OK, sounds like "Concrete Mathematics" (CM) is my next investment
Bought this book yesterday.[1] Looks good -- like Tim says, not as "intense and telegraphic" as 'The Art of Computer Programming', but with Knuth an author, bringing the same expertise. This is a text book for an actual course at Stanford. My initial reaction on reading these books is pleasurable, given how much it positively reinforces what I'd come up with in the 'Numeracy + Computer Literacy' series.[2] I'd sort of intuitively gravitated to Pascal's Triangle as a conceptual nexus, a "grand central station", and that's what these books do too, in the same context of talking about series. Knuth's Volume 1 even shows the tetrahedral packing of spheres (exploded view), a geometric interpretation of one of the Pascal columns. What's different about my Oregon Curriculum Network approach is that I develop this geometric connection more intensively, making use of Buckminster Fuller's concentric hierarchy as defined by 26 data points, plus a jitterbugging thereof -- which points I have the option to express in whole number coordinates, given the newfangled quadrays apparatus.[3][4] In going with polyheda as paradigm objects (in the OOP sense), I'm bringing in Computer Game Programming 101 (e.g. rotation matrices, even quaternions -- the 'Tomb Raider' engine is quaternion-based) which is more obviously relevant to a lot of kids -- as is spatial geometry in general (after all, we live in it). Also, whereas CM is earmarked as grad schooler or upper level, I'm pretty clear we have the option to alter the mix in the lower grades (pre-college) as we follow the CP4E thread where it most naturally leads (including into the math classroom). We already touch on a lot of these same topics at these earlier levels, but don't elaborate much (e.g. mention primes, but not Fermat's "little theorem" or the link to RSA encryption) because everything is geared towards an intensive calculus experience, for which you need precalc. Again, I have nothing against teaching calculus (was a calculus teacher myself for two years), and CM is full of Riemann sums, right along with the SIGMAs. And I didn't mean to say we should bleep over the chain rule or integration by parts, merely that it should be an option to NOT spend a _whole year_ doing calculus at the pre-college level AND to nevertheless be considered a top performing math student. In other words, if you want to be a "star" in math, you might do something more along the lines of CM (and my essay, ahem), and less along the lines of today's conventional AP calc course. These kinds of "remixings" happen all the time. Math ed is like music -- you go through phases, things come into vogue. I'm not saying we should get suckered by the latest fads (a lot of what the traditionalists are fighting as "fuzzy math" seems pretty faddish to me), but on the other hand, we need to be aware that long term trends alter the landscape in math, as in every other discipline. Change happens. My view is that pre-college math is out of synch with what kids could most use and benefit from. Calculus is over-stressed. Fluency with calculus ideas should be developed with an eye towards looking at other topics (a proof of relevance), with more intensive drilling in this subject saved for those most likely to need it professionally. Too much other good stuff is falling by the wayside in the rush to cram calculus into the final year of pre- college. We need a more accelerated path (i.e. a "first pass" tour of duty) through that material that doesn't get so bogged down in the nitty gritty and leave too many students turned off math for life. In making more room for other topics, we'll have the opportunity to phase in computer languages, Python included (it has a lot going for it, as do some of the others). Text books are too slow to match these needs. My approach is going to be based in cyberspace as the primary source medium, not text books. Some of our materials will be more like "finished goods", for teachers who want those (e.g. PDF handouts). But I'm primarily interested in ideas, with teachers customizing content to fit their local needs and students. A lot of this will be private sector and commercial, with curriculum supplies being sold via the same websites. Also working the DVD jukebox angle. Kirby 4D Solutions PS: I see Knuth has his own ideas about calculus reform, which I'm curious to read. Just have to find a way to get TeX files deciphered in Windows (or BeOS). [1] Ronald L. Graham, Donald E. Knuth, Oren Patashnik, Concrete Mathematics (2nd Edition), Addison-Wesley, 1994. [2] http://www.inetarena.com/~pdx4d/ocn/cp4e.html#python [3] http://www.inetarena.com/~pdx4d/ocn/oop7.html [4] http://www.teleport.com/~pdx4d/quadrays.html