Sandra Dodd

Amy wrote:

-=-I had one of these moments with my ds 8. I was busy doing
something and
he asked me "Mom shouldn't 30 be 20?" I stopped what I was doing
because in all my mommy years I've learned that in his thought process's
he's most likely correct [;;)] . I could have just said no 20 is 20 but
instead I looked at him and asked him in a completely curious way, "what
do you mean?" He said well 20 has 21 and so on and 30 has 31 and so on
but 10 doesn't. I thought about it for a few minutes, really trying to
figure out what he was meaning. And I said "do you mean like it should
be tenty one, tenty two and so on?" He looked at me with wide eyes and
said "YES!". I explained that I didn't know why they called it 11 and
12 and so on but that it meant the same thing! He seemed so pleased to
have clarity! And I was so pleased w/myself to have been able to take
the time to have understood him!! I felt privileged to have gotten to
be a part of one of those AH HA moments!!!-=-



Amy, I love these stories!

Does he still care?



Eleven and twelve are leftover evidence (along with dozens and
"gross") of base 12 days, and base 12 ties in nicely with 360
degrees in a circle and 12 months in a year.



After twelve, the numbers go

three and ten (thirteen)

four and ten (fourteen)...

At twenty (two tens: twa/twin/two) it seems to get "normal," but

thirteen

and

thirty both have to do with threes. Three and ten, and three tens...



so the English word for 81 means eight-tens-and-one.



Sandra

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

graberamy

> Does he still care?

I don't know, but I will see if he does!!! My right brain TOTALLY loves
these kind of explanations to trip my math trigger!!! THANK YOU!!

I never learned, until I took a math course for educators that the
numerals 0-9 where actually created in a sensible way. 0 had no angles,
1 had one angle, 2 had two angles and so on!!

Thanks for sharing that!!

amy g
--- In [email protected], Sandra Dodd <Sandra@...> wrote:
>
> Amy wrote:
>
> -=-I had one of these moments with my ds 8. I was busy doing
> something and
> he asked me "Mom shouldn't 30 be 20?" I stopped what I was doing
> because in all my mommy years I've learned that in his thought
process's
> he's most likely correct [;;)] . I could have just said no 20 is 20
but
> instead I looked at him and asked him in a completely curious way,
"what
> do you mean?" He said well 20 has 21 and so on and 30 has 31 and so on
> but 10 doesn't. I thought about it for a few minutes, really trying to
> figure out what he was meaning. And I said "do you mean like it should
> be tenty one, tenty two and so on?" He looked at me with wide eyes and
> said "YES!". I explained that I didn't know why they called it 11 and
> 12 and so on but that it meant the same thing! He seemed so pleased to
> have clarity! And I was so pleased w/myself to have been able to take
> the time to have understood him!! I felt privileged to have gotten to
> be a part of one of those AH HA moments!!!-=-
>
>
>
> Amy, I love these stories!
>

>
>
>
> Eleven and twelve are leftover evidence (along with dozens and
> "gross") of base 12 days, and base 12 ties in nicely with 360
> degrees in a circle and 12 months in a year.
>
>
>
> After twelve, the numbers go
>
> three and ten (thirteen)
>
> four and ten (fourteen)...
>
> At twenty (two tens: twa/twin/two) it seems to get "normal," but
>
> thirteen
>
> and
>
> thirty both have to do with threes. Three and ten, and three tens...
>
>
>
> so the English word for 81 means eight-tens-and-one.
>
>
>
> Sandra
>
> [Non-text portions of this message have been removed]
>

Barbara Chase

> I never learned, until I took a math course for educators that the
> numerals 0-9 where actually created in a sensible way. 0 had no
> angles,
> 1 had one angle, 2 had two angles and so on!!

How cool that it was done on purpose. When I was a kid I made a
connection between the number and the angles/points on the written
number in order to do quick addition. I had no idea it was
intentional. I can't wait to google more info....


Mahalo,
Barbara

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

graberamy

Here's a website that shows the angles in the numerals:

http://www.orthohelp.com/number.htm

amy g
iowa
--- In [email protected], Barbara Chase <bc@...> wrote:
>
> > I never learned, until I took a math course for educators that the
> > numerals 0-9 where actually created in a sensible way. 0 had no
> > angles,
> > 1 had one angle, 2 had two angles and so on!!
>
> How cool that it was done on purpose. When I was a kid I made a
> connection between the number and the angles/points on the written
> number in order to do quick addition. I had no idea it was
> intentional. I can't wait to google more info....
>
>
> Mahalo,
> Barbara
>
> [Non-text portions of this message have been removed]
>

Sandra Dodd

-=-When I was a kid I made a
connection between the number and the angles/points on the written
number in order to do quick addition. I had no idea it was
intentional. I can't wait to google more info....-=-

My cousin Nada was slightly older than I was (well... still is!) and
lived with us from the time she was nearly eight. She did addition
and subtraction by touching her pencil to different points on the
numbers, something she had figured out for her own purposes. Maybe
she had figured that out too! But I think she had an overlaying
pattern of some sort and started on the five point (of her imagined
pattern) and walked (like moves in a board game) to the new number.



Sandra

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

Sandra Dodd

-=-http://www.orthohelp.com/number.htm-=-

Maybe an ancient Phoenician manuscript explains that.

One of the first things I was interested in, historically, was the
history of writing. We had a dictionary that had older forms at the
top of every letter's beginning. I've done calligraphy for 30 years,
and tried before then to learn it on my own.

I've never seen a seven with a line at the bottom, ever.
I've never seen a nine that had more than one small curve at the
bottom. Usually it ends straight.

So maybe ancient phoenicians did more lines, but I can't imagine it
would've been efficient to write those numerals with three strokes
(as the 7 pictured there would've had) when using the numbers for any
practical purpose.

Maybe somewhere there were ideal forms that had those angles and the
written form was a representation of those. Like the dot patterns
that make up constellations of stars with their ideal overlays and
story connections.

And on fours, the fact that their line doesn't cross over the
vertical seems suspicious.

So I think what I'm asking is that nobody here "teach" children that
numerals have that many angles. Maybe say "might have once," but I
think that's as far as truth can go.

There are other cool number systems to look at. cuneiform/
Babylonian (oooh! wikipedia has a big number chart!)
http://en.wikipedia.org/wiki/Babylonian_numerals
and runes, though they vary place to place, are interesting.
Sometimes they needed to edges of a 90 degree surface, because they
were whittlings on split sticks, or carvings on the edge of worked
stones.

Look at the numbers here, which are akin to Roman on the small ones,
but really cool on big numbers:
http://www.omniglot.com/writing/hungarian_runes.htm

I've known runes as NW European things, and I don't know how far east
they went (or from where in the East they might've come).

Practicalities of formation will change depending on how the letters
are being formed. Sticks pressed on wet clay? Carvings with a
little knife? Chisel on a rock? (That's the explanation I've heard
most for Roman numerals: they needed to be made with a chisel.)
Stick on wax? Pen and ink on parchment? Ballpoint pen on notebook
paper? <g>

One thing about numbers, too, is that although we set them all on the
same line, same height, not long ago (within a couple of hundred
years) some went below the line (the real or imagined line), and some
were shorter.

As with lots of history, simplifying it can make it untrue. Let it
be complicated! Kids can grasp and appreciate complication. It
gives them more mysteries to look out for in their lives. If we act
as though everything cool has been discovered, maybe our kids won't
look around with the same curiosity and expectation as they will if
we tell them (truthfully) lots of history is right in front of us,
unnoticed!

Sandra

Joyce Fetteroll

On Apr 22, 2008, at 10:51 AM, Sandra Dodd wrote:

> So maybe ancient phoenicians did more lines, but I can't imagine it
> would've been efficient to write those numerals with three strokes
> (as the 7 pictured there would've had) when using the numbers for any
> practical purpose.

It looks like a cool theory but something looks off. Needing to
represent the number of dots that corresponds to a number feels
*really* old but the numbers in their present forms aren't.

This has a more authentic feel:

http://www.geocities.com/rmlyra/Numbers.html

(The first page is:
http://www.geocities.com/rmlyra/arabic.html)

The angle theory holds up for 1,2,3 and 4 and shows their ancient
forms. But then it breaks down and a circle represented a closed fist
for 5.

Joyce

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

Sandra Dodd

-=-I wrote to Dr Malka to ask for his references.

I note that all the other pages on this site "orthohelp" have been
deleted because the Dr. retired and was told that he could be sued
for leaving the info out there.
-=-

My husband, Keith, wrote that. He's big into math and history and
runes, so I showed him the discussion thusfar. Maybe he'll
correspond with the guy and get us some good references.

Sandra

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

Barbara Chase

> -=-When I was a kid I made a connection between the number and the
> angles/points on the written number in order to do quick addition. -=-
>
> She did addition and subtraction by touching her pencil to
> different points on the
> number.

My pattern worked in that way, I could easily touch the pencil to the
number. I had teachers that wouldn't let us use our fingers (the
first calculators) -- so I found this other trick. I never realized
that I hadn't told anyone about it until now.... well..... because it
felt like cheating. Bummer about that, because it was a cool trick.
I'm glad I get to share it now!!

In looking at the website w/ the angles I don't see the connection
with my own system. As Sandra pointed out, there are extra lines in
odd places. My system was more about end-points, corners, and I
counted curves. And, it is way faster than fingers but not nearly as
fast as using a calculator.

OMG, I loved looking at those Babylonian numerals. There is such a
beautiful symmetry and balance.... which is how numbers actually feel
to me. It's so curious that they chose to draw the bar across the
Y... it makes for a stable building block, which they then use for
larger digits. But then they have a shortcut for 9 (or maybe it's
just hard to see all the Y shapes... it looks like squares.)

> If we act as though everything cool has been discovered, maybe our
> kids won't
> look around with the same curiosity and expectation as they will if
> we tell them (truthfully) lots of history is right in front of us,
> unnoticed!
>

Yes. I was fascinated with math history when I was younger, and
loved to discover that my own musings had indeed been discovered
years ago. Somehow I felt more connected with my world when I would
find out.... It's fun to explore the ideas, to play around with
patterns and to find/invent new ways to express ourselves.

Just recently my dd has been learning how to ride a bike. While on
the bike she stuck her feet straight out in front and coasted for
awhile. She was so thrilled she called to me and said "Mom, look
what I just invented!" She is always inventing. I'm glad you are
reminding us/me that it's helpful to connect with our kids about how
cool it is that *they* are discovering the world -- even if someone
else discovered it before them. I was thrilled for her enthusiasm,
and let it be her trick.

Mahalo,
Barbara

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

graberamy

Last night after I found a picture of those numbers/angles I also found
lots of discussion(s) about whether or not it was factual. It seemed
the consensus was that it wasn't. I would have loved to have had a
computer at my finger tips when I was in college (well, one that wasn't
on dial up and took 3 minutes to get to each page,lol). That
angle/number info was in a textbook, I would have loved to been able to
debunk that in school!!

This has made math almost fun for me!!

amy g
iowa

--- In [email protected], Sandra Dodd <Sandra@...> wrote:
>
> -=-I wrote to Dr Malka to ask for his references.
>
> I note that all the other pages on this site "orthohelp" have been
> deleted because the Dr. retired and was told that he could be sued
> for leaving the info out there.
> -=-
>
> My husband, Keith, wrote that. He's big into math and history and
> runes, so I showed him the discussion thusfar. Maybe he'll
> correspond with the guy and get us some good references.
>
> Sandra
>
> [Non-text portions of this message have been removed]
>

riasplace3

>>When I was a kid I made a
> connection between the number and the angles/points on the written
> number in order to do quick addition. I had no idea it was
> intentional.

I did that too! This would be a good topic for the "Playing with
Ideas" blog.

Ria

Sandra Dodd

Look what I found about eleven and twelve!!!! SO cool.

So why aren't there a "oneteen" and a "twoteen" after ten? For
whatever mystical or religious reasons the number twelve was
important enough for its own unique monicker despite the fact that it
was "two left over" after counting to ten on one's fingers. For, of
course, the literal meanings of the words eleven and twelve are "one
left" and "two left" from the Germanic compounds "ain-lif" and "twa-
lif."





http://www.geocities.com/Area51/Station/6297/rune.htm



-=->>When I was a kid I made a

> connection between the number and the angles/points on the written
> number in order to do quick addition. I had no idea it was
> intentional.

I did that too! This would be a good topic for the "Playing with
Ideas" blog.-=-



Doing that now.



Sandra

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

Barbara Perez

All this talk about numbers and language has made me wonder...in Spanish, 11
and 12 BUT ALSO 13, 14, and 15 have "their own" name...(they are once, doce,
trece, catorce, and quince) and only on 16 does it start saying the regular
pattern 16 "dieciseis" (literally ten and six), 17 "diecisiete" (ten and
seven), etc..."Catorce and quince" (14 and 15 respectively) are particularly
difficult for young kids to remember because they are different enough from
4 and 5 (cuatro, cinco). At the same time, when learning French those few
numbers (13, 14, 15) were particularly easy for me to remember because of
the similarity with Spanish. I wish I knew enough latin/linguistics to
account for this! Does anyone know an explanation for this?
On Tue, Apr 22, 2008 at 3:21 PM, Sandra Dodd <Sandra@...> wrote:

> Look what I found about eleven and twelve!!!! SO cool.
>
> So why aren't there a "oneteen" and a "twoteen" after ten? For
> whatever mystical or religious reasons the number twelve was
> important enough for its own unique monicker despite the fact that it
> was "two left over" after counting to ten on one's fingers. For, of
> course, the literal meanings of the words eleven and twelve are "one
> left" and "two left" from the Germanic compounds "ain-lif" and "twa-
> lif."
>
> http://www.geocities.com/Area51/Station/6297/rune.htm
>
> -=->>When I was a kid I made a
>
>
> > connection between the number and the angles/points on the written
> > number in order to do quick addition. I had no idea it was
> > intentional.
>
> I did that too! This would be a good topic for the "Playing with
> Ideas" blog.-=-
>
> Doing that now.
>
> Sandra
>
> [Non-text portions of this message have been removed]
>
>
>


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

Pamela Sorooshian

Keith might like to see this, too:


<http://nostalgia.wikipedia.org/wiki/Arabic_numerals/Talk>

-Pam


On Apr 22, 2008, at 9:01 AM, Sandra Dodd wrote:

> -=-I wrote to Dr Malka to ask for his references.
>
> I note that all the other pages on this site "orthohelp" have been
> deleted because the Dr. retired and was told that he could be sued
> for leaving the info out there.
> -=-
>
> My husband, Keith, wrote that. He's big into math and history and
> runes, so I showed him the discussion thusfar. Maybe he'll
> correspond with the guy and get us some good references.



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