Drawing the Line...

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.

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
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.
--
Michael McIntyre ---- Silvan < snipped-for-privacy@users.sourceforge.net>
Linux fanatic, and certified Geek; registered Linux user #243621
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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'.

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
I'm with you on this. 1+1 still = 2
Political correctness never had anything to do with it.
-Jack

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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>
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
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
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
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 <><><><><><><><>
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
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. :)
--
Michael McIntyre ---- Silvan < snipped-for-privacy@users.sourceforge.net>
Linux fanatic, and certified Geek; registered Linux user #243621
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
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

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
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...)
--
Michael McIntyre ---- Silvan < snipped-for-privacy@users.sourceforge.net>
Linux fanatic, and certified Geek; registered Linux user #243621
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
Ok, I got it fixed. Glad I did too. Lots of cool responses.
John

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
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.

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
take your computer printout to Kinkos..blow it to the size you need, cut it out, trace on wood..

result
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

(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.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
- 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.
--
*******************
* Nehmo Sergheyev *
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
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

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

have
do
Use wire. It will stretch less.
-Jack
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

Site Timeline

Related Threads

    HomeOwnersHub.com is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.