Subject: Re: NASA scientist, and the like
From: Kirby Urner (pdx4d@teleport.com)
Date: Tue May 02 2000 - 11:51:16 EDT
>Not one suspension bridge in the world was built without a precise
>mathematical understanding of the shape of Martha's hanging chain.
>This might be an interesting thing to look into, and if I have
>the time, I'll get back to the group about my findings. Dating
>the catenary to the famous Bernoullis is easy enough. So, I guess
>the conclusion is that no suspension bridges were made (and in
>fact could not have been made) until society could evaluate cosh(x)
>to the fifteenth decimal place. Certainly, an interesting point
>of view.
>
>Adam Stinchcombe
I think this thread re how to demonstrate links between math
and the "real world" is valuable, and does address a central
concern of many students.
A couple points:
(a) even if I'm not going to be a NASA engineer, I appreciate
knowing what different people and disciplines are about. This
is going to help me think about my world, and the kinds of
jobs people do, and about what is possible, what's realistic.
So just knowing something about engineering or chemistry or
medicine or whatever is going to be useful to me, and if
threads in math class help me tie it all together, that's
great -- shows me how "math threads" are a kind of freeway
system of the mind.
(b) there's a lot of self-fulfilling prophecy feedback looping
that goes on vis-a-vis whether I'm even going to try at a
career path which includes needing some math skills. If
I can visualize a realistic pathway that gets me from here
to there, i.e. if I can see my way forward, then I might
give it a shot. Part of it is proving to myself that math
is something I can do, am not intimidated by, consider rather
enjoyable even. If I can get to this point, then maybe the
remaining obstacles won't seem so insurmountable.
Now, regarding point (a), I have this model of "math teacher
as storyteller" which I'd like to float here.
The idea is to develop the math curriculum more in the
direction of being able to recount, narrate, in such a way
as to:
(i) highlight the importance/relevance of math concepts,
including at the time in which they made their first
appearance (if, indeed they were important then -- or if
they weren't, that can be interesting too, i.e. some
math-related innovations end up having applications
only generations later, if ever)
(ii) give students access to a number of "cave paintings"
by which I mean primitive sketches or simulations of
how math is used, without getting too deeply into a lot
of nitty gritty details. A good example of this is how
Dr. Keith Devlin talks about how the difficulty in
factoring huge prime numbers is what's behind many
encryption algorithms -- his story makes sense, even if
he doesn't get into a lot of algorithmic detail (and in
some math classes, we _would_ go deeper into it).[1]
Regarding point (b) -- proving to myself that math is something
I can do and enjoy -- I have another suggestion, which is
to posit some alternate civilization, different from the
one in which we're currently immersed, and present some of
its math concepts (I call this "ET math"). Part of the
point here is to:
(i) give a stronger sense that math contains a lot of
inventiveness, which you can get across by showing how
"it could have been otherwise" e.g. humans _designed_
the XYZ apparatus, didn't receive it from the gods as
some a priori gizmo. By extention, you too are capable
of inventing, making up your own language games, and
this gets you into the mindset of a mathematician (as
well as the mindset of a game inventor)
(ii) give a stronger grounding in the philosophy of
mathematics, which includes making it be OK for kids
to express doubts, talk about their suspicion of
certain concepts, not have their "questioning of
authority" meet with dismissals. Because to question
authority, even regarding matters of logic, is what
it means to be a philosopher in a lot of ways. While
a game maker is "constructing", a philosopher is
"deconstructing", which means questioning, wondering,
sometimes kibbitzing -- which sounds irritating, but
you have to realize that the "philosopher" and the
"inventor" may be two sides of the same personality
i.e. I'm questioning my design, testing it, even as
I develop it. In other words, I'm self-aware and
self-critical (useful qualities, in any discipline).
I confess that I also have an ulterior motive re "ET math"
in that what I teach under this heading is math I actually
use in the real world. Long-time subscribers to this
list have seen me post about this before. My Oregon
Curriculum Network is supplying what we might well call
"Math from Mars" -- in the sense that it's rather alien
to modern-day culture in a lot of ways.[2]
Which gets me back to point (a), math teacher as story-
teller: understanding in what sense my "ET math" is
operating in the world today is a useful entre into current
and recent affairs. By having students "look over my shoulder"
into cyberspace, they get a particular slant on the world
which opens onto many partially overlapping narrative
accounts, including some that are highly polemical (I'm
a source of "technoinvective" in some contexts, as you'll
find if you start digging around a bit).
So... storytelling with math threads prominent + ET math
= a working combination which I've found sparks a lot
of student interest and enthusiasm.
I'm not practicing in the classroom these days, so my
experience may not be directly relevant (my students are
distance learners, who mostly telecommute for content),
but I do sometimes show up in classroom settings, and
have so far had quite a bit of positive feedback there
too.
My two cents.
Kirby
For further reading:
Math Teacher as Storyteller:
http://www.python.org/pipermail/edu-sig/2000-April/000330.html
ET Math:
http://www.teleport.com/~pdx4d/amtepost2.html
[1] Keith Devlin, 'The Language of Mathematics: Making the
Invisible Visible'
http://www.amazon.com/exec/obidos/ASIN/0716739674
[2] Oregon Curriculum Network
http://www.inetarena.com/~pdx4d/ocn/
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