Date: Mon, 15 Jul 1996 05:13:17 -0700
From: smitty2@ix.netcom.com (Donald W. Smith )
Subject: Institute
To: geometry-institutes@mathforum.org
Status: RO
Hello, everyone!
I am very excited to be a part of this program. I am looking forward
to a week filled with teaching ideas and exchanges with other math
educators. I am a sixth grade teacher at South Orange Middle School in
South Orange, New Jersey. Yes, that's the hometown of the Seton Hall
Pirates!! I am also looking forward to making some new friends and
mathematical connections.
Sincerely,
Karen Smith
smitty2@ix.netcom.com
Date: Mon, 15 Jul 1996 10:14:15 -0400
X-Sender: sandyshe@mail.snet.net
Mime-Version: 1.0
To: geometry-institutes@mathforum.org
From: sandyshe@SNET.Net (Sandy Sherman)
Subject: Middle School: Geometry/Math Concepts Using Art/Draw Programs
Hi,
I teach eighth grade at East Shore Middle School in Milford, Connecticut.
You can find out about some of my interests by visiting:
http://mathforum.org/workshops/sum96/sherman.sum96.html
This upcoming year, with my math students (all four levels, since we group
homogeneously in the eighth grade for mathematics), I want to focus on
buiding a conceptual understanding of geometry and mathematical concepts
using drawing programs. I plan on writing a series of math lessons which
are easily understood by middle school and elementary school teachers. I
will implement these lessons weekly with my classes using my powerbook
which will be connected to a large TV monitor I have purchased for every
day instruction in my eighth grade mathematics classroom. I will also test
these individual lessons in the field with my computer club students.
Interested students will create transparencies of their own
work/discoveries which I will print using an inexpensive Color Stylewriter
printer. The transparencies, along with a written report done by the
student (can be used as assessment), will be displayed in a central
location for parents, teachers and administrators at the end of the school
year. Interested parents will be called in to assist me in the discovery
type lab sessions I will conduct with students. In this way parents will
learn what we are doing and be available to assist me in managing to help
students in a lab setting where lots of individual interaction/attention is
needed. At the end of the year, if I can manage to save for a thermal
wax-dye sublimination printer, students can create mathematical t-shirts
and/or mugs of their perfected refined work. This will be a reward for
their year long efforts. One of our textbooks is entitled, "Integrated
Mathematics". These activities will supplement, reinforce and enhance
units of study (actually, chapters) from the text book. I really want ALL
levels of students to participate/gain from these experiences. Therefore,
I will be working on basic concepts (fractions, percents, decimal and so
on) in addition to more advanced topics for higher functioning eighth
graders.
I am interested in speaking to or writing to people who have interests
along these lines. My email address is:
sandyshe@snet.net
I have had a lot of family needs/commitments to address lately, but I am
going to try to participate in some of the on-line events.
I hope everyone has a good time.
Sandy Sherman
%+++---***///(){}[]<>!+++---***///(){}[]<>!+++---***///(){}[]<>!%
"Imagination is More Important Than Knowledge." Albert Einstein
Sandy Sherman
Mathematics/Technology
4640 Main Street
Stratford, CT 06497
(203) 378-9154
sandyshe@snet.net
%+++---***///(){}[]<>!+++---***///(){}[]<>!+++---***///(){}[]<>!%
Date: Mon, 15 Jul 1996 11:23:23 -0400 (EDT)
From: Suzanne Alejandre
To: geometry-institutes@mathforum.org
Subject: Middle School Activities - Things we're doing:
Things we're doing: This morning we are getting organized in the Lab. So far my thoughts to
get started on the Middle School activities include
1. Going through pages and looking for areas that could be enlarged.
The places I have found so far include
a. adding historical links to the tessellation pages (Islamic)
b. adding geographical links to the tessellation pages (Spain, Middle
East)
c. LogoWriter
d. creating a coloring activity to go with
http://mathforum.org/alejandre/magic.square/ben.lines3.html
e. adding to the factoring pages
http://mathforum.org/alejandre/factor1.html
2. Instead of adding to the factoring pages...try to think of a
series of thoughts in algebra and create a large area that presents
those algebraic thoughts geometrically with activities that would
be fun. [If you find that confusing :) it is because I am not
at all clear on that idea!]
3. One activity that would be fun to start with would be the
Coloring Activity. If you could look at
http://mathforum.org/alejandre/magic.square/ben.lines3.html
and think of how that could be colored to highlight the symmetry
that you see in the drawing...perhaps we could write questions
(covering a wide range of student abilities) to go along with
the activity.
>From the messages posted this morning to the Middle School group of
Geometry Institutes I see both Karen Smith's and Sandy Sherman's!
I am looking forward to your ideas.
Suzanne
Date: Mon, 15 Jul 1996 14:10:10 -0400 (EDT)
From: Suzanne Alejandre
To: geometry-institutes@mathforum.org
Subject: Middle School Activities - Things we're doing:
Things we're doing: I added my first page! It is the Spanish version of the Lo Shu and the
Story of Emperor Yu. It can be found by going directly to
http://mathforum.org/alejandre/magic.square/spanish.loshu2.html
Do any of you have students that read in Spanish?
Date: Mon, 15 Jul 1996 12:30:40 -0700
From: smitty2@ix.netcom.com (Donald W. Smith )
Subject: Middle School
To: geometry-institutes@mathforum.org
Dear Suzanne,
I was looking through your magic square pages the other night. I
thought about some sort of correlating art activity with that Ben
Franklin magic sqaure also. It almost reminds me of one of those name
"scribble" desgins that I often have my students do on the first day of
school. In language arts, they can also write a creative piece to go
with their design. (There's an integration for math and language
arts!!) I was also interested in finding out some background
information about that piece of art entitled "Parataxis." It was very
intriguing.
I also thought of something else since posting my last e-mail. Another
way of approaching the "coloring" could be like map-coloring where no
two borders that touch can be colored in the same color. Challenge the
students to color the design with as few colors as possible!!
While visiting the Metropolitan Museum of Art, I picked up a teacher's
resource folder that dealt with patterns in Islamic art. I would be
glad to share any of that information if you are interested. It's
available from the museum for purchase for approximately $15.00 and
it's a terrific resource.
Karen
smitty2@ix.netcom.com
Date: Mon, 15 Jul 1996 16:03:22 -0400 (EDT)
X-Sender: wheelock@mailhost.shore.net
Mime-Version: 1.0
To: sandyshe@SNET.Net (Sandy Sherman),
geometry-institutes@mathforum.org
From: wheelock@shore.net (Anne Wheelock)
Subject: Re: Middle School: Geometry/Math Concepts Using Art/Draw Programs
Hi, Sandy. I was wondering if you could tell us a little about how your
teaching and learning goals - and the way you implement these in your
curriculum, materials, assignments, etc. - will be different for your four
different classes of students. I am especially interested because I've been
trying to figure out how NCTM standards-based learning in the middle grades
actually varies from group to group. Thanks so much! Anne
At 10:14 AM 7/15/96 -0400, Sandy Sherman wrote:
>Hi,
>
>I teach eighth grade at East Shore Middle School in Milford, Connecticut.
>You can find out about some of my interests by visiting:
>
>http://mathforum.org/workshops/sum96/sherman.sum96.html
>
>This upcoming year, with my math students (all four levels, since we group
>homogeneously in the eighth grade for mathematics), I want to focus on
>buiding a conceptual understanding of geometry and mathematical concepts
>using drawing programs. I plan on writing a series of math lessons which
>are easily understood by middle school and elementary school teachers. I
>will implement these lessons weekly with my classes using my powerbook
>which will be connected to a large TV monitor I have purchased for every
>day instruction in my eighth grade mathematics classroom. I will also test
>these individual lessons in the field with my computer club students.
>Interested students will create transparencies of their own
>work/discoveries which I will print using an inexpensive Color Stylewriter
>printer. The transparencies, along with a written report done by the
>student (can be used as assessment), will be displayed in a central
>location for parents, teachers and administrators at the end of the school
>year. Interested parents will be called in to assist me in the discovery
>type lab sessions I will conduct with students. In this way parents will
>learn what we are doing and be available to assist me in managing to help
>students in a lab setting where lots of individual interaction/attention is
>needed. At the end of the year, if I can manage to save for a thermal
>wax-dye sublimination printer, students can create mathematical t-shirts
>and/or mugs of their perfected refined work. This will be a reward for
>their year long efforts. One of our textbooks is entitled, "Integrated
>Mathematics". These activities will supplement, reinforce and enhance
>units of study (actually, chapters) from the text book. I really want ALL
>levels of students to participate/gain from these experiences. Therefore,
>I will be working on basic concepts (fractions, percents, decimal and so
>on) in addition to more advanced topics for higher functioning eighth
>graders.
>
>I am interested in speaking to or writing to people who have interests
>along these lines. My email address is:
>
>sandyshe@snet.net
>
>I have had a lot of family needs/commitments to address lately, but I am
>going to try to participate in some of the on-line events.
>
>I hope everyone has a good time.
>
>Sandy Sherman
>
>%+++---***///(){}[]<>!+++---***///(){}[]<>!+++---***///(){}[]<>!%
>
>"Imagination is More Important Than Knowledge." Albert Einstein
>
>Sandy Sherman
>Mathematics/Technology
>4640 Main Street
>Stratford, CT 06497
>(203) 378-9154
>sandyshe@snet.net
>
>%+++---***///(){}[]<>!+++---***///(){}[]<>!+++---***///(){}[]<>!%
>
>
>
Anne Wheelock
wheelock@shore.net
Boston, Massachusetts, USA
Date: Mon, 15 Jul 1996 17:34:05 -0500 (CDT)
X-Sender: lanius@cml.rice.edu
Mime-Version: 1.0
To: sseasto1@swarthmore.edu (Sarah Seastone),
Suzanne Alejandre
From: lanius@cml.rice.edu (Cynthia Lanius)
Subject: Re: Spanish Lo Shu
I have Spanish speaking students who would be happy to help translate, after
August 19 that is.
At 03:11 PM 7/15/96 -0400, Sarah Seastone wrote:
>Yo -
>
>I've done some light editing on the Spanish version. It's not quite good
>Spanish yet but I'd need to use my big thick dictionary to make it elegant,
>and this is probably good enough. Was the person who translated it into
>Spanish a native speaker? (Because it doesn't quite read as if it's done
>by a native.)
>
>I put
>
>Traducido del ingl&ecute;s por Georgette Baker
>
>at the top of the page. Okay?
>
>Your faithful editor,
>
>- Sarah
>
>>Things we're doing: I added my first page! It is the Spanish version of
>>the Lo Shu and the
>>Story of Emperor Yu. It can be found by going directly to
>>
>>http://mathforum.org/alejandre/magic.square/spanish.loshu2.html
>>
>>Do any of you have students that read in Spanish?
>
>
>
>
*********************************************************************
Cynthia Lanius,
Program Manager
CRPC GirlTECH
visit http://cml.rice.edu/~lanius
http://www.crpc.rice.edu/CRPC/Women/GirlTECH
Date: Mon, 15 Jul 96 19:17:54 EDT
Mime-Version: 1.0
To: geometry-institutes@mathforum.org
From: dmiller@pcnet.com (Denise Miller)
Subject: Middle School: Geometry/Math Concepts Using Art/Draw Programs
>> I want to focus on
>>buiding a conceptual understanding of geometry and mathematical concepts
>>using drawing programs....Sandy Sherman
FANTASTIC TECHNOLOGY. Powerbook ... TV monitor ... Color STylewriter ...
I love it.
Denise Miller, who has been dreaming up ways to get a PowerBook for over a
year (don't ask me what I've already bought ...)
Cheshire High School
Cheshire, CT
To: geometry-institutes@mathforum.org
Date: 15 Jul 1996 19:25:08 -0400
From: salejan@empirenet.com (Suzanne Alejandre)
Organization: Math Forum
Sender: geometry-institutes-owner@mathforum.org
Subject: Re: Middle School
Hi Karen,
When you think of the Ben Franklin line design, can you write some
prompts if the students were to use it during a language arts
lesson?
If you find out any interesting background information on
Parataxis that would be great!
Yes, the idea of considering this as a map coloring problem was
something I thought of too....but...if you look at the design you
will see that there are two separate parts to the page.
I wonder if the Metropolitan Museum of Art is on the Web - even
more fun would be if the resource folder is on the Web?
Suzanne
From: anne_d._sandler@shhs1.ccsd.k12.co.us (anne d. sandler)
Reply-To: anne_d._sandler@shhs1.ccsd.k12.co.us
To: lanius@cml.rice.edu
Cc: sseasto1@swarthmore.edu, geometry-institutes@mathforum.org
Subject: Re: Re: Spanish Lo Shu
Date: 16 Jul 1996 01:08:50 GMT
Organization: shhs1
do you mean Spanish as a first language for the student or students who are
studying spanish and might be interested?
To: geometry-institutes@mathforum.org
Date: 15 Jul 1996 21:31:09 -0400
From: salejan@empirenet.com (Suzanne Alejandre)
Organization: Math Forum
Sender: geometry-institutes-owner@mathforum.org
Subject: Re: Math Buddies for students in grades 4/5
In article <960715185431_434825089@emout18.mail.aol.com>,
CHender403@aol.com wrote:
Hi Carolyn,
> Also, I looking for ideas for a math club next year with math activities
>using the internet. Anxiously waiting a response. Thank you.
You might like some of the ideas from the Web pages that I have
been developing this year. I have one on Tessellations and another
on Magic Squares - both are rather engaging activities.
Please look at the pages
http://mathforum.org/sum95/suzanne/tess.intro.html
or
http://mathforum.org/alejandre/magic.square.html
and then let me know if you think that they would be appropriate
as math club activites.
Suzanne
To: geometry-institutes@mathforum.org
Date: 15 Jul 1996 21:31:09 -0400
From: salejan@empirenet.com (Suzanne Alejandre)
Organization: Math Forum
Sender: geometry-institutes-owner@mathforum.org
Subject: Re: Spanish Lo Shu
In article <199607152234.RAA13148@cml.rice.edu>, Cynthia Lanius
(lanius@cml.rice.edu) wrote:
>I have Spanish speaking students who would be happy to help translate, after
>August 19 that is.
Hi Cynthia,
That would be super! We will keep in touch. I think that it would
be great to have different sections of my pages translated -
probably just start with the pages that the students find
interesting to translate.
Thank you,
Suzanne
Date: Mon, 15 Jul 1996 21:04:11 -0500 (CDT)
X-Sender: lanius@cml.rice.edu
Mime-Version: 1.0
To: anne_d._sandler@shhs1.ccsd.k12.co.us
From: lanius@cml.rice.edu (Cynthia Lanius)
Subject: Re: Re: Spanish Lo Shu
Cc: sseasto1@swarthmore.edu
Both actually. I teach in Houston, Texas at a school that is 80% Mexican
American.
At 01:08 AM 7/16/96 GMT, anne_d._sandler@shhs1.ccsd.k12.co.us wrote:
>>do you mean Spanish as a first language for the student or students who are
>studying spanish and might be interested?
>
>
*********************************************************************
Cynthia Lanius,
Program Manager
CRPC GirlTECH
visit http://cml.rice.edu/~lanius
http://www.crpc.rice.edu/CRPC/Women/GirlTECH
From: adler@pulsar.cs.wku.edu (Allen Adler)
Subject: Re: Spanish Lo Shu
To: geometry-institutes@mathforum.org
Date: Mon, 15 Jul 1996 21:22:45 -0500 (CDT)
MIME-Version: 1.0
As Suzanne Alejandre correctly points out, there are variations
in spanish usage from one country to another. However, another
point might be that mathematics has its own special usage and
merely being a native speaker does not necessarily imply mastery
of mathematical writing style. Mathematics is in effect another
language that needs to be rendered by a native speaker.
Allan Adler
adler@pulsar.cs.wku.edu
To: geometry-institutes@mathforum.org
Date: 16 Jul 1996 09:47:55 -0400
From: salejan@empirenet.com (Suzanne Alejandre)
Organization: Math Forum
Sender: geometry-institutes-owner@mathforum.org
Subject: Re: Re: Spanish Lo Shu
In article <80539614.63841695@shhs1.ccsd.k12.co.us>, anne d. sandler
(anne_d._sandler@shhs1.ccsd.k12.co.us) wrote:
>>do you mean Spanish as a first language for the student or students who are
>studying spanish and might be interested?
Either one would be fine. Actually I had been thinking of students
that would have Spanish as their dominant language...but...it is
just as valid to consider students who are interested in practising
their reading in Spanish.
Thanks for the idea! Anne.
Suzanne
To: geometry-institutes@mathforum.org
Date: 16 Jul 1996 10:13:49 -0400
From: salejan@empirenet.com (Suzanne Alejandre)
Organization: Math Forum
Sender: geometry-institutes-owner@mathforum.org
Subject: Re: Spanish Lo Shu
Lou's point is well taken. In quoting the translator I was trying
to show what her point of view was ... it really isn't my point of
view (which perhaps I didn't really clarify). As Lou states, the
translators who are native speakers of both English and Spanish
would be difficult to find. Then throw in the thoughts that that
person should be familiar with mathematical concepts in both
languages
and writers and you probably would have no translations! :)
My hope is that translations will be done which allow more access
to students who can read Spanish ... maybe as the "stories" or
directions are read there will be feedback that improves the
translations. So, the Emperor Yu story in Spanish is up ... and
the revisions will begin!
Suzanne
In article <9607160521.AA22423@talmanl.mscd.edu>, Lou Talman
(me@talmanl.mscd.edu) wrote:
>Suzanne Alejandre wrote:
>
>> only native speakers should do translations
>
>(quoting a translator as she did so).
>
>An interesting idea. Native speaker of *which language*? If only
>one of the two, why the bias? If both, then translators are gonna be
>hard to find.
>
>--Lou Talman
> Department of Mathematical & Computer Sciences
> Metropolitan State College of Denver
Date: Tue, 16 Jul 1996 08:37:14 -0700
From: smitty2@ix.netcom.com (Donald W. Smith )
Subject: Middle School
To: geometry-institutes@mathforum.org
Good morning!
Here are the answers in repsonse to the questions you posed--
#1. The only real writing prompt I use for the language arts lesson is
that when the students' name designs are completed (and they are
symmetrical designs -reflection symmetry) they do tend to resemble
"aliens." I tell the students to make up a story about their
character; ie. give it a name, what planet they're from, etc. and the
students take it from there.
#2. Couldn't the Ben Franklin designs be colored individually? Or,
each piece be done to be a reflection of the other? Or make each half
of each desgin symmetrical to each other? From there, make each piece
a reflection of one another?
#3. There is a web site for the Metropolitan Museum. The URL is
http://www.metmuseum.org. You can reach the gift shop by using the URL
http://www5.metmuseum.org. I looked at both of these areas and
unfortunately the publication I am referring to is not featured at this
time. I guess it would be impossible for them to include all of their
items. There was a toll-free # 1-800-468-7386. Let me know if you
need any other information regarding this material. I have a copy of
it in my personal library.
Hope these are of some help!
Karen Smith
smitty2@ix.netcom.com
From: adler@pulsar.cs.wku.edu (Allen Adler)
Subject: math and language arts
To: geometry-institutes@mathforum.org
Date: Tue, 16 Jul 1996 04:13:35 -0500 (CDT)
MIME-Version: 1.0
Status: RO
One poster has mentioned his interest in language arts and has
apparently taken an interest in the crossword called the Sator
Magic Square in this connection. In a separate discussion, the
difficulties of translating mathematics written in English into
mathematics written in Spanish has come up.
I would like to elaborate on my comment, in the latter discussion,
about mathematics being a language and see where it leads from the
standpoint of language arts.
Topic 1: Mathematical idiom
If you show someone an open bag of potato chips which still has some
potato chips in it, there are various circumlocutions to describe
it. "You want some chips? There's some left."
A mathematician will simply remark that there is a nonempty bag of
potato chips. The word "nonempty" is typical of mathematical idiom.
It doesn't normally arise in the parlance of nonmathematicians.
There are other key phrases and usages which, even if not unique
to mathematics, are standard mathematical usage which one finds
less often in common parlance. One is "if and only if". Someone
might say, "I'll give you a quarter if you let me copy your
homework." From a logical point of view, it is conceivable that
the quarter will be given even if permission is not granted to
copy the homework, but most likely the student intended the
word if to mean "if and only if".
Another is the tendency of some people to write "We have" before
displaying a formula or a conclusion. E.g., "Combining these two
identities and clearing denominators, we have x=7." or
"After a similar line of reasoning, which we omit here, we
have that the line opposite the largest angle is the largest side."
Another example involves words that mean one thing in English
and something entirely different in mathematics. An advanced
example is "limit" or "compact". But more elementary notions
such as "group" or even "relation" are already different.
One activity is to try to come up with amusing equivocations
that play on the different usages. E.g.,
"A group is a collection of individuals who associate and there
is usually an individual, called the identity element, with the
property that any individual who associates with the identity element
is no longer a member of the group."
I have not even scratched the surface. Anyway, exploring this aspect
of mathematics also involves the language arts.
One source to look at for some informal and formal discussions of
this, look at the discussion of the Dog Walking Ordinance, reprinted
in the Word Of Mathematics from a work of Robert Graves and Alan
Hodge.
Topic 2: Language Decipherment
Take an English speaking student and show him/her some mathematics
written in another language, preferably one with a lot of cognates
with English. There is a tremendous amount of information in whatever
tables or formulas the writing contains. The notation is likely to
be common to speakers of either language and that fact serves
to give the reader some idea of the context of the discussion even
if he/she doesn't know the language in question. Under such
conditions, one can often decipher enough of the language to make
sense of what is going on, even if one can't make a detailed
translation.
One of the pleasant features of decipherment is that one can form
hunches as to what the text actually says, but then one has to
check whether the proposed translation leads to correct mathematics.
Another is realizing that one is staring at a familiar usage
(e.g. if and only if) in a language one has never studied and
now knowing how to say that. In some cases, one might never
know how to look it up.
Topic 3: wff and proof
There is a game which was available when I was in high school
and which I still see advertised sometimes. It involves tossing
dice which have logical symbols on the faces and trying to
arrange them so as to arrive at the longest well formed formula
one can make with those symbols. It was called wff and proof.
This game can be used to illustrate another aspect of mathematics
and language arts.
One can also go further using predicate calculus. (BTW, calculus is another
good example of a word that has different meanings in mathematics
than in common parlance. Sometimes when people ask me what calculus
is, I like to tell them it is a substance found on the teeth of
mathematicians.)
Topic 4: Productions and natural language
I'm sure some very simple examples can be given to students to
illustrate some of the concepts of formal languages. Then one
can explain that similar ideas are being applied to study
natural languages.
One way to introduce the examples might be
as puzzles in which the students, after seeing that the teacher
accepts some strings of symbols and not others, have to guess
the pattern in the acceptable strings. Or a computer, with infinite
time and patience, can do the accepting and rejecting.
It can be pointed out that a computer program is a string of
symbols which the machine will accept or reject and that learning
to program in that language in part involves learning to distinguish
acceptable programs from unacceptable ones.
Similarly, learning a natural language, such as one's native language,
involves learning to recognize which strings of sounds or symbols
are acceptable in that language. Rules of grammar and usage amount
to trying to approach a description of the acceptable strings,
just as in the exercises one did at the beginning.
Maybe another variant would be to introduce "pig latin" or various
other modifications of ordinary speech and to specify or guess
the rules of formation.
Topic 5: Secret codes
Students can make up secret codes and pass notes using them.
Other students can try to decode them. The easiest would
be substitution codes.
This is to some extent a language art. It also involves some
statistical knowledge of the language. It wouldn't hurt to bring
to their attention the existence of such puzzles in the newspapers.
Incidentally, one can also use magic squares to encode secret
messages, although the messages might take up a lot of space.
Allan Adler
adler@pulsar.cs.wku.edu
From: adler@pulsar.cs.wku.edu (Allen Adler)
Subject: Two unfunded issues
To: geometry-institutes@mathforum.org
Date: Tue, 16 Jul 1996 05:10:11 -0500 (CDT)
MIME-Version: 1.0
Status: RO
Among the things I had hoped one would be able to discuss at
this conference are two issues which I have mentioned in the
web pages about me.
The first issue is the *accuracy* of the information one is putting
on the web in the form of web pages. There is a lot of information
on the web but much of it has a wide and, in my opinion, richly
deserved reputation for being unreliable. Why should it be otherwise?
Anyone can put whatever they want on the web.
Mention has been made of the desirability of collecting some good web
pages and making them available to teachers. That is laudable, but
how does one determine what is good? Is it that the pages give one
a warm, fuzzy feeling or the conviction that someone else will
surely want to read them? Or does it have something to do with
going through the documents in detail and checking everything?
The latter activity is much subtler than might appear at first sight.
It involves not only the statements in the pages one is looking at
but also all those in pages that might be linked to the pages one
is looking at, and so on through as many layers of linking as
one can go through. Even if the pages one links to are internally
consistent, they might be based on conventions, definitions or
notation that is inconsistent with those in your pages. In this
case, the standard of accuracy requires one to warn the reader of
any such inconsistencies before referring him/her to the link.
It is much more convenient to link to someone else's pages than
it is to summarize the same information in pages of one's own.
This presents anyone writing web pages with a fundamental
conflict of interests, since one has to weigh whether it is
better to link to the new pages, despite their faults, or to
write one's own summaries, or to do without the information.
In this connection, I think it is also desirable to make as sharp a
distinction as possible between information and advertising and
never to relinquish to a commercial site the right to make that
distinction for one. For example, some companies distribute
their catalogues in the form of web pages and embellish the
pages with some educational materials. It is not ok to just
link to the catalogue when it is a matter of providing the
educational material. One needs some standards to deal with
this kind of situation. I propose:
(1) If at all possible, do not use such material.
(2) If you do use it, ask for permission to make copies of the
html pages for one's own site with the pointers to actual
catalogue information removed (with acknowledgment, of course).
(3) Some readers of educational web pages do want to know about
the availability of products they can use in their classes
and that is a legitimate concern. However, it is best to
avoid implicitly or explicitly endorsing a single company.
It would be ok to have a link to a page describing the
availability of products from various companies and
links to their catalogues clearly identified as such.
(4) This last step further requires that one either investigate
the companies and their products or explicitly state that
their inclusion in the web page does not constitute endorsement.
Now let me turn to the second issue: the status of the old technology
(i.e. books and libraries) in the emerging literature of the new
medium called the world wide web.
As I mentioned above, it is a lot more convenient to surf around the
net looking for links than it is to tear oneself away from the
computer and go to the library to look at books. Even if one can
find a book, to make use of it, one has to extract the information
and make up pages. That is precisely what one would rather not do
if one can avoid it, at least from the standpoint of conservation
of effort. But it is also precisely what one ought to do in most
cases if one wants to make the best information available.
It is an error to assume that the readers of web pages will never
get off their takapoulis and go look at a book. Instead, if there
are excellent reference materials in the form of books, one should
refer to them and provide whatever assistance one can to someone
in going from the web pages to the book.
The web offers real opportunities to make great books better.
How many books have good things to say but lack indexes or
other user friendly features? Now, you can make up an index
for your own use and make it available to others in the form
of web pages. If you present some information based on a book,
by all means give page references to the book. If the book uses
different notation or somewhat different definitions, by all
means point this out.
The standards I have just described, and only partially described,
are in conflict with another accepted standard: the standard
according to which it is ok to put out inaccurate or deficient
information because the document is intended to be read only
by a teacher preparing a class and neither the teacher nor the
class will require that level of detail. This is an unfortunate
standard to adopt.
Let us try to remember what the purpose of descriptions of Classroom
Activities ought to be. We have a teacher, often with more credits
in education than in the subject he/she is assigned to teach. Often
these teachers are so overworked with lesson plans and grading and
administrative duties that they really don't have much time to spend
on developing new ideas for topics and investigating them thoroughly.
Assuming the teacher would otherwise be capable of such an effort
(which is not a valid assumption in many cases), it is certainly
convenient to be able to use a ready made lesson plan one can download
from a web site. But in many cases, the information contained n
the web pages will be all of the information that the teacher will
have on the topic. In that case, it is unforgivable to have anything
less than complete accuracy. It is simply not acceptable for the
teacher not to learn the topic at a much higher level than the
students do. In the past, we complained that students were ducking
their scholarly obligations by reading Cliff notes (or Barrons, or
whatever) instead of the classic literature that had been assigned
to them. Are we now to turn around and say that it is the teachers
who are supposed to read the Cliff notes to prepare their classes?
The mere fact that the web pages serve a utilitarian function
does not excuse us from the highest, or even the ordinary standards
of scholarship.
I have described these issues as unfunded because as nearly as
I can tell, they are. People apply for grants to produce something
that a funding agency can accept as a tangible result. A lesson
plan. A new course. A new communications gimmick. Having done so,
the matter is closed as long as no one shows up in the office with
pitchforks. Who is checking on the accuracy? Who is making sure that
the new gimmick is not used as such a fetish that its integration
into existing modes of communication and learning are not neglected?
One of the useful features of the internet, and also one of its
dangers, is that whatever one puts together in the way of web pages,
or other distributed materials (remember ftp?) is accessible to
tens of millions of netcrawlers. Formerly, when a teacher made an
error in a lesson plan, only a few dozen students were affected.
Now the same lesson plan can wind up in thousands of schools.
Well, it is nice that one can change the error as soon as one knows
about it. But as nearly as I can tell, people do not take pains
to keep track of version numbers. If a book has an error, one
can change it in the next edition, if there is a next edition.
And the next edition will be marked as the 2nd edition or the 3rd
edition, to distinguish it from earlier ones. The same is done with
software. You buy release 1.01 of your favorite software, you find
out it has a bug, you want for them to fix it and sell you the
software all over again as release 1.02 of the software. A system
is in place to keep track of changes.
There is nothing so new or so special about web pages that they
ought to be exempt from the sensible practice of keeping track
of changes by recording version numbers and keeping a log of
the changes.
There is a lot more to say, but I think this is a good place to stop
and let others have their say.
Allan Adler
adler@pulsar.cs.wku.edu
Date: Tue, 16 Jul 1996 15:26:46 -0400 (EDT)
X-Sender: keithk@mathforum.org
Mime-Version: 1.0
To: salejan@e2.empirenet.com
From: Keith Keyser
Subject: Magic Squares
Suzanne:
I do teach, but not mathematics. I am a social studies teacher from
Marple Newtown High School, about nine miles from Swarthmore College. I
attended the workshop back in the spring of 1994, and have been an avid user
of the internet since then. While I have spent a great deal of time with
the listserv mail lists, I have been focusing on the Netscape browser for
these last 7-9 months. What a treasure drove of information.
Anyway, I saw your E-mail to me and went to check out what you have
on the www. I specifically was interested in the Magic Square activities,
since my teaching deals with European history specifically. The Middle Ages
and Renaissance are integral parts of what I teach, and I try to insert the
cultural aspects of history as much as can be done. So the use of Albrecht
Duerer, the Italian Middle Ages, and the Lo Shu (our 9th grade non-western
cultures classes) activities are golden opportunities for not only
enrichment for my classes, but allow us cross-curricular opportunities as well.
The material I was testing was teriffic! ;o) I am just now in the
process of designing web pages, and am using various and sundry materials I
purchased. There seems to be no simple way to do this, but I am making
progress. I hope to design a web page for the Pennsylvania Council for the
Social Studies this year, giving information about the council and sharing
links to valuable resources on the www. I would like to be able to place
your Magic Squares in our cross-
curricular resources. Others should have the opportunity to use this
wonderful presentation that you have. After all, why should math teachers
have it all to themselves!?! Really, this is great stuff -- well developed,
when there is so much junk out there -- this is real quality.
I can tell you that I will use both the activities for the Magic
Square that are appropriate for my Western Cultures and Modern European
History classes. While you have these activities appropriate for the 5-8th
grades in math, in social studies it would be more appropriate in the
culture studies as an enrichment or in-depth activity. I already use some
mathematical analogies to the Renaissance artists like Leonardo, and the
Post Impressionist, Cezanne (triangles), so this will add greatly to the
material I am already presenting. Yours is much more thorough than what I
do, so if you have more on geometry/math and the masters, I would like to
make use of them.
In "checking out" your pages, I found one minor problem -- the "4.
Durer Magic Square with lines" link responds with a 404 URL Not Found error
message. Perhaps there is a typo there. All-in-all, this is top-notch
stuff. Thanks for sharing it with me.
--keithk
keithk@mathforum.org
Date: Tue, 16 Jul 1996 13:58:53 -0700
X-Sender: salejan@e2.empirenet.com
Mime-Version: 1.0
To: Keith Keyser
From: Suzanne Alejandre
Subject: Re: Magic Squares
Cc: sseasto1@swarthmore.edu
Hi Keith,
> Anyway, I saw your E-mail to me and went to check out what you have
>on the www. I specifically was interested in the Magic Square activities,
>since my teaching deals with European history specifically. The Middle Ages
>and Renaissance are integral parts of what I teach, and I try to insert the
>cultural aspects of history as much as can be done. So the use of Albrecht
>Duerer, the Italian Middle Ages, and the Lo Shu (our 9th grade non-western
>cultures classes) activities are golden opportunities for not only
>enrichment for my classes, but allow us cross-curricular opportunities as
>well.
As you use this it would be great if you could let me know about the
students' reactions. I always find it interesting to hear about real
classroom tested experiences.
>I would like to be able to place
>your Magic Squares in our cross-
>curricular resources.
Please do...and thank you very much for your praise!
I already use some
>mathematical analogies to the Renaissance artists like Leonardo, and the
>Post Impressionist, Cezanne (triangles), so this will add greatly to the
>material I am already presenting. Yours is much more thorough than what I
>do, so if you have more on geometry/math and the masters, I would like to
>make use of them.
If you have time could you tell me a little about the other mathematical
analogies that you present?
> In "checking out" your pages, I found one minor problem -- the "4.
>Durer Magic Square with lines" link responds with a 404 URL Not Found error
>message.
Thank you! I'll go check that right now.
Suzanne