This is a 'cross-post" of an item I put up on the math-teach forum at which I was first introduced to this forum by Mr. Kirby Urner. I'm pleased to have discovered you folks and would be as interested in your perspectives on my comments as I am in those of math teachers. One important strand in this discussion and throughout math-reform discussion, when it actually takes place, seems to boil down to a "content" versus "context" debate. I'm sure this is in many ways as false a dichotomy as nature/nurture. Nevertheless, talking about it as a dichotomy can lead to interesting discoveries. I, for one, think it is much more important how I and other teachers structure the context of a math classroom than what is on the "scope and sequence" chart. By this I don't mean better bulletin boards and seating charts! (any more than I define "class participation" as the typical waving of small hands in reply to a carefully leading question from the sage onstage). I mean, for instance, that how I build habits of real mathematical discourse into eleven-year-olds approaches to math is more important than whether I "cover" division of fractions. The former is pretty hard to do. The latter can often be a decent base upon which to build the context - we DO "do" division of fractions. My (relatively short) professional experience is that kids at all "levels" of math benefit from learning to ask and answer questions about each other's work - that most of them even, somehow (?!) do better on classic normed arithmetic-based tests at the end of the year. It is not just important to me because I find the theory and research compelling, but because of that actual classroom experience with 125 kds a year. We might disagree on the relative value of this. I'd like to hear more. The reason I mention it (and the reason I have turned what started out as a private post to a forum one) is that I am interested in your and others' opinions on the content-context question viz kids programming ! Personally, I always enjoyed programming for the ultimate "solvability" of its problems (notwithstanding a CS course I once took which showed me how hard it was to prove a program correct). With a good debugger environment and lots of stubborn patience any slapped-together program could be made to behave. And finding out why it didn't work was great fun. Although I hold a professional belief (and a personal one as a father) that kids and people "naturally" take to problem-solving and gain some form of true ego-energy from successes in that arena, I DON'T believe that the p.s. aspect of programming appeals to most kids - or, at least, that it is the best way to bring p.s. into a math curriculum. And I don't place it as a foundation for my desire to work more actual programming into the computer environment of my math (and English) students. The foundation for me, is context. I see programming as a tremendously valuable arena for kids, even young ones, to explore the notion of an algorithm and to discover how many different algorithms can lead to correct solutions. Programming also allows kids to explore the notion of "efficiency" in algorithms in general and the fact that even "efficiency" is context-based. (E.g. the notion that computers can process many brute-force algorithms with negligible loss of efficiency). This, then, allows me to ask them to reflect on relative efficiencies of paper-pencil arithmetic, mental-math, calculator usage and estimation. I've asked kids to write short programs to simulate the processes of paper-pencil arithmetic - e.g. the raw "symbol manipulation" imbedded in "sum up the ones column, carry the one, etcetera. Quite revealing for all concerned. Language and natural/artificial language processing viz programming can feed strongly into pieces of an English curriculum. A "parts of speech" unit is really cool if built upon a challenge to create an "alien" language. And exploring artificial languages give the sort of flicker-contrast discovery that found us Pluto. I think some of the content in the "How to think Like a Computer Scientist" site makes interesting reference to this notion of different forms of "language". Programs to make some"thing" do something - such as the Lego Mindstorms robotics control language or Logo (or a free, purely visual/icon-based "language" called DRAPE that I've found) add an important element to this mix. I'm not sure what it is, yet. Your thoughts ? Moving beyond this we wander into some fascinating areas of cognitive science and the like. The Python language is accessible IMHO, because it is interpreted. But the Object-Oriented model may be most accepted and most useful primarily because it matches the developed "event-driven" machine architectures of this era... I'm not sure they match human mode of cognition. maybe they do, though... Certainly discrete, sequential, "imperative" processing is NOT what goes on in the human mind. Some "sum-is-greater-than the parts" combinatorial explosion of capability arises from the neural "nets" that are at work, no ? A somewhat related phenomena crops up recently in robotics. The control code necessary to build a machine that can purposely move through a natural environment seems to require an immense database of discretely processable situations and seems to be flattening the curve of developments in the field. Recent work by has developed extremely simple (electronically) devices which incorporate seemingly simple analog circuitry that combines to create complex and lifelike-seeming "behaviors" from very simple machines. I think these are called "BEAM" robotics. Finally, I have the sense that "professional" mathematics has been transformed in some ways by computer-based access to powerful graphic modelling tools. I have spent quite a bit of time exploring the utility of these technologies for younger, non-professionals, Not so much the "Cabri" gemoetry explorers, and certainly not the flash-n-jazz"software" that is just drill-n-skill decked out in spangles. In particular, I've tried to engage younger (10-12 y.o.) kids with the idea of "proof" by exploring visual proofs using tools like Powerpoint and Flash. I'd be very interested in your and other's thoughts on these varied matters. -regards -da