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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382 Education Building *

1310 South 6th Street *

Champaign, Il 61820 *

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