HDTenEightyP/NetNews huggingface dataset:
From: Sheila.King@f315.n103.z1.fidonet.org (Sheila King)
Newsgroups: k12.ed.math
Subject: DOING HOMEWORK IN SCH    
Date: Sat, 12 Dec 92 10:15:00 PDT
Organization: FidoNet node 1:103/315 - Castle of the Four , Diamond Bar CA

Hi Jerry,

Nice of you to jump in.

-> am studying to be a math teacher. Middle school has always been my
-> target area. I must agree that instruction should not be for the
-> first 20 minuites of the class, leaving the rest for doing
-> "homework", however, if I cannot expect my students to do the work...
-> Where do we go from here??

Where are you planning to teach? In Oklahoma? Do you already expect that
your students will not be doing homework, or did you simply see that
someone else had commented that their middle school students don't want
to do it and assume it would be the same with yours?

I certainly don't have the answers. Indeed, if the students WON'T do
homework at home, I guess it is better to do it in class them have them
not practice math at all. These comments from you and others make me
wonder how widespread it is, that students do not do homework. You know,
in all the international comparisons I read about comparing students
from the U.S. with students from other nations, it is often mentioned
that U.S. students do very little homework. It seems to me that we
should not accept this as the status quo, but should do something to
change it. Of course, the question is what should we do?

Is it reasonable to send parents a letter on the first day of class (one
to be read and signed) explaining the importance of homework in math and
why the students must do it, and informing the parents that assignments
will be daily (or twice a week, or whatever...) and asking them to
support you by having their kid complete it? Of course, I realize that
in certain areas of the country this approach probably wouldn't work,
since the parents do not do the job of "parenting" their children that
they should.

Well, I can't think of anything else to say about this right now.
However, I do have some ideas about positive incentives for homework.
Ask me about them later, and I'll say some more on this topic...

Sheila
                                                                                                        

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From: Sheila.King@f315.n103.z1.fidonet.org (Sheila King)
Newsgroups: k12.ed.math
Subject: FACILITATION?            
Date: Sat, 12 Dec 92 10:44:00 PDT
Organization: FidoNet node 1:103/315 - Castle of the Four , Diamond Bar CA

Jerry,

About the Geometric Supposer you asked:

-> Is the program part of a package (can I get a copy without buying it,
-> or is it copy wrighted)?

The Geometric Supposer is a commercial package. It is marketed by
Sunburst, and you must purchase it. The one thing that I would be
cautious about, is that the Supposer is old technology and many programs
have come out since then which do much more than the Supposer. If you
already had a copy of it I would use it. But, if you have to go out and
spend money, then I would spend it on something else like the Geometer's
Sketchpad or Geodraw,  which do so much more.

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

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From: radcliff@csd4.csd.uwm.edu (David G Radcliffe)
Newsgroups: k12.ed.math
Subject: Re: Math prob...
Date: 17 Dec 1992 07:09:50 GMT
Organization: UW-Milwaukee Math Department
Distribution: na
NNTP-Posting-Host: 129.89.7.4

                                 2      2          2
You need to remember that (x + y)   =  x  + 2xy + y  .
This equality can be illustrated by a diagram:

	    x          y
      +------------+--------+
      |            |    2   |
    y |     xy     |   y    | y 
      |            |        |      The area of the large
      +------------+--------+
      |            |        |                       2 
      |      2     |        |      square is (x + y) .
    x |     x      |   xy   | x 
      |            |        |
      |            |        |
      +------------+--------+
            x          y

Now let us see why sqrt(a + b) is not equal to sqrt(a) + sqrt(b).
Consider the equation sqrt(a + b) = sqrt(a) + sqrt(b), and square both sides.
You get
                   2                       2
        sqrt(a + b)  =  (sqrt(a) + sqrt(b))

                   2           2                             2
	sqrt(a + b)  =  sqrt(a) + 2 sqrt(a) sqrt(b) + sqrt(b)
(Applying the above rule, with x = sqrt(a) and y = sqrt(b) )

	     a + b   =     a    + 2 sqrt(a) sqrt(b) +   b
	       0     =            2 sqrt(a) sqrt(b).

This last line is only true when a = 0 or b = 0.
In general, sqrt(a + b) < sqrt(a) + sqrt(b) unless a = 0 or b = 0.

Here are some challenging problems to ponder:

  1.  Show by a picture that (x + y)(x - y) = x^2 - y^2.
  2.  Show by a picture that the sum of the first n odd numbers is n^2. 
  3.  Show by a picture that (x + y)^3 = x^3 + 3(x^2)y + 3x(y^2) + y^3. 
  4.  Draw a picture which illustrates the method of completing the square. 
  5.  Prove the Pythagorean theorem c^2 = a^2 + b^2 as follows:
      Draw a square of side a + b.  Divide the square into a square
      of side c and four right triangles.  Then divide the same
      square into a square of side a, a square of side b, and
      four right triangles.  Conclude that c^2 = a^2 + b^2.

--
David Radcliffe                                
radcliff@csd4.csd.uwm.edu
From: Sheila.King@f315.n103.z1.fidonet.org (Sheila King)
Newsgroups: k12.ed.math
Subject: RE: FACILITATION?        
Date: Sat, 12 Dec 92 10:18:00 PDT
Organization: FidoNet node 1:103/315 - Castle of the Four , Diamond Bar CA

Keith (from  Dover-Sherborn High School),

You said:

-> Using the Geometry Supposer at the high school and involved in a
-> telecommunication
-> project (on Peacenet) in the junior high school.

I teach high school geometry. I have not had the opportunity to use
technology in my classroom yet (such as the Geometry Supposer). Next
year we are revising our geometry course and plan to implement
widespread use of the Mira. I hope it will really help our classes.

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

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Internet: Sheila.King@f315.n103.z1.fidonet.org
Newsgroups: k12.ed.math
From: kachun@spot.Colorado.EDU (Ka Chun Yu)
Subject: Re: Christmas geometrikites
Organization: University of Colorado, Boulder
Date: Sat, 12 Dec 1992 09:09:20 GMT

In article <26759.2B21B456@puddle.fidonet.org> Carol.Hooper@f89.n381.z1.fidonet.org (Carol Hooper) writes:
>I found a great geometry project that my class is embarking on Monday 
>and I thought I'd see if anyone else had completed such an activity 
>and how it went over.  This involves creating the "kite" with straws, 
>string, and tissue paper (but we are using Christmas paper) and then, 
>after discussion of vertices, area, perimeter, volume--combining them 
>in a large tree (which we are placing in the library).  I'd like to 
>ask for those who have tried this to let me know what topics of 
>discussion came out of the activity concerning the figure created and 
>also offer a copy of the activity to anyone who'd be interested.  
>THanks...........Carol
>

Back in my junior high math class, our winter holiday assignment consisted
of making polyhedrons out of paper and cardboard, decorating them, and
putting them up in the school Christmas tree.  The choice of polyhedrons
ranged from your usual Pythagorean solids to multifaceted shapes filled
with decagons, squares, hexagons, etc.  The one I made was (I think) the
truncated rhombidodecahedron (or something like it).  The teacher had a
book full of scores of different solids, photographs of models of each of
them, and pertinent information on their construction (e.g., number of
each type of polygonal face).  Students decided on one model they wanted
to make, and then made a test case using manila folder paper.  After 
finishing that, they went on to the final model.

I don't remember any associated activities that our teacher had us do.
However if a student in the class decides on a model requiring pentagons,
hexagons, or shapes with even more sides, then he/she will have to learn
about constructing these polygons geometrically with protractor and ruler.
(Or maybe even compass and ruler for even more fun.)  Related activities
could include calculating the total surface area of the solid; or verifying
relations between number of sides, number of edges, and number of vertices
on the Pythagorean solids.

I hope this helps.

>--  
>uucp: uunet!m2xenix!puddle!381!89!Carol.Hooper
>Internet: Carol.Hooper@f89.n381.z1.fidonet.org


-- 
*Ka Chun Yu               * Center for Astrophysics and Space Astronomy       *
*kachun@spot.colorado.edu * Astrophysical, Planetary, and Atmospheric Sciences*
*         --or--          * University of Colorado,  Boulder, CO 80309        *
*kachun@vela.colorado.edu * (303) 492-6857                                    *
From: Carol.Hooper@f64.n381.z1.fidonet.org (Carol Hooper)
Newsgroups: k12.ed.math
Subject: RE: DOING HOMEWORK IN SCH
Date: Sat, 12 Dec 92 20:03:30 PDT
Organization: FidoNet node 1:381/64 - Academy K12 Net, El Paso TX

Yes, no doubt......5% would benefit us more.  In addition, I really go 
for the idea that homework is the place to "work out the bugs," make 
mistakes and develop an understanding of the work.  I think the grade 
should be primarily for the effort, rather than for the correct 
answer.  Our school district is really working with the site-based 
management idea and I'm wondering how a fledgling like myself could 
get the "ears" to get them to consider changing the percentage for 
Math homework.  Yes, BTW, it is cross-curriculum which means that 
someone didn't think through the subject matter very well.  I will 
mention it to my dept. chair and see what reaction I get.  As he is 
more traditional, I don't hold my breath.  However, I guess I won't 
know till I try.  It certainly is the cause for a student's failure -- 
those zeros at 50% kill you, as you well know.  Plus it encourages the 
teacher to disregard low homeworks and only count "high" (average 
wise) homeworks.......Well, incentives for homework would be a real 
nice thing to have..............let me know.
Currently, I use my cooperative groups as incentive.  If everyone 
brings theirs in, the entire group receives an additional 2 to 5 
points depending on the difficulty and length of the assignment.  I 
would love more.  Thanks


--  
uucp: uunet!m2xenix!puddle!381!64!Carol.Hooper
Internet: Carol.Hooper@f64.n381.z1.fidonet.org
From: Carol.Hooper@f64.n381.z1.fidonet.org (Carol Hooper)
Newsgroups: k12.ed.math
Subject: Re: DOING HOMEWORK IN SCH
Date: Sat, 12 Dec 92 20:12:46 PDT
Organization: FidoNet node 1:381/64 - Academy K12 Net, El Paso TX

An interesting thought.  You know, people may think I'm off (probably 
already do, :-)!) but I can't complete Math activities "cold."  
Instead I must "warm up" by practicing first, getting in gear, etc.  
Then, it seemed easier when I was in Math-Mode.  So your idea has 
merit.  Can you address the frustration idea though?  For instance, 
let's assume (I'll use my grade level students 7/8th) that the student 
is lost...no idea as it is new material so they become frustrated and 
sit for the 10 minutes gazing into the sky despite repeated prompts 
from the instructor....how would you motivate the student to give it 
the ole' school try?


--  
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Internet: Carol.Hooper@f64.n381.z1.fidonet.org
From: Lisa.Hatch@f680.n260.z1.fidonet.org (Lisa Hatch)
Newsgroups: k12.ed.math
Subject: Re: Technology And Math
Date: Tue, 15 Dec 92 17:59:00 PDT
Organization: FidoNet node 1:260/680 - Gananda Central Sch, Walworth NY



 > I am presently using the Geometry Supposer software -
 > published by Sunburst
 > and developed by Judah Swartz at ETC (Educational Technology
 > Center) at the
Hi there!  Your project looks interesting.  Can you send me more 
information?  My address is Gananda Central School Richard Mann 
Elementary Building, P.O. Box 609, Macedon, NY  14502.  Many thanks, 
Lisa

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Internet: Lisa.Hatch@f680.n260.z1.fidonet.org
Newsgroups: k12.ed.math
From: Carol.Hooper@f64.n381.z1.fidonet.org (Carol Hooper)
Newsgroups: k12.ed.math
Subject: re: Geometric Constructions
Date: Sat, 12 Dec 92 20:11:33 PDT
Organization: FidoNet node 1:381/64 - Academy K12 Net, El Paso TX

Thank you for responding.  Can you explain how you "sewed" them into 
the muslin.  I'm trying to get a good picture of what sounds like a 
fascinating activity.


--  
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Internet: Carol.Hooper@f64.n381.z1.fidonet.org
From: Andrew.Probert@f20.n772.z3.fidonet.org (Andrew Probert)
Newsgroups: k12.ed.math
Subject: Re: imaginary numbers
Date: Sun, 13 Dec 92 21:02:10 PDT
Organization: FidoNet node 3:772/20 - IBM NZ Ltd Gate, Auckland

Hi, Russell. I hope you don't mind me butting in here.
Your question is a very good one. In fact I would encourage you to continue asking such questions since they are at the heart of what maths is all about, i.e. a language of symbols which do not necessarily have to have any inherent meaning. You see in maths, at least in my opinion, it is the relationship between the symbols and the patterns that they create that contain most of the meaning and not the symbols themselves. 
To attempt to answer your question

 RL>  I just finished reading your letter and decided that I would ask you
 RL> the question that my teacher didn't care to explain. What is an
 RL> 'imaginary number'? How can you get the square root of a negative
 RL> number? 

Essentially   i or the square root of minus one has no inherent meaning. Instead it represents an unknown which is implied by certain mathematical rlationships. For example, to solve for the roots of certain types of quadratic equations we assume the existance of  i or i-squared. We can then say certain things about the behaviour of such equations or functions, such as that they exhibit oscillation patterns, without necessarily being able to say anything about the imaginary ellement itself.
I'll pose you another tricky questiowhich is central to modern math.
What exactly does the zero symbol mean, and can the concept of complete absence have any inherent meaning in the real world? The answer is not a simple yes. In fact arguably the zero symbol has no inherent meaning. It simply helps mathematicians represent certain types of relationships they would not otherwise be able to represent.
Anyway, Russell think about what I have said. There is no reason why you have to agree with me... It is by disagreement that we learn.
Perhaps you can think of other examples of maths symbols that don't appear to have any inherent meaning.

P.S. I am no a teacher. In fact I am a student of economics at university in New Zealand, attempting to understand the world of maths just like you.

Anyway, bye for now,    Andrew


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From: Sheila.King@f315.n103.z1.fidonet.org (Sheila King)
Newsgroups: k12.ed.math
Subject: GEOMETRY CONSTRUCTIONS   
Date: Mon, 14 Dec 92 18:11:00 PDT
Organization: FidoNet node 1:103/315 - Castle of the Four , Diamond Bar CA

Howard,

Thanks for your reply about constructions.

-> because of two more advanced theorems of geometry and the nice
-> connections between Euclidean contructions and transformations,
-> especially inversion.  The two theorems are the Mohr-Mascheroni
-> Construction Theoerem and the Poncelet-Steiner Construction Theorem.

Whooosh! Those whizzed right by me ;-) I am not in the least familiar
with those two theorems.

I appreciate that students may sometime encounter these types of things
in the study of higher math *if* they go on to it. But I wonder how much
time and frustration should the class as a whole spend on classic
construction given that the likelihood any one of the students in the
class would study such material is very small. (Remember, it is an
average ablility course).

Still, I am not having an easy time deciding on this one (or I wouldn't
have asked the question). Besides which, I don't think that I alone have
the decision to make. There are four other geometry teachers at the
school who will have some say in this.

Rick Heptworth, the guy who wrote the Mira booklet which I plugged in a
recent message, seemed quite comfortable with the idea of discarding the
traditional construction methods. However, he does use compasses in his
class for drawing circles and measuring congruent segments. Perhaps
simply by using the tools in this way they would get a sense of
familiarity with them so that the theorems you mentioned above would not
be too difficult for them to understand.

-> It would be useful and beneficial to students to explore the
-> equivalence of constructions they perform with "patty papers" and the
-> same constructions with compass and straight-edge.  For example,
-> constructing a perpendicular bisector.

THIS is something that I had considered previously. I am very certain
that I will do at least *some* such things with my honors classes. I
wonder how the other teachers will feel about trying to get the more
average students to work on seeing that kind of equivalence.

-> Please keep us informed, Sheila, as you struggle with revising and
-> reforming your geometry curriculum.  I'd certainly like to hear how
-> the students react to it.

Will do.

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

--  
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Internet: Sheila.King@f315.n103.z1.fidonet.org
From: Sheila.King@f315.n103.z1.fidonet.org (Sheila King)
Newsgroups: k12.ed.math
Subject: RE: TEN QUESTIONS        
Date: Sat, 12 Dec 92 10:29:00 PDT
Organization: FidoNet node 1:103/315 - Castle of the Four , Diamond Bar CA

To: Stuart W. Marlatt

In a message to a student who asked about an explanation of imaginary
numbers you said:

-> Complex analysis is also a means by which all those bizarre integral
-> solutions you see in the back of your calculus book may be derived.
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

I think you were replying to a high school student who is not anywhere
near taking calculus (<grin>)

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

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From: Jerry.Saville@f2051.n147.z1.fidonet.org (Jerry Saville)
Newsgroups: k12.ed.math
Subject: FACILITATION?
Date: Fri, 11 Dec 92 12:26:00 PDT
Organization: FidoNet node 1:147/2051 - The O.U. BBS, Norman OK

 -=> Quoting Dover-sherborn High Schoo to All <=-


 DHS> I'm a 7-12 math teacher at Dover-Sherborn Regional Schools in
 DHS> Dover,MA. 
 DHS> Using the Geometry Supposer at the high school and involved in a
 DHS> telecommunication project (on Peacenet) in the junior high school.

I saw the Geometry Supposer mentioned in a Geometry class that I observed
just today. I am a student at Southern Nazerene University in Bethany Okla.
and am studying to be a middle school teacher. Do you use the computer much
in your classroom? Does every math teacher have one? Is the program part
of a package (can I get a copy without buying it, or is it copy wrighted)?
Is it helpful in teaching?
       Just thought I'd drop you a line!
                  thanx


... My other computer is a VAX.
___ Blue Wave/QWK v2.11


--  
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Internet: Jerry.Saville@f2051.n147.z1.fidonet.org
From: Dover-Sherborn High School <doversherhs@igc.apc.org>
Newsgroups: k12.ed.math
Date: 12 Dec 92 13:03 PST
Subject: Re: pre-algebra ideas...
Nf-ID: #R:1992Dec11.203952.1@vax1.umkc.edu:-551423179:cdp:1550000006:000:522
Nf-From: cdp.UUCP!doversherhs    Dec 12 13:03:00 1992


Scott - The Addenda Series from NCTM has some very good pre-algebra 
problems - the Addenda Series (in case you don't know) is a series of
booklet published by NCTM on various topics - ie. Dealing with Data and Chance
-Developing Number Sense in the Middle Grades-Geometry in the Middle Grades-
Patterns and Functions-Understanding Rational Numbers and Proportions - to 
name a few - they are about 18-20 dollars each.



NCTM - 1906 Association Drive, Reston, Virginia 22091 - they have an 800 #.

Hope they help.

Keith
From: Dover-Sherborn High School <doversherhs@igc.apc.org>
Newsgroups: k12.ed.math
Date: 17 Dec 92 18:02 PST
Subject: IBM Uploading Procedure
Nf-ID: #N:cdp:1550000007:000:285
Nf-From: cdp.UUCP!doversherhs    Dec 17 18:02:00 1992


This is Keith (doversherhs.@igc.apc.org) -

Could anyone help me with IBM procedures ... I have a MAC?  What I would
like to know how to do is take a message from word processing and send it
on e-mail.  Uploading, I believe?   

Thanks in advance for anyone's help.

Take care.

Keith
Newsgroups: k12.ed.math
Subject: pre-algebra ideas...
From: rbeaudoin@vax1.umkc.edu
Date: 11 Dec 92 20:39:52 CST
Organization: University of Missouri - Kansas City
NNTP-Posting-Host: vax1.umkc.edu


	Hi there -- i am a long-term sub at Fort Osage
Junior High in Independence, MO, looking for some good ideas
in pre-algebra for some very disciplined students.... 

Scott Bounds

RBEAUDOIN@VAX1.UMKC.EDU
Newsgroups: k12.ed.math
From: marlatt@spot.Colorado.EDU (Stuart W. Marlatt)
Subject: Re: TEN QUESTIONS        
Organization: University of Colorado, Boulder
Date: Mon, 14 Dec 1992 23:39:06 GMT

In article <29306.2B2B0A06@puddle.fidonet.org> Sheila.King@f315.n103.z1.fidonet.org (Sheila King) writes:
>To: Stuart W. Marlatt
>
>In a message to a student who asked about an explanation of imaginary
>numbers you said:
>
>-> Complex analysis is also a means by which all those bizarre integral
>-> solutions you see in the back of your calculus book may be derived.
>
>I think you were replying to a high school student who is not anywhere
>near taking calculus (<grin>)
>
>Sheila
>coming to you from Diamond Bar, CA (in Los Angeles County)

Sorry about that - sometimes I forget where I am. (In fact, although
I follow this newsgroup, I'm not currently actively involved in
education (from the distribution side, anyway). My wife does teach,
so that is my k12 interest.

A related question, however. How many high school students _do_ take
calculus? We had a intro-calc class in my school (I didn't take it -
didn't make the cut), but I get the idea that many schools don't offer
this. In contrast, many of the foreign students I have had the priviledge
to know during graduate school seem to consider calculus a typical
high school math course.

I read a quote recently (and forget who said it), from an early 
educator (circa 1350?) who considered arthimatic to be rather advanced
for the general public, and that while it should be offered in schools,
only the 'cream of the students' would take it. Of course, we now
see it taught from kindergarten, at some level, and most students get
algebra, geometry, and maybe some trig. Is the day coming when the
majority of students will get a taste of calculus before leaving
high school?


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