Hand delivered to MLC on November 5, 1997, converted from
Word 6.0 to HTML by Internet Assistant for Microsoft Word 2.04z,
HotDog 3.0.9, and the author, and published to the web within
hours. Hyperlinks added.
Wednesday, November 05, 1997
Dear Sir - The attached
Quadrays and the Concentric Hierarchy contains some
printing anomalies, tracing to the fact that its native context on
the web has no concept of 8½" x 11" paper, so the browsers
have to do their best to supply their own parsing. iExplorer
3.02 seemed to offer the best compromise, despite the
lengthwise slice through some of my graphics and characters. I
thought the exercise worthwhile however, since I wish to refer to
this paper in this memo and you may not have the web at your finger
tips (I understand you're going back and forth to New Jersey a fair
amount these days - I used to be a high school math teacher in
Jersey City by the way). As a curriculum writer for McGraw-Hill in the
1980s, I discovered a lot of convergence in the subject areas of
math and computers (not an original discovery I realize) but felt a
lot of artificial barriers were being retained between these
subjects, in part owing to differences in typography - I was
learning to think like a text book publisher. In the computer
world, for example, people were using the ASCII character set for
everything, whereas mathematicians still had the luxury of skilled
typesetters at their disposal, and could therefore keep getting
away with lots of greek letters, sprawling matrices, integral signs
and the like. As a student at Princeton, prior to this
McGraw-Hill experience, I fell in love with APL (A
Programming Language), originally developed as a chalkboard math
notation by Kenneth Iverson at Harvard. You needed a special
keyboard, because most the characters were non-ASCII, and the
result was an ability to do matrix operations in extremely compact
notation - approaching and perhaps in some cases surpassing the
compactness of standard math typography. But in the computer world,
APL had a public relations problem because it was considered 'too
cryptic' i.e. programmers used to FORTRAN or PASCAL would go nuts
trying to decipher an APL program which might accomplish the same
results in less then half the number of lines. Since my McGraw-Hill days, our computers have
gone more than half-way towards accommodating math text
typographies. For example, my copy of MathCad 6.0 is
perfectly capable of putting lots of greek letter terms under a
large radical sign, and embedding this gizmo (computer term for
"interface element") into a 3 x 3 matrix, which automatically
stretches to include these more elaborate terms. Using the ability
of many paint programs to capture rectangular areas directly off
the computer screen, we can turn these typographies into GIFs
(pictures), embeddable in web pages. This means we no longer need
to rely on specialized Postscript or LaTex solutions when seeking
to duplicate the million dollar look of fancy math text books. We
can bring our mathematics directly to the web browsing public at
large, minus any deterioration in quality in the "look and feel"
department - in fact we can easily go a lot further with our
graphical materials than budget conscious paper-based publishers
would want to attempt in their mass circulation text books. But there's more. MathCad formulae are "live",
meaning they actually accept real or complex number inputs and
compute results. Plus a version of Maple's symbolic processor (part
of the package) will do its best to simplify complex algebra
without knowing anything about the values the variables may or may
not contain. In conclusion, I think at the university level at
least, math students are finding that computers are an absolutely
critical aid when it comes to doing mathematical work, both from a
computational standpoint, and from a publishing standpoint
(the focus of this memo). When you combine the ability of
contemporary math software to both simulate the traditional
typographies and to execute garden variety ASCII code, you have a
dynamite combination. Add to this picture the ability of computers
to do ray tracing and virtual reality modeling (VRML), and you're
looking at what must become the 21^{st} Century
standard tool set for most mathematically literate
individuals. My question for the Math Learning Center, and
others in the K-12 teaching profession, is how prepared will our
students be by the time they reach college age? Right now, a lot of
focus seems to be on whether calculators, especially graphing
calculators, are a positive, or how to make sure that they are used
positively. My feeling is this calculator discussion is a dress
rehearsal for a larger and more important debate about the role of
full fledged computers in the mathematics curriculum. Computers are
actually easier to program than calculators, because of the
latter's memory limitations, and their graphical abilities vastly
outshine those of calculators. Because the Math Learning Center is a champion of
more visual and intuitive approaches to mathematics, and because
computers are among the most sophisticated tools available when it
comes to supporting the visual imagination in connection with this
subject, my expectation is that teachers will increasingly be
looking to MLC for leadership as the shape of the new math
curriculum starts to become clear. Teachers will be feeling pressure from students,
who are learning from television, movies, the internet and other
media, that computer skills are critical to their futures - and
we're not just talking about the ability to use a wordprocessor or
navigate a spreadsheet. The idea that computers are primarily
"business tools" and should be treated like fancy typewriters or as
specialized vocational machinery, like factory metal-working
lathes, rather than as serious, generic, core technology in many
subject areas (including in the humanities), is completely
obsolete, and our students know it. I believe the attached paper, plus the memorandum to Dr. Cowen (somewhat
redundantly expounding these same points), well demonstrates the
many opportunities facing us, as well as the many challenges. My
hope is that MLC is going to be ahead of the learning curve and
ready to trail blaze, in line with its existing purpose and
mission. The many discussion threads launched or continued at the
Oregon Math Summit of 1997 at OSU, by both teachers and presenters
(including myself) suggests that we Oregonians are up to doing some
serious brainstorming about the future of the curriculum. My intent
is to be one of the participants in this process, both locally and
more globally (given the internet, that distinction is becoming
harder to make), and to serve as an ally of MLC's when and if it
appears that my particular talents and skills might prove
useful. Please keep me in mind as a potentially friendly
source of assistance. In the meantime, I continue to explore other
channels and to increase the quality and substance of my
communications with key educators in our community. Sincerely, Kirby Urner For further reading:
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