To be honest, I haven't been following the Carnival of Math much since it's inception; my new job keeps me busy enough that I barely have time to keep the blog going, and so I haven't really looked much at recent editions. In fact, I completely forgot that I was hosting it again until I started receiving
submissions.
Much to my disappointment, it appears that spam has managed to invade even the carnivals. Close to half of the submissions that I received were blatant spam, including one for a penis-enlargement pill. But hey, when a theme hits me in the face, I run with it. So, welcome to the Carnival of Math: Spam Edition!
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For those of you who just want to be able to see the articles, here's the list, in table form.
| Author | Title |
|---|---|
| Anne Glamore | Beyonce and I Fail Long Division |
| Charles Daney | Rings and Ideals |
| Dave Marain | Educating our best and brightest: Alec Klein Interview |
| Dave Marain | Last minute PSAT prep |
| David Eppstein | Batting Averages |
| Eric Macaulay | Equivalence |
| jd2718 | Puzzle: last one left over |
| Mark Dominus | The square of the Catalan Sequence |
| Mark Dominus | Relatively prime polynomials over Z2 |
| Martin Cooke | Two "proofs" that 1 + 1 = 0 |
| Slawomir Kolodynski | Groups and neutral elements |
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Nice theme!
The more math writing I see, the guiltier I feel about not finishing that supersymmetry series. Time to start drawing some diagrams. . . .
The long division article (and especially its comments) was depressing. This line:
There are infinite combinations of complications that I shudder to contemplate, for I'm sure they await Finn (and thus me) in the future. Dividing one fraction into another! Dividing a square root by an integer! Dividing percents! Dividing a negative number by another negative number, as if that ever happens in real life!
bothered me. None of those should take more than a couple minutes for an adult to learn. Seriously:
Dividing fractions: Flip the divisor and multiply.
Dividing a square root by an integer: Square the integer, put it inside the square root sign, and divide.
Dividing percents: Divide them like normal numbers?
Dividing a negative number by another negative number: drop the negative signs and divide like normal.
Fully understanding that takes a little longer, but not much. Maybe textbook publishers should put out a parents' guide that offers concise, adult-level explanations so parents can more easily help children with their homework.
Adam:
I agree. I was very surprised - and depressed - when I received that as a submission from the Carnival. Not just that an adult had a problem with something as simple as basic arithmetic, like long division, but that they thought that it was so benign, so unremarkable that the weren't even embarassed to advertise the fact in public, and to actually submit it to a collection of math articles.
Illiterate adults are ashamed of that, and hide it. Innumerate adults often seem to accept it. Part of the problem that I've faced in my 5 semesters of teaching Algebra in university, 1 semester teaching algebra-intense Astronomy in college, and a summer of teaching algebra to inner city teenagers is this. Students with math anxiety, exacerbated by having failed it once, twice, even three times before, is their peers, parents, and even other teachers saying "Oh, I didn't like math and couldn't do it either; don't worry about it."
As to "Dividing a negative number by another negative number: drop the negative signs and divide like normal." -- for both multiplying and dividing negative numbers, I drilled the students on this catchy phrase, adapted from the famous poster parodying Desiderata: "two wrongs don't make a right, but three do." Our version was: "two wrongs make a right, but three don't."
After having them work enough examples in homework, I led them to self-discover that a negative number to an even power is positive, and to an odd power is negative. One student who was technically homeless summarized it: "two wrongs make a right, but three don't, but four do, but five don't, ..."
None of them could evaluate (-1)^100 in the first week of class. 6 weeks later, everyone got that right on the final exam.
Only 1/3 of students clinically diagnosed with "Math Disability" a.k.a. "Dyscalaculia" have their brains wired to make formal Math impossible for them. 2/3 of these severely math-challeneged students, child or adult, CAN learn it, if they have a good teacher, which they've typically never had before. A teacher who can explain the same thing in a dozen different ways, each way useful to a student with the appropriate learning style.
Most Teacher's Colleges don't teach how to teach, that way, except perhaps for the few who earn a M.Ed. in Math Education. Evern those rarely have any familarity with the academic mathematics community, nor have published a Math paper in a journal or a conference.
Scotland invented compulsory universal free education about 500 years ago, so that everyone could read the Bible and interpret it for themselves, and not rely on the hierarchy headed by the Pope. Stll, teaching was not "professionalized."
In the USA through the start of the 20th century, rural communities simply hired young ladies to be teachers, pointed them to the one-room schoolhouse, and gave them little money and limited respect. In the cities, big school systems evolved bureaucracies and "professionalization" of teachers.
Then came Sputnik, which was the biggest shock to America since Pearl Harbor, and until 9/11. Schools were changed tremebdously, in teacher training, and in curriculum. I am directly a product of that, having been 6 years old ain October 1957. Thuirsday night I gave my final exam in Communications Studies 151: Public Speaking for Teachers. I spoke on how Sputnik changed me, and made the education system for my fellow teachers. I got the highest possible score from thr national-award-winning Speech professor.
But the momentum from Sputnik has decayed. America's public school systems have failed. "No Child Left Behind" is, on the face of it, Unconstitutional (to the founding fathers, who left this to the States). "No Child Left Behind" makes things much, much worse.
Now, will we have another "Sputnik moment?"
Al Gore thinks that we had it, and the Nobel committee agreed. But Global Warming is not a Sputnik Moment. Katrina is not proven to be a Global Warming problem.
I spoke this week with Bruce Murray, former head of JPL, co-founder with Carlk Sagan and Lou Freidman of The Planetary Society.
"History does not repeat," he said.
Mark, you are a good teacher. But the need is so vast, and growing, that the USA is losing the new space race, and the economic race, and the outsourcing race, and the respect of the world.
This is a crisis. It goes beyond an adult acting as if arithmetic, which my son mastered by age 7, was incomprehensible black magic, and posting that on a blog thread. But the two are linked.
Still, as George "Fuzzy Math" Bush said recently, asking for renewal of "No Child Left Behind" --
"Childrens do learn."
QED
All very true, and mildly comforting to blame the innumerate. But somewhere along the line we failed or are failing or are being beaten... In the US, even people who can do long division, most can't explain why it's important. And so many can't do it.
Part of the NCTM's lousy Standards... document was an intention to get more of the students who weren't learning much math to learn a bit more. They got it all wrong, of course, but the challenge remains.
Mark:
The original author submitted that? Interesting. It does tell us some more useful things, though -- several of the comments were about teachers grading on methodology rather than ability to solve the problem. The issue of what's needed to allow parents who haven't done long division in twenty-five years help their children with math homework is certainly worth some discussion among the math community at large.
When is the next Math Carnival? To whom do I send my submission?
please stop saying "adult"
when you mean "nonmoron".
it makes you sound like
educationists or something.
Pretty sure there's an error in the Catalan Sequence post. The functional equation satisfied by the series V he gives is V = 1 + s*V^2, not V = s+V^2. Unfortunately, I don't think comments are enabled on that blog.
Actually, I submitted the article not for a critique of MY math skills, which are good enough (as a humor columnist, I certainly exaggerate!) but to point out that math IS intimidating to many people (as English and science are to others) yet parents are expected to draw upon ancient memories to help our children through homework problems on occasion.
My 3d graders are being taught to add from left to right, instead of from right to left as I was taught, and it's quite difficult to help them add three digit numbers to three digit numbers, for example, when to me they are doing it backwards.
I imagine some of you might have the same problem if asked to parse a sentence or write a narrative memoir, which are other items my sixth grader is learning this year. I could do these things in my sleep, which is why I'm writing a blog and practicing law and not contemplating the Catalan Sequence. I don't even know how to make those squiggly things on my keyboard!
I think Adam's comment (#8) sums it up perfectly.
Y'all can go back to your string theory now!!
Thanks,
AG
ms. glamore means #6, of course, not #8.
of course one is always glad of the extra attention.
that was a joke. (some readers are evidently
so humor-impaired as to have overlooked the tone
of her post altogether ...)
in other news, the next carny is at squareCircleZ.
but then, on the other hand, JFGI.
i tried posting this a couple days ago but was stopped
by the "having problems commenting?" demon.
let's see how it goes today.
I receive about 10 spam letters on my working e-mail despite the strong anti-spam protection. This makes me mad. But no one of my administrators can cope with it.