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

TO: Bob San Soucie, CEO, Math Learning Center
FR: Kirby Urner, curriculum writer, 4D Solutions
RE: MLC and the emergent 21st Century math curriculum

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 21st 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.


Kirby Urner
Voice: 503 232 7159
Web: http://www.teleport.com/~pdx4d/kirby.html

For further reading:

Synergetics on the Web
maintained by Kirby Urner