Date: Apr 22, 1995 3:15 AM
Author: Tim Hendrix
Subject: Re: where's the mAth?  so?

On Friday,April 20,  Ted Alper wrote:
>
>>Wait! What do many of these connections mean? For example,...Some of
>>these connections seem a bit tenuous. Does an English teacher
>>get excited by "Less than Zero" because it's written in the same
>>language as Shakespeare?

>
Ted, I apologize for listing the myriad of possible connections without
going into detail for each, but I did not feel that it was the
appropriate>time to do so...Moreover, in the class described, recogninzing
the possible
connections was not a terminal point...Some of those connections had
already been explored by the persons in greater detail and recognition of
the synapse was all that was needed...some of those connections seemed
intriguing, but the students would have to do more study to develop the
connections...it just depends on the individual student, class, context,
etc.
>>
>>In any case, the problem with laundry lists of connections, stripped
>>of details, is that it is precisely the substance of the math that is
>>interesting. It's one thing to say "gosh factoring numbers has
>>applications to cryptography" -- what do you do with a fact like that?
>>Blink and say "oh" -- and quite another to show HOW.

>
I agree wholeheartedly that the substance of the mathematics is the most
important part of the connection...just citing the connection in a list is
only an trite index...it is up to the instructor and the student to explore
the connections as fully as possible ( including discard of the ones that
are tenous or trite). The key here is a matter of level of understanding,
and interest...when working with seventh or eighth graders, the simple
connection to cryptography may be enough to peak their interest...as they
become more interested, they will learn more to access the application and
to understand the connection. With college students, hopefully the
connections are explored more explicitly...in between earlier grades and
college, all sorts of variations of exploration occur.
>>
>>(That's a nice modern application, I suppose -- somewhat against my
>>original position -- though the mathematics involved is hardly new,
>>only the application to cryptography is. Still, I can see working
>>things like this into the standard curriculum -- certainly not because
>>students need to know the math behind public key encryption to compete
>>in the 21st century (or the fermat-euler theorem, for that matter),
>>but simply because it is a pretty and accessible modern application of
>>classical math)

>
Amen!
>>
>>Similarly, my complaint with the current invocations of fractals, and
>>particularly chaos theory and such is its lack of content, at least at
>>the level I've read about it in popular articles (this stuff is a
>>little out of my field). I don't find pretty pictures and vague
>>sentiments mathematically enticing. One needs enough details to be
>>able to start at least trying to work out for yourself *some* of the
>>implications...

>
Of course!
>
> If your regular class work is such a drudge (which

>>seems to be the general consensus here), and all the spicy stuff is
>>vague, what do your students take from this?

>
Whoa!!! I know that this is a rhetorical question for all, but I will
answer it personally...regular class work is not a drudge in my class
hopefully ( I can only fantasize, project, and interpret student enthusiasm
dreamily!)...Moreover, the spicy stuff is sometimes vague, sometimes
not...Hopefully, I mix with discretion the amount of interconnection we are
able to address in class meaningfully...sometimes, the porridge is
hot...cold...just right...
>>
>>As someone who actually DID love math from an early age (am I the only
>>one on this list?)


Nope...I have been a "mathematician" and a "mathematics teacher" from the
age of 8...Seriously, I can relate to your mathematical evolution...

>
>>I'm all for mathematics cheerleading when it involves getting
>>students to think about problems that they know enough about to find
>>interesting, and can discover or be taught enough about to make
>>noticable progress in a reasonable amount of time.


So why all the argument? We agree essentially--just don't assume that (1)
because I don't give an exegesis of every mathematical connection
I>mentioned on the list, that I don't understand the connections myself
or>that I don't have students explore these more concretely... or (2)
that>every student at every level must have our mathematical
"sophistication" in
order to benefit from interconnection...the first time that I saw
undergraduates connect the binomial distribution to Pascal's triangle to
combinatorics...(a straightforward connection), I was amazed at the
lightbulbs that started flashing...exactly the revelation you described in
your own evolution.


To list members: I apologize for the lengthy response that may not seem
most appropriate for list posting, but I am very concerned that we, as math
educators, make these interconnections in mathematics with our
students...we address connections in the Standards often as connection to
real life application...but what Ted and I seem to be dancing around is
that mathematics is a beautifully interconnected web...we want students to
become entangled with this web and explore it as much as possible...maybe
along the way, we will all learn some new math and how it is useful...
>

*****************************************************
Tim Hendrix (hendrix@uxa.cso.uiuc.edu) *
Division of Mathematics Education *
Department of Curriculum & Instruction *
University of Illinois *
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