SETTING THE STAGE ================= I take some credit for sparking a lot of debate on math-thinking-l this month. If you check the archive, you'll see that's been a pretty quiet list for awhile. We have something to talk about now: the move to fold computer science into the regular math track at the high school level. The politics are as follows: students don't have a lot of time for an elective computer science course that doesn't fulfill basic requirements. In an increasingly technological world, people are finally starting to get wise to the fact that there's simply no excuse for only using scientific calculators, keeping real computers at bay, relegated to some other course. Math teachers are starting to see that they might want to including some computer programming as a part of the mix. A lot of us thought this was happening with the first PC revolution. Logo and BASIC were big back then and it looked like mathematics would be using those. This was not to be in most schools however. I was working at McGraw-Hill at the time, on computer literacy materials, mostly for the junior high age group and above. Then came the second revolution, the open source revolution, which made pretty much all the software they'd need free of charge, even though schools could still budget for commercial packages if they wanted. Surely this relief from software costs would motivate a major shift? Yes, in some schools it has, but North America may not be the leader of this trend, except in pockets like Portland perhaps, an open source capital according to Christian Science Monitor (2005). Linus Torvalds lives here, as does Ward Cunningham, the inventor of the Wiki, etc. LINK TO PHILOSOPHY ================= So where does Wittgenstein and philosophy enter this picture? Imagine different subcultures practicing computer skills in various walks of life, all wanting to have some kind of footprint at the high school level. In part it's a recruiting issue. That's why the Army is always sniffing around the schools, looking for kids who might want to join. College departments need a next generation as well. Speaking of which, my daughter is getting all these mails from the colleges, even though she's only a sophomore. My gut reaction is why would we give these institutions a lot of money when they're not sharing our heritage, are bleeping over tetrahedral mensuration and all that goes with it, which adds up to "another tomorrow" (different from endless Orwellian war on terror). http://controlroom.blogspot.com/2010/02/necklace-theory.html Colleges don't teach my culture, and yet expect me to pay them... looks ugly. What might change in a year or two? Anyway, the functional programming group is really anxious to cash in on Computational Math or whatever we call it. Army Math? Think of those recruiting commercials showing young people finally getting to learn with technology -- except not bait and switch this time, not just using enticing eye candy. Are we talking about a more professional army then? This new course, being brainstormed in Oregon among other states (I presume other states are paying attention), will give you a year of math credit and yet will allow you, in my vision at least, to learn about Google Earth, programming, SQL (structured query language), Unicode, von Neumann architecture, TCP/IP (watch 'Warriors of the Net') along with a lot of math topics such as number types, vectors, polynomials, polyhedra... all that good stuff. I've been running some pilots, writing them up, posted some history, partly for for Maria's benefit (she was asking if we had results on the ground): http://mail.geneseo.edu/pipermail/math-thinking-l/2010-February/000543.html My computer skills tribe is more object oriented (OO) than functional (FP) and this is somewhat disturbing of the equanimity in this particular archive, as the FP camp is resolute in casting the OO people as mathematically naive, full of mumbo jumbo, and to blame for most of the bad software that's out there (indeed, most of it is OO based I think that's safe to say, once you count all that Javascript in everyone's web browser). My thread with Rex distills the issue. I want to explicate the meaning of the capital greek letter Sigma, used as a summation symbol in math, by putting some computer code side by side. The idea is: a Greek letter notation all by itself may be intimidating, but if you see a simple translation into running code, you'll be able to go back and forth, like seeing in stereo. Both notations (the greek one and the machine one) become more readable in light of the other. So far so good. But then I propose to use something like this on the computer side, which looks pretty straight forward. This is actual Python code and the range function returns integers between start and stop non-inclusive of the upper bound, which is why the added 1 (to keep the stop value in the picture). def sigma (function, start, stop): total = 0 for index in range ( start, stop + 1): total = total + function (index) return total This would correspond to b SIGMA [ f ( i ) ] i = a where f is some function and SIGMA is that capital greek letter. What the functional programmers tell me is that for-loops of this kind, which feature a "mutable variable" (one that changes), actually requires very deep mathematics beyond the capacity of anyone in high school to understand. You already need a college degree, probably in mathematics, to understand what's going on under the hood in the above looping structure. Therefore using for-loops of this kind should be inadmissible at the high school level. http://mail.geneseo.edu/pipermail/math-thinking-l/2010-February/000615.html To me, this comes across like an absentee landlord, in some high tower someplace, telling me I can't share heritage with my students because I don't "own the math" whereas the absentee landlord understands it very well (is the owner-controller). By monopolizing authority over what "math" is (controlling that turf), the functional programmers plan to shove aside the object oriented programmers. Interesting strategy. Will it work? They will not have such an easy time finding a toe hold or footprint. Their languages will be discounted as too "anti-mathematical". http://mail.geneseo.edu/pipermail/math-thinking-l/2010-February/000553.html To my ears, saying the math is "too deep" around for-loops is like saying 1 + 1 = 2 is "too deep" for high schoolers too, because they haven't understood Principia Mathematica yet. The idea of math being part of our ordinary language and common heritage, not beholden to high tower (ivory tower) formalists and their "rigor" (mortis) is the idea Wittgenstein champions. He brings mathematics back to its anthropological roots, where it weaves seamlessly with the rest of culture, as a socio-economic activity, a form of collaboration, a set of rule-following language games (redundant but why not spell it out) that bear a family resemblance to one another. http://mail.geneseo.edu/pipermail/math-thinking-l/2010-February/000592.html CONCLUSIONS ============ This is actually a somewhat important debate with lots at stake, in terms of how we design the next generation of high school math course. What irks me is how academic philosophers have let themselves off the hook when it comes serving in an air traffic controller role. We have issues regarding the philosophy here, and a need for decision-making. I think philosophers should serve more like referees, especially those trained in Wittgenstein's methods of investigation. In the debate above, I'm obviously in a biased role, am more a player on the field than a referee. I post back to this archive to leave some trace of what it looked like, in the midst of wars.... Kirby ========================================== Need Something? Check here: http://ludwig.squarespace.com/wittrslinks/