whoosh" and "pop..." and I said "There's a word for words that
sound like the thing they name." So we discussed that "quack" and "bow wow"
and "meow" which we think of as copying that animal's sound aren't the same
in all languages.

That's a lot of language discussion for 24 hours for someone who can't even
read.

SO I could easily say that in and around spelling and language, Holly
understands much more than the kids her age who learned to read "by the
book," and on schedule. When they're fifteen those kids might also have
picked up a lot of linguistic history and terminology and there will be no
difference. But at the moment, Holly is coming at the whole reading and
spelling thing with an analytical viewpoint most beginners don't have at all.

I like it. Her learning is not like the model teachers believe is necessary.

Sandra

Nancy Wooton

on 3/20/02 9:49 PM, SandraDodd@... at SandraDodd@... wrote:

> One of the things was Holly asking me to spell "please," and it being too
> long for her to remember two rooms away. So I wrote it down. She said six
> letters for one syllable was too much. I told her "thought" was worse.

One of my favorite "hang man" words is "strength." Eight letters and only
one vowel <ggg>

Nancy


--
The appropriately beautiful or ugly sound of any word is an illusion wrought
on us by what the word connotes.
--Max Beerbohm, writer, critic, and caricaturist (1872-1956)

Kate Green

I was on the treadmill a few weeks ago and my mind was wandering so I
started trying to figure out how many more segments I had to go based on
how fast I was going. I got mentally into some fractional stuff and kind of
had those "aha" thoughts where I really felt that I finally had worked out
what adding and playing around with fractions was all about. It was weird
as it was this mental picture of the patterns.
Anyway that's at 38 with 5 graduate level stats classes behind me. It's all
about figuring it out when YOU want to and not when someone else says you
must.

Kate

At 05:49 AM 3/21/02 +0000, you wrote:
>
> I usually don't get myself through long posts, but that was a great
> one pam!
> I had to figure out how to multiply fractions for some costumes I was
> making for my kids play, and I couldn't remember what to do. We were
> at a rehearsal, so I called this 13 yo kid over and asked him if he
> knew how to do it, and though he said he worked on that in school, he
> couldn't remember either.
> I used my brain and
> wholes and saw how many
> wholes I had and figured out how much material I needed. THEN I
> It was strangely empowering.
> Joanna
>
>
> --- In AlwaysLearning@y..., PSoroosh@a... wrote:
>>
>>
>> Let me rephrase what I wrote before about Rosie doing worksheets
> with her
>> friend - I got carried away and didn't say what I really meant in
> there at
>> all. First, Rosie WANTED to do the worksheets and play school and
> she was
>> totally HAPPY doing it. She was not disturbed in the LEAST by the
> fact that
>> she got all the math problems wrong and all the spelling words
> wrong except
>> one. She gets it that she's not learning the same stuff at the same
> time as
>> every other kid and that she knows more about some things and they
> know more
>> other things. Also - I misunderstood about the mom grading the
> problems, the
>> kids graded each other - the mom gave them the answers to do it
> with, I
>> guess. Anyway, that wasn't really relevant - it didn't bother Rosie
> to have
>> her papers graded, it was part of what they were playing - she was
> ENJOYING
>> it. No problem at all there.
>>
>> My point was that if you're unschooling, you have to be aware that
> your kids
>> may get into these situations where they openly demonstrate that
> they clearly
>> don't know what other kids of their exact age are being taught and
> it could
>> be embarrassing or upsetting - to the kid or to the parents. COULD
> be!!!
>> Wasn't at all in our case.
>>
>> The point I was trying to make was unschoolers come to a problem
> late, but
>> with a maturity of thought that school schedule doesn't allow. When
> I said
>> Rosie can think more clearly than the other girl - I was thinking
> about the
>> opportunity she has to think more clearly about the stuff before
> she learns
>>"" it. I didn't mean she just thinks more clearly, in general,
> about
>> anything and everything. Here is an example of what I was thinking
> about
>> (none too clearly, myself, given how very badly I expressed it):
>>
>> When my older daughter was about 6 or 7, she had a friend (Mary)
> who had an
>>"" in
> school. He
>> apparently practiced, out loud, so much that Mary memorized them
> too. Much
>> was made over this by their teacher - a 1st grader knowing all her
>> multiplication facts - very exciting.
>>
>>"" for some 4th
> graders
>> and Mary was part of it. One day I heard one of the other girls
> explaining to
>> Mary that multiplication was really just a shortcut for doing
> repeated
>> addition. This was clearly a new concept to Mary -- she'd learned
> to DO
>> multiplication so young that she hadn't been able to really think
> clearly
>> about it at that time and, since then, she'd just done it without
> giving it
>> any thought and had, apparently, never realized that multiplication
> was
>>"" operation, but just another way to do
> addition.
>>
>> Contrast that to how an unschooled child I know learned
> multiplication. She
>> added and added, she would add 8+8+8+8+8+8+8 for example, two
> numbers at a
>>"Every time I want to add up seven
> eights, it is
>> always going to be 56 so I can just say that seven eights is fifty-
> six and
>>"Yep. And if you
> want, you can
>> just do the same thing for lots of numbers, like four fives or
> three nines or
>>""" says the child - that is very cool.
>"I can
>> show you how to make a table so you can do it for all the numbers
> from 1 to
>>" So they did that and the
> child
>> memorized the multiplication facts because she was THRILLEd with
> the concept
>> of being able to do addition so quickly.
>>
>> Now, this is a simple example, most people (but not all, by any
> means), come
>> to realize that multiplication is really repeated addition, pretty
> quickly.
>>
>> However, take more difficult concepts and apply the same approach.
> How many
>> adults can quickly and easily explain why dividing one fraction by
> another
>> gives an answer that is BIGGER, not smaller. Why is 1/2 divided by
> 1/4 equal
>> to 2? Most adults will say because you get it by inverting and
> multiplying so
>> 1/2 divided by 1/4 becomes 1/2 times 4/1 which is 4/2 which is 2.
> BUT that is
>> just a technique to DO it, not an explanation of the underlying
> concept. What
>> are you really doing when you divide one fraction by another?
>>
>>"To divide one fraction by another you invert
> and
>>" and make them practice doing it over and over, then that
> may very
>> likely be as clear as their thinking ever gets about that. But if
> you wait
>> until it comes up in some interesting relevant context where they
> really need
>> to or want to divide one fraction by another and take THAT
> opportunity to
>> investigate and understand it - then the child will be able to
> think about it
>> more clearly.
>>
>> The time that some kids spend doing worksheets will be time that
> unschooled
>> kids spend doing other things. The other things are not likely to
> be things
>> that would show up in testing, for example, for kids that age. As I
> said, 5th
>> graders are not getting tested on world geography, for example.
> This is a
>>"" curriculum
> stuff - either
>>"" to
> do it and,
>> heck, I'll even admit that could be the best choice for their
> family and
>> maybe I'm making a terrible mistake not doing it too. I'm not
> omniscient and
>> can't predict the future. However, IF someone is going to unschool -
> then
>> their kids get to learn things on their own timetable and I really
> believe
>> that one of the huge benefits is that, when they DO learn things,
> they do it
>> because of their own choice/interest and that is conducive to more
> clear
>> thinking, more focus, more in-depth understanding, of what they are
> learning.
>>
>> I hope that makes more sense. Rosie's friend is a great kid and she
> and her
>> family are great friends of ours and I certainly didn't mean to say
> that she
>> isn't just wonderfully bright and intelligent. Her family is more
> of an
>> eclectic homeschooling family, not radical unschoolers like us, and
> they
>> spend plenty of time following their children's interests and
> supporting
>> I'm just really glad that they're homeschooling
> and have
>> found a way to do it that works well for them.
>>
>> My point was that radical unschoolers ought to be aware that they
> are
>>"" having their kids know stuff at certain ages at least
> partly
>>"" better, if we let
> them wait
>> until they are ready and wanting to learn it (whatever it is). Of
> course,
>> some of it they'll never get to - that's another reality.
>>
>> I worry about parents who want to radically unschool and, at the
> SAME time,
>> satisfy spouses or friends or relatives that their kids really are
> learning
>>"" to them if the
> child doesn't
>> learn long division until she's 13 instead of when it is taught in
> schools at
>> about 9 years old. So - you sort of need to be clear in your own
> heads about
>> whether or not that kind of delay is okay with you and whether you
> feel
>>"" like that. I
> sort of
>> see that as the purpose of this list, really, to help each other
> understand
>> the benefits of it, especially for people who get
>"" flung
>> at them by concerned spouses and others. They need to know that
> there are
>> real reasons why some of us think that it is better to not teach
> something
>>"" according to schools.
>>
>> --pamS
>>
>>
>> [Non-text portions of this message have been removed]
>
>
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zenmomma *

>>It might not really seem "just fine" to them if the child doesn't
learn long division until she's 13 instead of when it is taught in schools
at about 9 years old. >>

When would a child learn long division naturally in real life? Personally, I
have always just used a calculator the few times it has come up in my life.
Maybe I'm not seeing all the times I've really been using it without
realizing. I *am* confident that Conor could learn long division if he
wanted/needed to. I'm just not able to picture a scenario where it would
come up naturally.

What am I missing?

~Mary

_________________________________________________________________
Chat with friends online, try MSN Messenger: http://messenger.msn.com

[email protected]

On Thu, 21 Mar 2002 05:46:20 -0700 "zenmomma *" <zenmomma@...>
writes:
> When would a child learn long division naturally in real life?
Personally, I
> have always just used a calculator the few times it has come up in
> my life.

Perhaps people who can find calculators quickly don't need to learn long
division <g>. I never can...

I used long division to figure our gas mileage on the drive out here. It
wasn't crucial to know the exact answer, so I guess I could have
estimated, but it was something to do while driving, so I didn't. It was
important to at least have a ballpark, so I wouldn't end up out of gas
somewhere where the prices were really high, or somewhere with no gas
stations at all.

Dar

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In a message dated 3/21/2002 9:56:48 AM Pacific Standard Time,
freeform@... writes:


> > When would a child learn long division naturally in real life?
> Personally, I
> > have always just used a calculator the few times it has come up in
> > my life.

I guess I'm not sure what "naturally" means to you. I don't think that
they're likely to just pick it up unless someone takes the time to explain it
to them and help them do it a little - so it won't be naturally in that
sense. It isn't any different than learning to ride a bike, though. They see
a reason to do it (that seems natural, to me, but if it doesn't to you, then
it could be this step is the stumbling block), they see other people doing
it, they decide they want to try it, they might try it on their own based on
what they've seen other people doing and that might work or it might not,
they may ask for help, they may flounder a bit and someone may step in and
offer help, or someone might just step in early in this whole process and
say, "Do you want me to help you learn that?"

They can learn multiplication when they find they need to add the same number
over and over... 8+8+8+8+8 etc. I mean - they can just use a calculator for
that, too -- nothing wrong with that. But even punching in 8+8+8+8+8+8 etc
into a calculator is a pain - you can forget how many eights you already
punched in or you can accidentally hit the wrong key and have to start all
the way over, etc. Teaching multiplication BEFORE a kid has experienced any
sort of frustration with repeated addition is sort of silly since the kid
won't appreciate why multiplication is useful and it'll just seem like
another operation to learn just for its own sake.

So - they can learn division, too, the same way. When they find they are
doing repeated subtraction. When Roxana wanted to go to New York City to see
Cats on Broadway, she asked me how far it was and how far we could drive in a
day - she wanted to figure out how many days it would take to drive there and
back. So she started with 3,000 and started subtracting 350 miles, over and
over, to see how many times she'd have to subtract it to cover all 3,000
miles. She made a mistake somewhere and realized she needed to start ALL over
and she groaned aloud. I was walking by and I said, "I can show you a
shortcut way to do that." She wanted to learn, so I should her some simple
division like 6 divided by 3 and then 60 divided by 3 and then 69 divided by
3 and then 69 divided by 23 and so on until she could do 3,000 divided by
350. It took about 20 minutes or so. She was THRILLED and even asked for more
problems to practice on. THEN I told her, "This is long division" and she
said, "I can't believe it - why do people say that they hate it, this is so
convenient." <G>

I don't know how you can MAKE such a situation happen in your home - how you
can make it come up naturally like that. It has to do with the parent being
aware of the kids' interests and focus and stuff like that. In some ways,
this is really hard work - it doesn't seem like it to those of us who just
sort of do it naturally, but I know that to my mom and my sisters it looks
like hard work for me to always be thinking things like, "Oh, I wonder if
that would be something Roxana (or Rosie or Roya) would be interested in -
and remembering to introduce her to it."

I think our society is in a strange sort of place - we have so much
opportunity - such enriched environments - that we can just pass on formal
schooling and live in our stimulating and wonderful environments with
attentive and doting parents who focus on supporting their own kids' learning
and our kids can do ANYTHING with it. In the past or in other places, kids
did the same thing - learned by hangin' out with the important adults in
their lives - but the expectations were that they would end up DOING mostly
what the adults in their lives did. Our expectations are so different - we
expect our kids to find their own way, not follow in our footsteps, and we
expect and they expect that they'll find stimulating, fulfilling, work that
makes them truly happy, not just develop skills so that they can be
productive members of society and support themselves and maybe their own
family. It is pretty amazing to live in a time and place where we have the
luxury to do this. And I can see why it is scary and seems way too risky to
lots of people.

--pam


[Non-text portions of this message have been removed]

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In a message dated 3/20/2002 9:50:15 PM Pacific Standard Time,
Wilkinson6@... writes:


> I usually don't get myself through long posts, but that was a great
> one pam!
> I had to figure out how to multiply fractions for some costumes I was
> making for my kids play, and I couldn't remember what to do. We were
> at a rehearsal, so I called this 13 yo kid over and asked him if he
> knew how to do it, and though he said he worked on that in school, he
> couldn't remember either.
> So I sat there and really though about it. I used my brain and
> mentally put together the fractions into wholes and saw how many
> wholes I had and figured out how much material I needed. THEN I
> figured out/remembered the formula. It was strangely empowering.

Wow. Cool. Can I use this example when I give talks about learning math?

--pam


[Non-text portions of this message have been removed]

joanna514

> > So I sat there and really though about it. I used my brain and
> > mentally put together the fractions into wholes and saw how many
> > wholes I had and figured out how much material I needed. THEN I
> > figured out/remembered the formula. It was strangely empowering.
>
> Wow. Cool. Can I use this example when I give talks about learning
math?
>
> --pam

Yup.
Joanna