Those of us who do not believe in static math still face the same challenge of not enough qualified applicants.
The relevant work / study tracks go unfilled, and the new construction we most need remains in storyboard phase (i.e. "on the drawing board"), albeit sometimes in somewhat alluring futuristic comic book format.
We don't have the drivers, the vehicles, the simulators, the math labs, the outdoor gear. We lack the basic competence to compensate ourselves to do the right thing. We're confused about wealth and money, about synergy, about work.
Grownups bumble about touting these many theories, but in practice their plans for a better tomorrow just don't seem to gel. Finger pointing ensues. The blame game sucks up a lot of energy, meaning less work / study occurs, less homework gets completed.
We lack qualified managers in other words, though we're maybe not short on students who try really hard. We haven't enough generalists, nor specialists, ready to usher us in to our 21st century. The curriculum is broken. The opportunity costs are tremendous. We live in squalid poverty, as a species and as individuals, in comparison to what we might enjoy were we to have our act more together.
So yeah, it's not a pretty sight. If the Martians were wanting to invade, now might be a good time. Humans look pretty weak and wimpy. Heads full of straw, alas.
On the other hand, we have television and the Internet and are finding effective ways to share information with one another that doesn't take as much time, nor that much in the way of resources once the existing infrastructure is factored in.
Thanks to jet travel, I was recently able to have another meeting with Anna Roys, who is based in Alaska, even as I watch recorded webinars archived at Maria Droujkova's site. I'm not at all unique in having access to this shared infrastructure, the institutional wealth of our Global U.
Did I take the Gulfstream V to this meeting? No way. How about the Boeing Business Jet? Not that either. That's science fiction lifted from a book I've been reading (hey, mentions Portland, dovetails with a Willamette Week article I like to cite).
My access to the infrastructure was much closer to average, in terms of my methods of transport.
[ Anna wanted to know why I'm the only one talking about sphere packing if that's indeed an important topic at any level. Like, you'd think if mathematicians really thought sphere packing was relevant, I wouldn't be some lone voice in the wilderness, some wolf howling at the moon (an image I've used in my "CSN Esoterica" on Youtube).]
Anyway, more later. Got pictures to upload, some of them maths- related.
On Sun, Nov 28, 2010 at 3:30 PM, Jonathan Groves <JGroves@kaplan.edu> wrote: > Kirby, > > Even if the ones conducting these studies seem to believe that math is > static or at least what math ought to be taught in K-12 is static, > their studies do make a good point: If most teachers do not have the > understanding of math to teach current curricula meaningfully--which > are often not much different from curricula decades ago--then they > definitely do not have the understanding of math to teach any > updated versions of curricula that you or anyone else may offer. > > But you are correct in that the attitude that school mathematics > is static is a poor and misleading one. Mathematics itself has > exploded in the last century and continues to explode, yet the > K-12 and early college math curricula, with relatively few > exceptions, have grown little in decades. Yet curricula in > science and other subjects have grown more than curricula in > mathematics in past decades. It is a shame that most people > have a better notion and even decent understanding about the > latest ideas in science and technology than in mathematics. > > This static attitude about mathematics is indirectly addressed > in Al Cuoco's article "Mathematics for Teaching" when he > mentions that many educators teach mathematics as if it is > a mere collection of human knowledge rather than as a way > of thinking. That is, they teach mathematical facts as > mathematics itself rather than as the products of > mathematical thinking. However, seeing mathematics as a > pursuit and development of ideas, as a way of thinking, as > exploration, as problem solving, etc. will help educators > go a long way in helping them to see that mathematics is > not static. How can one have a static view of mathematics > while also holding this view of mathematics as a way of > thinking and exploration rather than as just accumulated > knowledge? > > Speaking of updating math curricula, I would also add that any > such goal includes de-emphasizing certain skills that are > not needed much today. For instance, some computational skills > are still good for today, but there is no need to emphasize > computational skills as we try to do today and have tried to > do for many decades. We have seen some of that in the last > century with the removal of the traditional square root > algorithm, tables of logarithms, logarithms for computation, > trigonometic tables. Some books may still include such tables > but not as older books used to do, and today's students > rarely look at what few of these tables remain in their books > since their calculators can compute these values for them. > > > > > Jonathan Groves