Text identical to archival version, embedded hyperlinks
activated. Note that I've used NCMT throughout, but it should be
NCTM (National Council of Teachers of Mathematics) MEMORANDUM October 30, 1997 TO: Kenneth Ross, Department of Mathematics, University of Oregon FR: Kirby Urner, 4D Solutions RE: NCMT Standards, Geometry, 1999 Dear Sir -- I am exploring the MAA website and learning about the connections between MAA and NCMT at the level of providing endorsements, sharing minutes of proceedings and so on, and decided to send you a background memo re my own attempts to engage the NCMT in productive discussions. As a recent workshop presenter and participant at the Oregon Math Summit organized by Norma Paulus and Maggie Niess at OSU, I discovered a lot of professional math people were advocating bold, new experimental approaches designed to galvanize student interest, while the rank and file were more concerned about the looming prospect of harder standardized tests, drilling for which would leave little room for any radical departures from the norm. For me, this was the central tension in the conference. Ralph Abraham, one of the invited superstars, was especially aware of the dichotomy between those who see mastery in mathematics as an ability to pass a set of standardized tests, versus those such as himself who have waged career- long battles to bring new thinking into the curriculum -- a battle which Dr. Abraham said often put him at odds with more conservative collegues, who were also many times those for whom he had the most professional respect. My angle on this situation, an analysis I shared with a number of teachers at this symposium, is that those with a commitment to the advance of mathematics have an advantage over those more interested in consolidating past gains, in the following sense: the Platonic Realm (as Sir Penrose called it -- another invited superstar) is always a source of fresh material, some of which will be of relevance to students in K-12, and, simply by virture of its being new, will not be a part of the current standard. In other words, people who source the curriculum have the ability to stay one step ahead of those who wish to codify the subject into a set of standardized tests (in actual practice, the same person may perform both roles, wear two hats, as I suspect is the case with many professionals in orbit around the NCMT). Ralph Abraham, for example, had recently returned from Italy where he's been working with folks on a calculus text which will segue into dynamical systems theory (e.g. chaos math and fractal geometry) far more effectively than what currently passes for a standard calc text today. This new text will then set new standards (Ralph has also migrated all of Euclid's constructions onto the web, complete with explicit step-by-step graphics). I think the first objection to my thesis that will pop into a lot of minds is that fresh material only shows up at the 'frontier' in any discipline, and in mathematics that frontier is a territory which only PhDs are qualified to pioneer. As far as K-12 is concerned, this model suggests, the curriculum is more or less set in stone, with the main challenges having to do with fine tuning within broad brush parameters that are unlikely to change in the foreseeable future. But I'd argue a different model, and invoke historical evidence that the curriculum is vulnerable to suprising changes at all levels: in my own short lifetime, the K-12 curriculum has already changed considerably, in many ways in response to changes in technology and expectations about the future of the econosphere -- i.e. changes of a kind that are only accelerating. We have good reason to expect that geometry in the 21st century, for example, will not be studied in K-12 just the way it is today -- which brings me to the title of my Math Summit workshop: 'Beyond Flatland: Geometry for the 21st Century'. Finally, I come back around to the topic at hand: my interest in engaging the NCMT more specifically about changes in curriculum standards we probably should be anticipating and starting to codify for the benefit of tomorrow's test makers and exercise framers. Back in February of this year, I sent a memo to the NCMT, which I then enhanced with a few graphics and uploaded to my website as well (the trajectory followed by several of my memos). It featured some background thinking about how curricula change over time (as here, but more briefly expressed) and went on to hypothesize what a typical 1999 geometry exercise might look like (on CDROM). The memo is at http://www.teleport.com/~pdx4d/ncmtmemo.html and is one of the web pages I use to provide introductory level access to the synergetic geometry shared via my own website and a host of others. Since 1999 is only just a little more than a year away, it seems not too early to start drafting some of the new curriculum essentials and getting feedback from professionals, both inside and outside the classroom, regarding the most effective, student-friendly, and technology-leveraging approaches we might take with an eye towards overhauling some aspects of K-12, in the arena of spatial geometry in particular. Thank you for you attention to this matter and I hope you will let me know of any NCMT professionals in your sphere with special expertise in spatial geometry who might be willing to share with me any early drafts of 1999 curriculum standards materials. |
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