HDTenEightyP/NetNews huggingface dataset:
From: choy@skorpio.usask.ca (I am a terminator.)
Newsgroups: k12.ed.math
Subject: Re: INTEGRALS
Date: 25 Jan 1993 16:55:57 GMT
Organization: University of Saskatchewan, Saskatoon, Canada
Distribution: world
NNTP-Posting-Host: skorpio.usask.ca

In article <1jmn8cINN3n9@usenet.INS.CWRU.Edu>, cb919@cleveland.Freenet.Edu (Mike Bolduan) writes:
|> 
|> David Radcliffe:
|> 
|> YES!!!!
|> You said it much better than I could have. It is a matter of 
|> definition and a definition is "what we say it is". We have the 
|> right to define anything we want in any way we wish. It is a 
|> "bad" definition (and hence should probably not have been 
|> made) if it leads to "nastiness" (e.g., contradictions) down the 
|> road.

The definition may not be so bad. It get's us away from a lot of
trouble (see <1jkfe8INN7ou@access.usask.ca>). How can you >> verify <<
the limit to be zero when it heads to -infinity coming from the left
and to +infinity coming from the right?

|> This reminds me just a tad about the huge debate a couple of 
|> years ago about the meaning of 0^0. (and please let's just let 
|> sleeping dogs lie!)This also is a matter of how we wish to 
|> define something.

Hmm. What can you do? Consider lim x->0 0^x. Then consider
lim x->0 x^0. Then consider the definition of exponentiation.
a^x means exp(x ln a). But ln x is not defined at x=0 !

|> BTW I would highly recommend a couple of books for 
|> people interested in calculus as it (should) be taught these 
|> days:
|> 1) The new material by the Harvard Consortium published 
|> by Wiley
|> 2) The book by Dick and Patton which integrates (sorry 
|> 'bout that!   :-))  technology into the class)
|> 3) Calculus by Gilbert Strang which is a VERY interesting 
|> book (although 'tain't cheap!)

I really like Modern Calculus and Analytic Geometry by R.A. Silverman.
I got it used for $8. It looked like new though, so I pity the previous
owner.

-- 

Henry Choy
choy@cs.usask.ca

What rolls down stairs alone or in pairs            This has been brought to 
Rolls over your neighbor's dog?                     you by the numbers 4
What's great for a snack and fits on your back?     and 9 and the letter P.
It's Log, Log, Log!  -- "The Log Song", from            -- Big Bird
                         Ren & Stimpy

Math is tough!       -- Barbie
Newsgroups: k12.ed.math
From: cmsbern@radford.vak12ed.edu (Bernard Class)
Subject: calculator use in the classroom
Organization: Virginia's Public Education Network (Radford)
Date: Wed, 27 Jan 93 18:10:19 GMT

Dear Fellow STudent,
     I think your dad should reconsider his objections towards
calculators.  Once you get past arithmetic, you will find that
the skillful use of calculators will come in handy in higher
mathematics.  Our math teacher allows us to use calculators in
most activities and we do a lot of pre algebra.
Scott BAker, et al

---
****************************************************
****************************************************
Bernard Seventh Graders--cmsbern@radford.vak12ed.edu
Christiansburg Middle School--Where Education is not
an expense but an investment---&&&&&&&&&&&&&&&&&&&&&
From: choy@skorpio.usask.ca (I am a terminator.)
Newsgroups: k12.ed.math
Subject: Re: heres a question
Date: 25 Jan 1993 18:10:16 GMT
Organization: University of Saskatchewan, Saskatoon, Canada
Distribution: world
NNTP-Posting-Host: skorpio.usask.ca

In article <41295.2B62BCAE@puddle.fidonet.org>, Brian.Mcdonald@p4.f18.n128.z1.fidonet.org (Brian Mcdonald) writes:
|> how many polygons are there that all its sides are longer than any of its 
|> diagonals

All right! A COUNTING problem. Counting and categorizing are said to be the
two hardest topics in math. So let the count begin! Ha Ha Ha Ha (thunder
and lightning)

I submit the triangle to the count. For all x, if x is a diagonal of a
triangle, then every side of the triangle is longer than x. This is

                                  true

because triangles have no diagonals. 1 Ha Ha Ha Ha (thunder and lightning)

I ask
  (1) Prove that every polygon has a convex corner.
  (2) What comes after the triangle? (Can I say 2 Ha Ha Ha Ha
      3 Ha Ha Ha Ha?)

-- 

Henry Choy
choy@cs.usask.ca

What rolls down stairs alone or in pairs            This has been brought to 
Rolls over your neighbor's dog?                     you by the numbers 4
What's great for a snack and fits on your back?     and 9 and the letter P.
It's Log, Log, Log!  -- "The Log Song", from            -- Big Bird
                         Ren & Stimpy

Math is tough!       -- Barbie
Newsgroups: k12.ed.math
From: cmsbern@radford.vak12ed.edu (Bernard Class)
Subject: tesslation video
Organization: Virginia's Public Education Network (Radford)
Date: Wed, 27 Jan 93 18:16:18 GMT

Hello,
     I teach 7th grade mathematics and love tessalating.  I use
them to teach many basic geometrical principals.  I have tons
of neat stuff on tessalations that I purchased with some grant
money I received for a proposal I wrote on a tessalations unit.
However; to directly address your request for a video:  there
is a wonderful video put out by Roland Films on ARt called
"Adventures in Perception".  My students loved it.  IT focuses
on M.C. Escher's work.
Heidi Bernard


---
****************************************************
****************************************************
Bernard Seventh Graders--cmsbern@radford.vak12ed.edu
Christiansburg Middle School--Where Education is not
an expense but an investment---&&&&&&&&&&&&&&&&&&&&&
From: Sheila.King@f315.n103.z1.fidonet.org (Sheila King)
Newsgroups: k12.ed.math
Subject: RE: INTEGRALS            
Date: Fri, 22 Jan 93 18:20:00 PDT
Organization: FidoNet node 1:103/315 - Castle of the Four , Diamond Bar CA

To: Brian Harvey

-> >So, what you're saying is that any time a sum or difference involves
-> a >divergent series, there is no answer to the sum or difference? Is
-> this >true in all cases?
->
-> Right -- this is the *definition* of "divergent"!

OK, I'm learning something. Actually, this whole discussion has made me
feel the need to get out a few calculus books and read the chapters on
divergent/convergent series again. Last time I covered that material was
two summers ago, and I sure *thought* I understood it. I guess I've just
forgotten some of the particulars.

-> The best you can say is that
->
->       lim [a -> 0] <integral from -2 to -a> + <integral from a to 2>
->
-> is zero.

OK, this statement makes a great deal of sense to me. So that particular
limit above is zero, but the integral from 0 to 2 of 1/x is divergent.
OK. Thanks,

Sheila
coming to you from Diamond Bar, CA (in Los Angeles County)
                                                                                                         

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From: choy@dvinci.USask.Ca (Henry Choy)
Newsgroups: k12.ed.math
Subject: Fun for algebra people
Date: 27 Jan 1993 22:51:53 GMT
Organization: University of Saskatchewan
NNTP-Posting-Host: dvinci.usask.ca
X-Newsreader: TIN [version 1.1 PL6]


Take any n positive numbers x1,...,xn such that their product is 1.
Prove that their sum is greater than or equal to n. On what conditions
would the sum be n?


Prove that

 n + n + ... + n = 2^n
 0   1         n   

where

  n
  m

means n choose m and 2^n means 2 to the exponent n.

n choose m means the number of different subsets of m elements that
can be chosen or constructed from a set of n elements. Show that

                    n!
n choose m = n = ---------
             m   m! (n-m)!

where p! means 1 x 2 x ... x p (those are multiplication signs, not
the letter x).

--

Henry Choy
choy@cs.usask.ca

What rolls down stairs alone or in pairs            This has been brought to 
Rolls over your neighbor's dog?                     you by the numbers 4
What's great for a snack and fits on your back?     and 9 and the letter P.
It's Log, Log, Log!  -- "The Log Song", from            -- Big Bird
                         Ren & Stimpy

Math is tough!       -- Barbie
From: radcliff@csd4.csd.uwm.edu (David G Radcliffe)
Newsgroups: k12.ed.math
Subject: Ability vs. effort
Date: 24 Jan 1993 22:01:42 GMT
Organization: UW-Milwaukee Math Department
NNTP-Posting-Host: 129.89.7.4
X-Newsreader: TIN [version 1.1 PL8]

There is an article in the January 1, 1993 issue of Science which
compares the mathematics achievement of Chinese, Japanese, and 
American children.  The article finds that American students continue
to lag far behind their Asian peers.  Only 10% of Japanese fifth
graders and 8% of Japanese eleventh graders had scores which were
lower than the average score of their American counterparts.

Eleventh graders from each country were asked the following question:
"Here are some factors that may influence students' performance in
mathematics: a good teacher, innate intelligence, home environment,
and studying hard.  Only 27% of American students chose studying
hard, as opposed to 72% of Japanese students.  However, 54% of American
students selected "a good teacher", versus 14% of Japanese students.

The teachers of eleventh graders were asked the same question.
93% of Japanese teachers chose "studying hard", and 7% chose "innate
intelligence".  However, only 26% of American teachers thought that
studying hard was the most important factor, while 41% selected
innate intelligence.

I think that these attitudes are very destructive.  In my limited
teaching experience, students have often told me that they are
not "math people".  When I try to emphasize concepts rather than
algorithms, students are resentful.  I think the reason for this
is that my students don't really believe that they can understand
mathematics, so they memorize procedures and hope to bluff their
way through the course.  They are not necessarily lazy, but they
become frustrated easily; if they can't solve a problem in a few
minutes, then they give up.

Any comments are welcome. 

---
David Radcliffe
Graduate Student, Dept of Mathematics
University of Wisconsin, Milwaukee
(INTERNET) radcliff@csd4.csd.uwm.edu
Newsgroups: k12.ed.math
From: kachun@spot.Colorado.EDU (Ka Chun Yu)
Subject: Re: INTEGRALS            
Organization: University of Colorado, Boulder
Date: Thu, 21 Jan 1993 23:01:13 GMT

In article <40112.2B5EBAC4@puddle.fidonet.org> Sheila.King@f315.n103.z1.fidonet.org (Sheila King) writes:
>To: Ka Ya Chun
>
>-> I{-2,2} 1/x dx = -1/x^2 [-2,2]
>
>Didn't you just do the derivative of 1/x instead of the integral?

Major oops there.  Boy do I feel like a dope--especially having read
through so many of the responses to your post.  Yes, you're right.
Replace those silly -1/x^2 's with ln x 's.

>
>Sheila
>coming to you from Diamond Bar, CA (in Los Angeles County)
>                                                                        

--kachun
From: radcliff@csd4.csd.uwm.edu (David G Radcliffe)
Newsgroups: k12.ed.math
Subject: Re: heres a question
Date: 26 Jan 1993 22:31:18 GMT
Organization: UW-Milwaukee Math Department
NNTP-Posting-Host: 129.89.7.4
X-Newsreader: TIN [version 1.1 PL8]

Brian Mcdonald (Brian.Mcdonald@p4.f18.n128.z1.fidonet.org) wrote:
: how many polygons are there that all its sides are longer than any of its 
: diagonals
: ?????????????????????????peace and i'm outa here

There are infinitely many.  Consider the polygon ABCD, with
A = (-2,0), B = (x,1), C = (0,0), and D = (x,-1).  If x > sqrt(3)
then all the sides are longer than the diagonals.

If you allow polygons to intersect themselves, then you can draw an
n-pointed star with this property provided n is odd and greater than 4.

Is it possible to find a pentagon which does not intersect itself
with this property?  Is there an equilateral polygon with 4 or more
sides having this property?  Can you prove that no convex polygon
with 4 or more sides can have this property?  Are there other conjectures
about this problem which you find interesting?

--
David Radcliffe                                
radcliff@csd4.csd.uwm.edu
From: Jon.Riley@p0.f25.n137.z1.fidonet.org (Jon Riley)
Newsgroups: k12.ed.math
Subject: Re: star trek teaching
Date: Tue, 26 Jan 93 13:48:14 PDT
Organization: FidoNet node 1:137/25.0 - The Back Door, Venice FL

  Ok ypu can say that Juan Luke Pircard has responiblities and so 
does the Student in life.  The crew always does criticle think to get out of situations.  Put the  Student in a criticle stiuation and ask him/her "How would you get out of this?"
 
Write me back, I might have some other ideas!
 
 
Jon Riley



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From: Sheila.King@f315.n103.z1.fidonet.org (Sheila King)
Newsgroups: k12.ed.math
Subject: RE: INTEGRALS
Date: 20 Jan 93 02:07:00 GMT
Organization: FidoNet node 1:103/315 - Castle of the Four , Diamond Bar CA

To: Ka Ya Chun

-> I{-2,2} 1/x dx = -1/x^2 [-2,2]

Didn't you just do the derivative of 1/x instead of the integral?

Sheila
coming to you from Diamond Bar, CA (in Los Angeles County)
                                                                        

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From: Brian.Mcdonald@p4.f18.n128.z1.fidonet.org (Brian Mcdonald)
Newsgroups: k12.ed.math
Subject: heres a question
Date: Thu, 21 Jan 93 19:19:26 PDT
Organization: FidoNet node 1:128/18.4 - D-20 Ed Network, Colorado Springs CO

how many polygons are there that all its sides are longer than any of its 
diagonals
?????????????????????????peace and i'm outa here



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From: Mark.Sanders@f41.n116.z1.fidonet.org (Mark Sanders)
Newsgroups: k12.ed.math
Subject: surprising answer
Date: Tue, 26 Jan 93 18:22:46 PDT
Organization: FidoNet node 1:116/41 - Metro-Net, Nashville TN

Here's a little question I pose in my math classes to illustrate the power 
of exponents. If you had a piece of paper .001 inches thick and you folded 
it in half 50 times, how thick would it be?   ( Of course you can't
actually fold a paper more than about 10 times...   but if you could... )
When you tell people the answer in miles, they always look at you with an
expression on their face that says: " Why are you lying to me? "
I teach high school in Lebanon, TN  USA.     If you need me to give the
answer, reply please.


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From: Sheila.King@f315.n103.z1.fidonet.org (Sheila King)
Newsgroups: k12.ed.math
Subject: STRANG'S CALCULUS TEXT   
Date: Sun, 24 Jan 93 11:06:00 PDT
Organization: FidoNet node 1:103/315 - Castle of the Four , Diamond Bar CA

Well, now that this discussion has been going on about integrals and
such, and I've seen this guy Strang mentioned both here, and in private
e-mail that I received, I figure I've got to check this text out. It
seems very highly recommended.

So, can anyone tell me who publishes the book? How about an ISBN number?
Copyright date?

Thanks,
Sheila
coming to you from Diamond Bar, CA (in Los Angeles County)
                                                                                                          

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From: Carol.Hooper@f105.n381.z1.fidonet.org (Carol Hooper)
Newsgroups: k12.ed.math
Subject: RE: STUDENT TEACHING     
Date: Wed, 20 Jan 93 22:36:25 PDT
Organization: FidoNet node 1:381/105 - Hawks BBS K12Net, El Paso TX

The book is fantastic...as is it's sequel!


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Newsgroups: k12.ed.math
Subject: Re: Ability vs. effort
From: pmacfar@eis.calstate.edu (Paul MacFarlane)
Date: Wed, 27 Jan 1993 03:02:54 GMT
Organization: Calif State Univ/Electronic Information Services

radcliff@csd4.csd.uwm.edu (David G Radcliffe) writes:
> There is an article in the January 1, 1993 issue of Science which
> compares the mathematics achievement of Chinese, Japanese, and 
> American children.  The article finds that American students continue
> to lag far behind their Asian peers.
[part deleted]
> 
> The teachers of eleventh graders were asked the same question.
> 93% of Japanese teachers chose "studying hard", and 7% chose "innate
> intelligence".  However, only 26% of American teachers thought that
> studying hard was the most important factor, while 41% selected
> innate intelligence.
[more deleted]

> 
> I think that these attitudes are very destructive.

[more deleted]

I completely agree with you.  As someone very much into Piagetian
psychology, it seems to me that, in some sense, everyone needs construct
mathematics for themselves.  I've always wished that there were no word
'teach' in the English language, and like Spanish, we would use a word
with the implication of 'show,' instead.  When people lack
the belief that they can understand mathematics, they simply won't.

By the way, for an outstanding article on the same general subject, see
the December 1992 Scientific American.  It presents results similar to the
Science article you cite, and it also explores the differences in teaching
style, societal support, school structure, etc., that account for the
differences in math/science learning. For me, it was amazingly clear and it
also exploded some stereotypes and mis-impressions I had had about Asian
schools.

Paul MacFarlane
Danville, California
pmacfar@eis.calstate.edu
From: Sheila.King@f315.n103.z1.fidonet.org (Sheila King)
Newsgroups: k12.ed.math
Subject: CALCULATORS IN SCHOOL    
Date: Fri, 22 Jan 93 18:12:00 PDT
Organization: FidoNet node 1:103/315 - Castle of the Four , Diamond Bar CA

Dear Christina,

In your message to Brian Bridal you said:

-> I am in Year 5 in Blackalls Public School and I do not
-> agree with having calculators out all the time in class.
-> They are a help sometimes but the let silly kids be lazy
-> and not use their brains.
-> My dad teaches too. In some classes, he gives rewards to
-> kids who don't use calculators. Some kids end up faster
-> without them.

I am glad to see a student such as yourself with such a fine outlook. It
seems to me that you understand just what calculators are. As you say,
"sometimes a help", but certainly not necessary at all times.

Best of luck to you in your maths class, and thanks for posting in this
area.

Sheila King
K12_Math echo Moderator
coming to you from Diamond Bar, CA (in Los Angeles County)
                                                                                                               

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From: bh@anarres.CS.Berkeley.EDU (Brian Harvey)
Newsgroups: k12.ed.math
Subject: Re: INTEGRALS
Date: 21 Jan 1993 16:45:15 GMT
Organization: University of California, Berkeley
NNTP-Posting-Host: anarres.cs.berkeley.edu

Sheila.King@f315.n103.z1.fidonet.org (Sheila King) writes:
>So, what you're saying is that any time a sum or difference involves a
>divergent series, there is no answer to the sum or difference? Is this
>true in all cases?

Right -- this is the *definition* of "divergent"!

>But there are techniques for evaluating limits that tend to infinity
>minus infinity. These are commonly taught in first year calculus in the
>chapter including L'Hopitals rule. How are these different from this
>example?

Those are limits of functions that are well-behaved except at one
point.  For example, if you take lim [x->0] (sin x)/x then you are
looking at a situation in which (sin 0.0001)/0.0001 is well-defined,
and all those values approach a limit.  And even then, you can't say
that the limit *is* the value of (sin 0)/0.  That expression has no
value.

In the original question, the integral is the lim [delta x -> 0] of a
sum of areas of tall skinny rectangles.  Each finite value of delta x
already is problematic, because each includes one or two rectangles
right at the y axis that are infinitely tall.

The best you can say is that 

	lim [a -> 0] <integral from -2 to -a> + <integral from a to 2>

is zero.  That's true; as a approaches zero the two integrals have larger
and larger magnitudes, but their sum is still zero for any nonzero a.
From: Christina.Macpherson@f405.n622.z3.fidonet.org (Christina Macpherson)
Newsgroups: k12.ed.math
Subject: Rotten kids in my class
Date: Mon, 18 Jan 93 16:07:28 PDT
Organization: FidoNet node 3:622/405

To: Brian Harvey

Hello,
I am in Year 5 in Blackalls Public School and I saw
your message about kids mucking up in class and making
teachers annoyed.
The painful kids in my class are just show offs. They
don't care that they waste time.
I like maths but most kids don't. The reason they don't
learn much is that they always talk over the teacher.
Even my brother mucks up when teachers don't stop him
being silly.

Yours,
C.L.M. - Blackalls Park, Lake Macquarie City, Australia


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Newsgroups: k12.ed.math
From: mgibson@vdoe386.vak12ed.edu (Mary Lou Gibson)
Subject: Tesselations
Organization: Virginia's Public Education Network (Richmond)
Date: Wed, 27 Jan 93 15:47:42 GMT

I am looking for videos on the topic of Tessalations.  I
understand that about a year ago there was a program on the
Discovery channel on the topic.  Does anyone know the name of
the show or the date on which it appreared?  If you have any
information please leave me a message at     
mgibson@vdoe386.vak12ed.edu
Thanks,  Mary Lou Gibson
From: Chris.Meek@f236.n107.z1.fidonet.org (Chris Meek)
Newsgroups: k12.ed.soc-studies
Subject: NATIVE AMERICAN EDUCATION
Date: Wed, 27 Jan 93 13:34:00 PDT
Organization: FidoNet node 1:107/236 - The International L, Babylon NY

Jerry,
  I think it's great that OU is finally taking steps to start a NAS program.
I attended OU from 1983-1985 and found their social sciences programs a little
 on teh lite side. I hope the program works out. Boomer Sooner!


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From: Iain.Macpherson@f405.n622.z3.fidonet.org (Iain Macpherson)
Newsgroups: k12.ed.soc-studies
Subject: CIVIL WAR
Date: Sun, 17 Jan 93 08:34:36 PDT
Organization: FidoNet node 3:622/405

JW>I am looking for a Civil War buff to write to.  I am a real big
JW>civil war buff.  Please write me if you are a CIVIL WAR BUFF!!!

       I am just re-watching the DOCUMENTARY mini-series ``The Civil War'' on SBS-TV , Australia.

       My university major was North and Central American History.

       Maybe you might find me interesting enough to `talk' to.


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From: Don.Peet@p0.f126.n137.z1.fidonet.org (Don Peet)
Newsgroups: k12.ed.soc-studies
Subject: International response
Date: Wed, 20 Jan 93 08:59:38 PDT
Organization: FidoNet node 1:137/126.0 - Global Vision, Sarasota FL

I saw your Email about the Netherlands.  There were no responses from 
there but did you notice that England and Finland have some response sim 
ialr to what you wanted.  Also in Virginia there's a contest involving 
presidents.  All are here in Area 59.



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