Douglas6 wrote:Clearly Jim Manley is MUCH more tuned in to this than myself, but from a theoretical standpoint, I don't see the applicability of computers to math(s) anymore than to philosophy, or I suppose literature. Excepting of course you can look up novels and philosophers much more easily with a computer, and similarly you can display applied mathematical results much more easily, but I don't see how computers help with training math concepts more particularly than any other discipline. Leibniz, Newton, Peano, Frege, Russell, Whitehead et. al. seemed to get by without computers. What am I missing?
Hi Douglas6 - the issue isn't whether a given person can
learn math(s) with or without computing (notice that I don't use the hardware term "computer(s)" - there's a LOT
more to computing than just the hardware or even the software). It's how effectively as many people as possible
can learn math(s) (or any of the other disciplines you listed, for that matter). I think we can agree that Leibniz, Newton, Peano, Frege, Russell, Whitehead, et al, were probably "smarter" than the average bear, and definitely better-prepared to be educated than the typical student with whom I interact on a daily basis (bears make it through circus training all the time, but I challenge you to get any
teenager to do any of those tricks bears can do with aplomb!
). This is a point that is missed by almost everyone both within and outside the education community, so don't feel bad if you missed it as an innocent bystander - WE ARE NOT TRYING TO EDUCATE JUST THE LIKES OF LEIBNIZ, NEWTON, PEANO, FREGE, RUSSELL, WHITEHEAD, ET AL.
Sorry for yelling, but it's damned hard to get that point across to almost anyone, especially the more advanced someone is in the bureaucracy and particularly within academia. Those folks were already interested in the subject matter, partly because they were often trying to solve a problem - how to gain an advantage in billiards in the case of Leibniz, you probably didn't know, or why the planets traced the orbits they did, in Newton's case (yes, there were theoretically interesting aspects, too, but Necessity IS a Mother!). We should also be mindful that the pace of advances in STEM areas has become a bit more intense than in the times of Leibniz and friends - they had to wait decades to centuries for the Next Big Thing to be discovered or created. However, we witness them now on a nearly daily basis, or could if only we weren't so distracted by the Sports Illustrated Swimsuit Edition, Cool Ranch Doritos Tacos, and yammering spokes-geckos. A big reason for that increased pace is because we've managed to educate a whole lot more people to much higher levels in ever-widening swaths of real estate, much more efficiently on a resource basis, if not an average-outcome basis (increased knowledge and abilities).
However, the modern-day educator has to try to compete with the likes of Biebers, Kardashians, Honey Boo-Boos, Snoop Dogs/Lions, YouBoob Kitties ... well you probably get my drift. Home situations are not the Leave It to Beaver kind (or whatever is considered 1960s family "normal") these days - there is more often than not no father figure or even any mature male influence in most kids homes, and that's a known recipe for disaster when it comes to creating low self-esteemed, depressed underachievers, and even criminals of the future, much less hoped-for model citizens with advanced degrees - there are way too many distractions, including lack of good nutrition in the worst cases (80% of the kids in my school district qualify for the national free school lunch program). I'm not saying we need to all become better rappers, music video producers, nasty spoiled housewives, misbehaving celebrities, etc., than those constantly in the headlines, but we need every other edge, trick, advantage, and surprise that we can conjure up, and computing can help with that.
If you can make demonstrating a mathematical principle interesting, why wouldn't you do that instead of just a plain-vanilla presentation that's been done the same way since Pythagoras was roaming the streets of Athens? For the life of me, even at my advanced age (I'm older than Sputnik), I can't believe how some educators can drone on doing every lesson exactly the same way as they have for decades before, and then wondering why Jane or Johnny can't calculate, let alone compute. Even multi-millionaire professional sports athletes often have to change up their pitch/swing/delivery/pass-offense/stroke/bowl/etc., in order to remain relevant on the field/court/pitch/alley for very long, and I would find the boredom of decades of such repetition enough to want to end it all. I often imagine what the Great Minds of the past could do with the tools we now have - they certainly wouldn't turn their noses up at them for every single thing they did for work or entertainment (well, except for maybe Socrates, but he was always such a crank!). Ask Stephen Hawking what he thinks of computing technology the next time you get a chance, OK?
Of course, it doesn't help when a student doesn't have a driving need to learn anything, especially something that requires mental effort as education does, because Mommy and/or Daddy and/or The State will always provide. It's one of the side-effects of giving away everything - eventually everyone expects everyone else to fulfill their needs even when they have the capacity themselves, and that's the definition of a societal collapse in the making. In the worst case, we may have to wait for an existential threat to make itself obvious as to why kids need an education. In the meantime, we'd better make the best use of the tools at hand to get them interested, at a minimum, before they find themselves yet-another art historian (oops!
) flipping burgers or mopping floors for a career and we find ourselves unable to defend ourselves via ever-more-complex technologies, keep our economies going through viable infrastructure, and even keeping ourselves adequately fed. For those who may say, "Well, if they can't pull themselves up by their own bootstraps, screw 'em.", we never know where the next Hawking, Einstein, Newton, Leibniz, et al, is going to come from, and it could very easily be some homeless kid who in no way was responsible for his plight. We don't have the luxury of only educating those who are lucky to wind up in nice private schools due to the "genetics lottery" as Bill Gates puts it. Most kids really are curious, thoughtful, and imaginative at a young enough age, until the educational system and societal "norms" beat that out of them (HR weenies and drone managers hate curious, thoughtful, imaginative people, partly out of jealousy and mostly out of fear of being usurped and tossed aside, usually for good reason).
I hope I've shed some light on where the problems lie that are unique to our circumstances, and what computing can
do to help, but not necessarily by any means.