So I just started this thread on 'Calculus Mountain' on math-learn: http://www.mathforum.com/epigone/math-learn/slingsamwang
Basically, I'm arguing that we should evolve the computer science track into an alternative numeracy track, skirting calculus mountain yet providing plenty of useful mathematics. This track will co-exist with, and compete with, the current precalc-calc track, which today monopolizes K-12 as the only gateway into college level technology tracks and careers. """ Let kids electing a discrete math and computer science track excel in their own direction, according to alternative criteria. College and corporate admissions officers should be open to this alternative mix of skills, which are on target for so many real world positions (I know this first hand). """ [ http://www.mathforum.com/epigone/math-learn/slingsamwang ] This isn't a new approach for me. I've long push a three-pronged agenda along these lines: I. Math through Programming -- use a computer language, esp one w/ an interactive shell, to explore concepts and help make them concrete [1] II. Math through Storytelling -- integrate better with the historical record, e.g. talk about the role of cryptography in warfare and commerce, or about the importance of 'ciphers' (Arabic algorithms) to the European Renaissance [2] III. Beyond Flatland -- integrate better with spatial geometry via computer graphics, especially around polyhedra and polyhedral numbers [3] The excerpt below is from a background paper I prepared in advance of my presentation at Pycon 2004 -- a presentation I was unable to make owing to family illness and an abortive sojourn in DC (I'm trying Pycon again this year, but I'm not formally presenting anything): """ And so I see the encroachment of computer science into the high schools as at least initially somewhat competetive with the traditional curriculum. For the first time in a very long time, the pre-college mathematics curriculum is getting a makeover from a neighboring discipline. The ecology is being disrupted. For example, there's potential here for computer science to be cast as an underdog, recruiting students (and teachers) who are dissatisfied with a mathematics track that seems to lack immediate relevance. Whereas the calculus will remain important, it's somewhat debatable whether a high degree of proficiency in integration by parts by the end of high school, is any more worthy a goal than mastery of regular expressions (both technical skills), especially if a conceptual grasp of the calculus is an element in both scenarios. """ [ http://www.python.org/pycon/dc2004/papers/15/ ] I consider all of this groundwork essentially complete and ready to withstand real world testing. I think the open source community is well positioned to assist with this agenda, and thanks to these links to the Fuller School, has a lot of leverage for raising living standards more generally, i.e. by focusing attention on an artifacts-and-technology based approach to social change. There're no political strings attached to this agenda, or if you find some, feel free to snip them, or attach others. We just want to improve the math-science-humanities curriculum all around. If that's seen as "liberal" (OK by me), then it's liberal in the sense of "liberal arts" i.e. it's about keeping an open mind, which in turn means keeping the vital shared knowledge base free and open source (a long term goal of serious scholarship -- not new to this era). Kirby Adjunct Faculty Portland State University [1] the ISETL curriculum was consciously developed along these lines (thanks to Tim Peters for alerting me to this). APL/J have always been promulgated with an eye towards math pedagogy (Iverson himself helped me with my 'Jiving in J' paper: http://www.4dsolutions.net/ocn/Jlang.html ). Scheme and Python have likewise made forays in this direction (thanks to Danny Yoo for pointing me to that RSA-in-Scheme web page). [2] Here's an interesting quote from Bucky Fuller. He's speaking off the top of his head, i.e. this is the transcript of an audio recording: =========== 034 The word cipher has secret connotations for this reason. Because people used it, they needed to use it, you understand "I've got to do my own calculations" but if I get caught so I must be very secretive. Gradually the significance of the cipher permeates society, particularly the young student world that was literate. So the students of Northern Italy and Southern Germany began to realize more and more the significance of the cipher, and the positioning of numbers to do their own calculations. Young peoples' faces are less familiar than the older peoples' faces, and so the young people could get away with what the older people couldn't, so approximately the year 1200, 500 years after the Arabic numerals came into the Mediterranean world, that the treatise was written, that's 1200, and 300 years later it was impossible to ever again enforce the prohibition against use of the cipher. And this is a wonderful date we're talking about 1500, five hundred years ago. And this is exactly when Copernicus comes in. Here was Copernicus, suddenly, with the capability to calculate; and calculating the positions and some of the interrelationships of these, what we call the planets, he came to the conclusion that our earth was also a planet, and behaving in relationship to the sun the way the other planets were. 035 And this opened up a completely new excitation of humanity. =========== >From 'Everything I Know' transcript of the audio tracks, 1997 (the actual recording was made in the 1975). [3] To the polyhedral numbers thread (which connects to Pascal's Triangle ala the 'Book of Numbers' by Conway and Guy), I add Bucky Fuller's concentric hierarchy in the CCP sphere packing context. Basically, 12 balls around a nuclear ball in the CCP conformation define a * cuboctahedron (volume 20) the voronoi cells of which are * rhombic dodecahedra (volume 6) embedded in which sphere-embracing cells are * an octahedron as long face diagonals (volume 4) and * its dual cube as short face diagonals (volume 3) in which cube are embedded * two tetrahedra as face diagonals (each of volume 1) Animated GIF: http://www.grunch.net/synergetics _______________________________________________ Edu-sig mailing list [email protected] http://mail.python.org/mailman/listinfo/edu-sig
