Joan

> <<but are there any writers who are able to let me in on their sense of wonder,
> on their
> AHA's and on what grips them in mathematics?>>
>
> Do they have to be "real writers," or can they be people here?

I think that the people here ARE real writers and I'm really enjoying reading all
of the real writing, too.

> Would you feel better having a bought book in your math section than just
> actually
> trying the ideas here?

I was thinking of it as more of a complementary thing. I try the ideas here; I'd
also like to snuggle up with a good book. I can read and reread a book and come
back to it over time. I can sleep on a single idea, or find out more about it, or
take a month (or years) away and go back to it and see how my ideas have changed,
or how I understand more or differently. I can ask somebody else to read it and
we can talk about it.

Threads on email lists move on and spread out, and I can't seem to catch up with
or savour ideas. I feel rushed into sorting, sifting and responding off the top
of my head. Perhaps this will change as I adapt to this method of communicating.




********** ***********
I'm trying to think through "Keith's notes". There's a lot in there to take in:

"Math is a highly structured abstract modeling tool and requires a strong
sense of discipline, but ..."

I'm trying to figure out what an "abstract modeling tool" is. I'd been thinking
that the purpose of mathematical modeling is to make the abstract a little more
concrete. I can't yet make sense of this. It'll take some time and maybe further
input from others.

With a book I can take the time, or ask others privately, or look for other
resources, if I still don't get it. I'm so slow with it that I'll feel like a
dope if figure it out and bring it up on the list a couple of months from now.

"A true math student must possess a strong passion for discovery in a realm
which has little direct connection to the world of our five senses."

But right now, I think, or I believe, that I can only discover the world through
my five senses.
What or where is this realm which is mostly indirectly connected to the world I
know?

"Think of your everyday actions, then look at how
they can be represented with math. Scaling of cooking ingredients (ratios),
boiling water (physics or chemistry), bouncing a ball (physics), watching
the moon circle the earth (geometry), (as in why does a ball fall to earth
but the moon does not?). Find art with a protractor, compass, straight
edge, (like the Greeks) or just play with graph paper (geometry & trig).
Look for symetry in nature or man made artifacts (ratios again). Look for
applications of fractions (ratios, division, combinatorics). Talk about the
lottery or statistics in elections or sports."

So is math the tool to create models of these real world things so that you can
generalize from a real situation to an abstract or imagined situation?


************* *********************




> So will having more books with words about math help a family in which
> patterns don't jump out and dance?

I don't know. Maybe books with illustrations of dancing patterns (and words about
why it's math) would help .

For some families, patterns jump out and dance. Some members of our family seem
to need to dance the patterns themselves, but the patterns are still jumping out.

*************** ******************


> The original charge here that some libraries have no books on math is really
> interesting. Math doesn't come in words very well. I have a couple of
> "books on music" which have no written-out music, and have no CD or record or
> tape, and have few pictures, just words. They're WEIRD, even those I know
> lots about.

I'm getting that words don't communicate math very well and as we can't experience
music through words, we also can't experience math through words.

Someone who can't read musical notation, though, is still able to listen to the
music, recognize it as music and be moved by it. They won't "get it" with the
same depth a musician would, but they'll catch something.

The notation for math is--numbers, graphs and lines? Or only for some math?
Can someone who can't read math notation still experience the beauty of it and be
moved by it?


Anyway, I'll take up the suggestions I've found here and lurk some more.

Joan


P.S. I used the phrase "supply teaching" in my last post. It's just another name
for substitute or occasional teaching.

[email protected]

In a message dated 12/2/2001 9:36:00 AM Pacific Standard Time,
les.carlson2@... writes:


> So is math the tool to create models of these real world things so that you
> can
>

You're thinking that math is one thing - that it can be described as having
"a" purpose. There are lots of pre-planned or hoped-for or unexpected
real-world applications of things thought up by people who really were just
"playing around" with ideas in a purely abstract realm. Does that help at
all?

--pam


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

[email protected]

> Can someone who can't read math notation still experience the beauty of it
> and be
> moved by it?
>

Yes. That's what I was trying to say but I didn't say it as succinctly.

Someone can feel the patterns dancing, and think in that "music" and BE
mathematically minded and still not read mathematical notation.

And I'm positive that the notation will make more sense to someone who knows
what math-music sounds like AFTER they're familiar with it than if you just
try to start (as school does) with the notation itself, as though the
notation IS math; as though musical notes on paper WERE music. They are not.
They're a graph of music, an abstract modeling tool (to borrow Keith's
phrase).

Sandra



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

Diane

> With a book I can take the time, or ask others privately, or look for other
> resources, if I still don't get it. I'm so slow with it that I'll feel like a
> dope if figure it out and bring it up on the list a couple of months from now.

Please don't feel like a dope, and please DO bring it up. You're not the only one with
math fears, anxiety, and questions. I always enjoy math discussions on unschooling
lists.

> "A true math student must possess a strong passion for discovery in a realm
> which has little direct connection to the world of our five senses."
>
> But right now, I think, or I believe, that I can only discover the world through
> my five senses.
> What or where is this realm which is mostly indirectly connected to the world I
> know?

This realm is in the recipe that makes a 9x13" pan and you have a 9x9" pan; it
connects the two. It's in the difference between fixed expenses and variable expenses
in running a household or business.

> So is math the tool to create models of these real world things so that you can
> generalize from a real situation to an abstract or imagined situation?

Right. Or vice versa. You're imagining the 9x13" pan and you really have the 9x9" pan.
You're imagining the budget and you have the money that needs budgeting. (as you can
probably tell, I tend to be a very concrete thinker, but also like math)

:-) Diane

[email protected]

In a message dated 12/2/01 12:35:53 PM US Eastern Standard Time,
les.carlson2@... writes:


> Threads on email lists move on and spread out, and I can't seem to catch up
> with
> or savour ideas. I feel rushed into sorting, sifting and responding off
> the top
> of my head. Perhaps this will change as I adapt to this method of
> communicating.
>

I'm so glad to read this. I just started email lists a few months ago and
feel the same way. I know my own learning style is slow. Not as in I'm not
very bright, but as in I take awhile to chew on an idea, accept it or reject
it, incorporate, dissect, etc. I too feel rushed when I keep up to date on
these lists. I've given up. Now I just read a lot, and process it off list.

Something that boosted my ego was learning the AyurVedic explanation of body
types. I'm a Kapha which is slow moving, in body and thought. Usually pretty
calm and slow to learn, also slow to forget. Good at maintaining foundations.
There are also Pitta and Vata and each has their own pace at life/learning.
These descriptions have given me a lot of insight into my own self. And it
helps that now I don't feel bad going at my own pace. I don't mind telling
someone, "Please say that again, a little slower". Books are also good for me
because I can stop and process, and pick it up again when I'm ready.


Brenda, who jumped over here and bailed from the 'other' list and is enjoying
it thoroughly!


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

[email protected]

In a message dated 12/2/2001 4:13:44 PM Pacific Standard Time,
spdrweb28@... writes:


> I'm so glad to read this. I just started email lists a few months ago and
> feel the same way. I know my own learning style is slow. Not as in I'm not
> very bright, but as in I take awhile to chew on an idea, accept it or
> reject
> it, incorporate, dissect, etc. I too feel rushed when I keep up to date on
> these lists. I've given up. Now I just read a lot, and process it off list.
>

I think that those who take longer to chew on things should feel free to
refer back to old threads. Just say, "I've been thinking about this for a
while and .....". I think that even those of us who post up a storm, fast
and furious, have the ideas floating around in our heads after that and
coming back later to the same discussion can let us re-examine our thinking
and see if something new has developed in there (in our brains) during the
"break."

--pam


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

[email protected]

In a message dated 12/3/01 10:25:35 AM, PSoroosh@... writes:

<< I think that those who take longer to chew on things should feel free to
refer back to old threads. Just say, "I've been thinking about this for a
while and .....". I think that even those of us who post up a storm, fast
and furious, have the ideas floating around in our heads after that and
coming back later to the same discussion can let us re-examine our thinking
and see if something new has developed in there (in our brains) during the
"break." >>

Absolutely.

I've been hanging out a lot with a friend from jr. high and on. We were out
of contact for years, but now we talk once a month or so for hours. We go
back to conversations a month or a year or a decade old, and it's wonderful.


Last night three other families came over for a reunion of our old
babysitting co-op from when our now-teen kids were toddlers and six and so.
It was great to revisit some ideas we had in those ideas and look at them
again. And two of the teen girls who DID go to school, both are jrs. now (16
or so, second-to-last year, for commonwealth-school readers) needed to go
home early to work on homework, and were both stressed about school and
saying they hated it. One mom reminded her kid that she had always had a
choice, and she had given her the reminder before school started.

Most of the kids who were here homeschool. There were eleven kids here. It
was great. Oh--and Kira from Minneapolis, who wasn't in the homeschooling
group, but is a 21 yr old homeschooler of my long acquaintance who stopped
here on her train-trek around the country.

Taking years to mull over ideas and progress and patterns is a great thing.
Any old topic is as good as any new topic.

Sandra