Page 6 of 7
"New Math" is__ _easy_ __for me to date. I'm 50, and my brother is 3 years
younger. He had the 'new math' stuff inflicted on him in grade school.
I didn't. Same shool system, same school. Mostly even the same teachers.
(we both tended to be 'far in advance' of class-level, due to parental
involvement. e.g. reading and vocabulary skills at 11th-grade level,
in__ _fourth_ __grade -- not a way to make friends with classmates!)

"New math" involved introducing a number of 'abstract mathematical concepts' -- primarily the basics of 'set theory', at an early stage in the educational process; frequently to the detriment of 'drill' on basic arithemetic skills.

For those who survived the process --__ _and_ __managed to retain an interest
in the subject -- "advanced math" (probability theory, trigonometry,
calculus, etc.) classwork, later, was ***much*** easier.

Most of the 'concepts'/'ideas' behind the 'new math' teaching were good; the implementation***was*** flawed, in large part by pushing the abstract
concepts ***too*** early.

Well, hell. I am 46 and that song was an eye-opener for me. I can't even imagine subtracting "upwards" as he described the "old math" way. Seems much more difficult and non-intuitive to me. Now all the concepts about "sets" were just silly, but to subtract 173 from 342 why would you be taking 3 from 2 or 8 from 4?

Dave Hall

It's all a matter of 'viewpoint'. <grin>

Rather than 'play games' with the number you're "subtracting from" -- i.e., 'borrowing' from the 'next higher place' -- they play games with the number that they are subtracting (e.g. when you would do a 'borrow', they do the same subtraction from the 'ten larger' value, and then,***instead*** of the
'borrow', they 'add one' to the next digit of the number they're subtracting.
Thus, they subtract 'one more than the original' from the first number,
rather than subtracting from 'one less than the first number'. The result
***is*** equivalent, and you only have to worry about a -single- position at
a time. Even when, say, subtracting 9, from 2,000,000,008.

You try to subtract 9 from 8, but it's too big. classical math would have you do the 'borrow' from the 10's column,__
_but_ __there's nothing there to borrow from, so you have to keep going
till__ _eight_ __places, and convert the 2,000,000,008 into 1,999,999,99(18).

New style goes like this: subtract right-most digits 8 -9

doesn't fit, treat the upper digit as ten bigger ("don't worry" about where that 'ten' comes from): 18 -9 = 9

Now, consider the 'tens' digits, and***ADD***ONE* to the lower digit, to
make up for the ten you added above --__ _ignore_ __the 'ones' digits, we're
done with them:

0 8 -(1) 9 ==== = 8

doesn't fit, treat the upper digit as ten bigger ("don't worry" about where that 'ten' comes from):

10 8 -(1) 9 ==== = 9 8

Now, consider the 'hundreds' digits, and***ADD***ONE* to the lower digit, to
make up for the ten you added above --__ _ignore_ __the 'ones' digits, we're
done with them:

0 08 -(1) 09 ==== == 98

doesn't fit, treat the upper digit as ten bigger ("don't worry" about where that 'ten' comes from):

10 08 -(1) 09 ==== == 9 98

etc., etc., ad nauseum. or at least until you run out of digits. <grin> Note that whenever things "don't fit", you 'add ten ones', and then at the next stage, you 'subtract one extra ten', so things***do*** come out
right.

Note that you -never- are considering more than one digit from each number at a time, and that there is only a__ _single_ __'borrow digit' at any time.
(***UNLIKE*** the old-style method, where you had to adjust__ _eight_ __digits
at one time.)

The 'new style' method__ _is_ __better suited for manipulating -large- numbers
'in your head', faster, and with lesser probability of error. ***WHY*** it
works__ _is_ __harder to understand, _and_teach_, ***unless*** you have an under-
standing of 'decomposing' the subtraction into a series of operations, and
understand that you can do "equivalent transformations" to the individual
pieces of that series, ***without*** affecting the answer.

One of the points 'new math' teaches, although it is -never- expressly so mentioned,***is*** that 'decomposition' of big problems into a series of
littler ones,

Aside: until _well_into_ college, nobody__ _ever_ __tells you "what it is"
that they're trying to teach -- the best you get is a 'bunch of examples',
from which ***you*** must deduce/'internalize'/"generalize" the -process-.

"Problem solving" is a skill that__ _nobody_ __knows how to ***teach***.
Even those who__ _do_ __it well, don't know how they learned it.

Anybody who__ _does_ __figure out how to (a) teach it, and/or (b) test for
the ability to__ _learn_ __how to do it, will get ***RICH***.

Actually, "WTF's" are a__ _fourth_ __grade course. <guffaw>

It's all basic 'set theory' stuff. The properties of a 'collection of objects' -- properties which are separate from the individual objects that make up the set. "Mode" is a fancy word for 'the most commonly occurring value'. "Mean" is what you think of a the 'average' -- add 'em all up, and divide by the number of items. And there's also 'median' -- sort 'em in order, and pick the one physically in the middle of the sorted list.

It's like ordering "500 bd ft of FAS" lumber by phone. You__ _don't_ __know what
size each individual piece will be, but you__ _do_ __know things about the
'totality' of the order. A "500 bd ft" order is s 'new math' concept --
you don't know the precise details of each board's dimensions; and you ***DON'T***
***NEED***TO*, to know that is, or _is_not_, sufficient for your needs.

This is actually one of the 'core concepts' that "new math" sets out to instill -- that you***can*** "get answers" ***without*** having to know__ _all_ __the
'details'.

I'm in the same county as you, and I remember when my daughters were in middle school and high school they had some very odd stuff having to do with drawing parabolas and other graphing techniques where they actually learned to estimate what a curve would look like on a graph without having to plot any points. They did pretty well with it too. Some math professor at Virginia Tech apparently decided students weren't getting good enough instruction before college, so he helped develop the curriculum. In other words, your kids may be getting stuff unlike anywhere else. On the other hand, the new Standards of Learning requirements have had a big effect on things as well, and my kids just missed that, so it may be different now than it was 10 years ago.

I know the feeling. I was OK till they started in on that graphing stuff. Did your kids get the "mini computers?" Those through me for about 10 minutes till I realized it was just binary arithmetic being done in a funny way.

Bill Ranck Blacksburg, Va.

DON'T count on it:

e.g: Mix 1 cup water, and 1 cup alcohol. measure the result***carefully***.
It comes up several percentage points short of a pint.

Or: One raindrop running down the left side of the window One raindrop running down the right side. They run__ _together_.__

1+1 = 1

And we won't discuss how many rabbits you get, when you put one male and one female in the same cage.

<evil grin>

A) a pantograph B) do it 'full size' on the computer, and print it in 'posterized' form i.e., a bunch of separate pages, that you but together to make the full-size image. C) same as B, but use 'iron on tranfer' material to transfer the pattern to the wood.

(which

exact

result

and a

ideas?

Find the centers of the arcs for the oval. Dimension the distances and lay it out from the center. Then just draw your radii from the centers.

have

do

Use wire. It will stretch less.

-Jack

#### Site Timeline

- posted on October 16, 2003, 2:23 am

"New math" involved introducing a number of 'abstract mathematical concepts' -- primarily the basics of 'set theory', at an early stage in the educational process; frequently to the detriment of 'drill' on basic arithemetic skills.

For those who survived the process --

Most of the 'concepts'/'ideas' behind the 'new math' teaching were good; the implementation

- posted on October 17, 2003, 3:30 pm

Well, hell. I am 46 and that song was an eye-opener for me. I can't even imagine subtracting "upwards" as he described the "old math" way. Seems much more difficult and non-intuitive to me. Now all the concepts about "sets" were just silly, but to subtract 173 from 342 why would you be taking 3 from 2 or 8 from 4?

Dave Hall

- posted on October 15, 2003, 11:25 pm

CW wrote:

No, it really isn't. You still get to the same place, but the route has changed. They do subtraction from right to left, without carrying anything, somehow or other.

They're also teaching things at different times. Introducing third graders to statistics, for example. Stuff I've never even heard of before. Modes and means and WTFs.

I'm glad my son's math scores are in the 98th percentile, because I'm too stupid to figure out his homework.

No, it really isn't. You still get to the same place, but the route has changed. They do subtraction from right to left, without carrying anything, somehow or other.

They're also teaching things at different times. Introducing third graders to statistics, for example. Stuff I've never even heard of before. Modes and means and WTFs.

I'm glad my son's math scores are in the 98th percentile, because I'm too stupid to figure out his homework.

--

Michael McIntyre ---- Silvan < snipped-for-privacy@users.sourceforge.net>

Linux fanatic, and certified Geek; registered Linux user #243621

Michael McIntyre ---- Silvan < snipped-for-privacy@users.sourceforge.net>

Linux fanatic, and certified Geek; registered Linux user #243621

Click to see the full signature.

- posted on October 16, 2003, 3:24 am

It's all a matter of 'viewpoint'. <grin>

Rather than 'play games' with the number you're "subtracting from" -- i.e., 'borrowing' from the 'next higher place' -- they play games with the number that they are subtracting (e.g. when you would do a 'borrow', they do the same subtraction from the 'ten larger' value, and then,

You try to subtract 9 from 8, but it's too big. classical math would have you do the 'borrow' from the 10's column,

New style goes like this: subtract right-most digits 8 -9

doesn't fit, treat the upper digit as ten bigger ("don't worry" about where that 'ten' comes from): 18 -9 = 9

Now, consider the 'tens' digits, and

0 8 -(1) 9 ==== = 8

doesn't fit, treat the upper digit as ten bigger ("don't worry" about where that 'ten' comes from):

10 8 -(1) 9 ==== = 9 8

Now, consider the 'hundreds' digits, and

0 08 -(1) 09 ==== == 98

doesn't fit, treat the upper digit as ten bigger ("don't worry" about where that 'ten' comes from):

10 08 -(1) 09 ==== == 9 98

etc., etc., ad nauseum. or at least until you run out of digits. <grin> Note that whenever things "don't fit", you 'add ten ones', and then at the next stage, you 'subtract one extra ten', so things

Note that you -never- are considering more than one digit from each number at a time, and that there is only a

The 'new style' method

One of the points 'new math' teaches, although it is -never- expressly so mentioned,

Aside: until _well_into_ college, nobody

"Problem solving" is a skill that

Anybody who

Actually, "WTF's" are a

It's all basic 'set theory' stuff. The properties of a 'collection of objects' -- properties which are separate from the individual objects that make up the set. "Mode" is a fancy word for 'the most commonly occurring value'. "Mean" is what you think of a the 'average' -- add 'em all up, and divide by the number of items. And there's also 'median' -- sort 'em in order, and pick the one physically in the middle of the sorted list.

It's like ordering "500 bd ft of FAS" lumber by phone. You

This is actually one of the 'core concepts' that "new math" sets out to instill -- that you

- posted on October 16, 2003, 3:33 pm

I'm in the same county as you, and I remember when my daughters were in middle school and high school they had some very odd stuff having to do with drawing parabolas and other graphing techniques where they actually learned to estimate what a curve would look like on a graph without having to plot any points. They did pretty well with it too. Some math professor at Virginia Tech apparently decided students weren't getting good enough instruction before college, so he helped develop the curriculum. In other words, your kids may be getting stuff unlike anywhere else. On the other hand, the new Standards of Learning requirements have had a big effect on things as well, and my kids just missed that, so it may be different now than it was 10 years ago.

I know the feeling. I was OK till they started in on that graphing stuff. Did your kids get the "mini computers?" Those through me for about 10 minutes till I realized it was just binary arithmetic being done in a funny way.

Bill Ranck Blacksburg, Va.

- posted on October 15, 2003, 11:50 pm

I'm with you on this.
1+1 still = 2

Political correctness never had anything to do with it.

-Jack

Political correctness never had anything to do with it.

-Jack

- posted on October 16, 2003, 3:30 am

DON'T count on it:

e.g: Mix 1 cup water, and 1 cup alcohol. measure the result

Or: One raindrop running down the left side of the window One raindrop running down the right side. They run

1+1 = 1

And we won't discuss how many rabbits you get, when you put one male and one female in the same cage.

<evil grin>

- posted on October 16, 2003, 4:39 pm

wrote:

When there is alcohol concerned it is quite common for some to go missing. Or for the measurement to go awry.

Is it single or double paned glass?

Not really

this is some variety of exponential series, not addition.

-Jack

When there is alcohol concerned it is quite common for some to go missing. Or for the measurement to go awry.

Is it single or double paned glass?

Not really

this is some variety of exponential series, not addition.

-Jack

- posted on October 18, 2003, 2:11 am

On Thu, 16 Oct 2003 03:30:10 GMT, snipped-for-privacy@horatio.agresource.com ()
wrote:

But let's say you have two (2) spoons and you multiply those two spoons by zero (0) spoons.

What the heck happened to the original two spoons?

Bc snipped-for-privacy@centurytel.net

_______________________________________________________________________________ Posted Via Uncensored-News.Com - Accounts Starting At $6.95 - http://www.uncensored-news.com <><><><><><><> The Worlds Uncensored News Source <><><><><><><><>

But let's say you have two (2) spoons and you multiply those two spoons by zero (0) spoons.

What the heck happened to the original two spoons?

Bc snipped-for-privacy@centurytel.net

_______________________________________________________________________________ Posted Via Uncensored-News.Com - Accounts Starting At $6.95 - http://www.uncensored-news.com <><><><><><><> The Worlds Uncensored News Source <><><><><><><><>

- posted on September 28, 2003, 2:34 am

JackD wrote:

That's what we called'em too, back in Home Ec. I guess that was somewhere in the same timeframe. Hmmm... 1984ish... Wow, almost 20 years ago.

There's always Silly Putty. :)

That's what we called'em too, back in Home Ec. I guess that was somewhere in the same timeframe. Hmmm... 1984ish... Wow, almost 20 years ago.

There's always Silly Putty. :)

--

Michael McIntyre ---- Silvan < snipped-for-privacy@users.sourceforge.net>

Linux fanatic, and certified Geek; registered Linux user #243621

Michael McIntyre ---- Silvan < snipped-for-privacy@users.sourceforge.net>

Linux fanatic, and certified Geek; registered Linux user #243621

Click to see the full signature.

- posted on September 29, 2003, 6:52 pm

This is intersting... I see your reply, but I can't see the reply you
replied to, nor my original message, or any messages in between... Is it
just my new server, or have some messages gone missing????

John

John

- posted on September 29, 2003, 10:16 pm

John Smith wrote:

I'm too lazy to investigate, but chances are it's your news server. Things get lost from time to time. Having more than one server is the best insurance against that, but that's only convenient if you're running your own local news spool to pull from different sources and put things together. (leafnode on Linux or Hamster on Windows...)

I'm too lazy to investigate, but chances are it's your news server. Things get lost from time to time. Having more than one server is the best insurance against that, but that's only convenient if you're running your own local news spool to pull from different sources and put things together. (leafnode on Linux or Hamster on Windows...)

--

Michael McIntyre ---- Silvan < snipped-for-privacy@users.sourceforge.net>

Linux fanatic, and certified Geek; registered Linux user #243621

Michael McIntyre ---- Silvan < snipped-for-privacy@users.sourceforge.net>

Linux fanatic, and certified Geek; registered Linux user #243621

Click to see the full signature.

- posted on September 30, 2003, 1:07 pm

Ok, I got it fixed. Glad I did too. Lots of cool responses.

John

John

- posted on September 30, 2003, 5:24 am

Actually, if you use a laser printer, you can transfer the lines onto
the wood with an iron. It's hard to get a real clear image since the
toner wants to stick to the paper almost as well as the wood, but the
resulting line is usable. I used to make hobby printed circuit boards
that way.

- posted on September 26, 2003, 5:15 pm

take your computer printout to Kinkos..blow it to the size you need, cut it
out, trace on wood..

result

result

- posted on September 26, 2003, 5:16 pm

A) a pantograph B) do it 'full size' on the computer, and print it in 'posterized' form i.e., a bunch of separate pages, that you but together to make the full-size image. C) same as B, but use 'iron on tranfer' material to transfer the pattern to the wood.

- posted on September 26, 2003, 5:47 pm

(which

exact

result

and a

ideas?

Find the centers of the arcs for the oval. Dimension the distances and lay it out from the center. Then just draw your radii from the centers.

- posted on September 26, 2003, 6:10 pm

- John Smith -

(which

exact

result

and a

ideas?

- Nehmo - If the "oval" is actually an ellipse, you can easily draw it by driving nails at the two foci and placing a loop of string around the nails and a pencil. Position the pencil so that the loop of string is tight and forms a triangle with vertices at each nail and the pencil. Draw the ellipse by keeping the string tight and moving the pencil in an orbit around the foci. http://www.mhhe.com/physsci/astronomy/fix/student/chapter4/04f14.html

Out of curiosity, what was the application for your wood oval? A tabletop?

For complicated-shape image transfers from a computer to a flat piece of wood, you might try some type of projection system.

(which

exact

result

and a

ideas?

- Nehmo - If the "oval" is actually an ellipse, you can easily draw it by driving nails at the two foci and placing a loop of string around the nails and a pencil. Position the pencil so that the loop of string is tight and forms a triangle with vertices at each nail and the pencil. Draw the ellipse by keeping the string tight and moving the pencil in an orbit around the foci. http://www.mhhe.com/physsci/astronomy/fix/student/chapter4/04f14.html

Out of curiosity, what was the application for your wood oval? A tabletop?

For complicated-shape image transfers from a computer to a flat piece of wood, you might try some type of projection system.

--

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

* Nehmo Sergheyev *

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

* Nehmo Sergheyev *

Click to see the full signature.

- posted on September 30, 2003, 1:42 pm

I was wondering if anyone would distinguish an oval from an ellipse :-).
I'm a math geek, but I didn't want to give it away on my original post by
using words like ellipse...

Yes, it was for a table top for my living room. I got a new oscollating sander and I wanted to play with it a bit. The trick was that there was a glass inlay which meant there were two concentric elipses. And because the center ellipse had to be exactly a quarter inch smaller than the glass, it had to be extremely accurate. (I cut the inside oval before I got the glass, which ended up being a mistake because the glass was a touch smaller than I expected, and therefore instead of a simple cut with a 1/4" rabbit bit, I had to build a special guide jig for my router table).

I thought of the string method, but the most inelestic string seemed to have about a eighth of an inch give on it for the size -- of course that could do with the string slipping on the pencil a bit as well.

I really like the laser printer with iron suggestion! I imagine the local kinkos has a laser printer that can print on large enough paper (I find using multiple pieces of paper adds a degree of inacaruacy).

Gluing the paper on is also neat, but then how do you remove the glue and paper from the wood (without effecting the stain)? If there's a special type of glue for that, that would definately rank up there with the laser printer method.

Thanks for all the responses

John

Yes, it was for a table top for my living room. I got a new oscollating sander and I wanted to play with it a bit. The trick was that there was a glass inlay which meant there were two concentric elipses. And because the center ellipse had to be exactly a quarter inch smaller than the glass, it had to be extremely accurate. (I cut the inside oval before I got the glass, which ended up being a mistake because the glass was a touch smaller than I expected, and therefore instead of a simple cut with a 1/4" rabbit bit, I had to build a special guide jig for my router table).

I thought of the string method, but the most inelestic string seemed to have about a eighth of an inch give on it for the size -- of course that could do with the string slipping on the pencil a bit as well.

I really like the laser printer with iron suggestion! I imagine the local kinkos has a laser printer that can print on large enough paper (I find using multiple pieces of paper adds a degree of inacaruacy).

Gluing the paper on is also neat, but then how do you remove the glue and paper from the wood (without effecting the stain)? If there's a special type of glue for that, that would definately rank up there with the laser printer method.

Thanks for all the responses

John

- posted on September 30, 2003, 4:27 pm

have

do

Use wire. It will stretch less.

-Jack

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