December 28, 2006 @ 11:09 am | Filed under: Math
Hat tip to Boing Boing for the link to a Science News article about how some mathematicians are using knitting and crocheting to create physical models of mathematic principles, from simple Mobius strips to, um, whatever this thing is. A hyperbolic plane! That’s it!
During the 2002 winter holidays, mathematician Hinke Osinga was
relaxing with some lace crochet work when her partner and mathematical
collaborator Bernd Krauskopf asked, "Why don’t you crochet something
useful?" Some crocheters might bridle at the suggestion that lace is
useless, but for Osinga, Krauskopf’s question sparked an exciting idea.
"I looked at him, and we thought the same thing at the same moment,"
Osinga recalls. "We realized that you could crochet the Lorenz
I am SO using that line on Jane the next time she is at loose ends. "I know, darling, why don’t you go crochet the Lorenz manifold?"
BoingBoing includes links to other nifty math-craft posts (including instructions for the aforementioned Lorenz manifold).
The packers are here. I am sitting still long enough to nurse the baby, but I will take great care not to convey excitement or frenetic activity because PEOPLE WANT TO TAKE AWAY MY DR. PEPPER. Oh, look, I blew it already. Ah well. I’m a woman in labor, remember? Right about now Dr. Pepper is my equivalent of a nice hot bath. (Says the woman who spent most of her last labor in the tub. NOTHING beats a hot bath during labor.)
Anyway. Jane thinks you should entertain yourselves with her favorite website today: Absurd Math.
September 19, 2006 @ 8:21 pm | Filed under: Math
An opinion piece in yesterday’s New York Times ("Teaching Math, Singapore Style") discusses the recent decision by the National Council of Teachers of Mathematics to revert to the old-fashioned method of teaching math by drilling the basics.
…[I]n the late 1980’s…many schools moved away from traditional mathematics instruction, which
required drills and problem solving. The new system, sometimes derided
as “fuzzy math,’’ allowed children to wander through problems in a
random way without ever learning basic multiplication or division. As a
result, mastery of high-level math and science was unlikely. The new
math curriculum was a mile wide and an inch deep, as the saying goes,
touching on dozens of topics each year.
Many people trace this
unfortunate development to a 1989 report by an influential group, the
National Council of Teachers of Mathematics. School districts read its
recommendations as a call to reject rote learning. Last week the
council reversed itself, laying out new recommendations that will focus
on a few basic skills at each grade level.
Under the new (old)
plan, students will once again move through the basics — addition,
subtraction, multiplication, division and so on — building the skills
that are meant to prepare them for algebra by seventh grade. This new
approach is being seen as an attempt to emulate countries like
Singapore, which ranks at the top internationally in math.
Sounds like the NCTM is thinking along the same lines as many home educators. The Singapore Math curriculum—a series of math texts and workbooks originally used in Singapore primary schools—is quite popular with American homeschoolers. What’s funny is that I’ve always thought the Singapore math books jumped around a lot, which is the opposite of the approach Singapore-the-country is being lauded for in this article. That was actually something Jane enjoyed about the 2nd-grade Singapore Math workbooks: they included fractions, geometry, and graphs along with the multiple-digit addition and subtraction that was the main focus of that year’s material. (But they do include a lot of drill in the basic processes, especially if you use both the workbooks and the non-consumable texts.)
Jane loved the puzzles and riddles in the workbooks: in the early grades, Singapore Math feels more like a puzzle book than a math text, what with the games and the cartoon illustrations.
A little way into the third-grade book, Jane got bored with Singapore and asked if we could go back to Math-U-See. We switched, and she’s been cranking away with MUS ever since. It’s an approach that really works for her; she loves Steve Demme’s sense of humor, she enjoys his explanation of the concepts, and the DVD format really appeals to her. She likes to watch the DVDs with a markerboard in front of her, and she’ll pause every time Mr. Demme sets up a problem, solving it before he does, to see if she got the right answer.
She tends to watch three or four lessons in a gulp, and then she’ll go back to them later, one by one, doing two or three of the six workbook pages that make up each lesson. When we reached the fractions book (Epsilon, I think it is?), she watched that DVD like I watch the BBC’S Pride and Prejudice: in binges, over and over. Even now, she still sometimes asks for it, although she has moved on through the Zeta level (decimals and percents) and the Pre-Algebra, which she is just finishing up. I’ve been looking at the Algebra level, trying to decide whether to order it here in Virginia where the sales tax is lower but we’ll have to move it, or wait until we get to California. (You order through regional distributors so you wind up paying sales tax from just about every state, I think.)
Rose likes Math-U-See too, but she enjoys a bout of workbookery from time to time—at which point we whip out the Singapore books for a week or two.
But I digress. I’m intrigued by the NCMT decision; I’ve heard about the fuzzy math but graduated high school a few years before the 1989 report that introduced it.
We use Math-U-See too, but I didn’t see where there this story was going until Kathy Jo explained:
Sam (five-year-old son): “Mama, I don’t know if I do eight or nine. They both suck.”
Ahem. Alright, this one both shocked and confused me for a moment, and I wasn’t sure whether to laugh or be horrified. I asked him to repeat himself to be sure I understood correctly– and I had. And then I finally realized what he was trying to tell me.
He’s been doing Math-U-See, and I love the way it teaches the math facts to the little guys. You see, nine wants to be ten, so when it’s added to another number, it sucks away one unit from the other number like a vacuum cleaner. Sam hasn’t completely mastered the nine math facts yet, but he’s gotten very fast at giving me the answers. So today we started the eight math facts. It turns out that eight also wants to be ten, so it sucks away two units from the other number.
Hence, when he came across the problem 9 + 8, he wasn’t sure which way to figure out the problem as eight and nine both suck.
Good golly, is that funny. An hour later, I’m still giggling.
There’s a good geography story in Kathy Jo’s story, too. My kids have soaked up a lot of geography over dinner, both with map placemats or (their favorite) sometimes I put a large world map under a clear vinyl tablecloth on the dinner table. The plastic bugs me, or else I’d leave it that way all the time. Whenever I do ditch the pretty blue cotton tablecloth for the map & plastic combo, the kids get very excited. Their peas are quite the little globetrotters. (“Mom, look, it rolled to Peru!”)
And then there’s our old pal Mr. Putty. He has become such a part of the family that I stuck him up there in the sidebar alongside all the kids. These days he is spending a lot of time in Egypt during our read-aloud of The Golden Goblet. Then he moseys to Rome. When we go swimming, somebody dunks him in an ocean: his goal is to visit every major body of water on Earth by the end of next month. I think that includes rivers and lakes. My children really love pool season.
Speaking of geography stories, Karen had a good one this week.
March 20, 2006 @ 7:11 am | Filed under: Math
From Unity of Truth: “Are all infinities the same?”
Well, it seems obvious that that there must be twice as many numbers if you count the half numbers as well as the whole numbers, and three times as many if you count the 1/3 numbers as well as the whole numbers – indeed six times as many if you count halves, thirds, and whole numbers.
But what is obvious is not always true.
There are no more half numbers than whole numbers, because if you line up all the half you can count them – using whole numbers — for as long as you want. So there aren’t any more.
Read the rest.
Jane is hooked on this free math game called Absurd Math: Pre-Algebra from Another Dimension. She has ciphered her way through Panhandler’s Paradise and the Toxic Templex and keeps begging me for a turn at the computer so she can see what comes next.
Many thanks to Trina from our local homeschooling list who shared this link for an incredibly nifty way to multiply. Too cool!
A while back, Wonderboy’s OT gave me a booklet to read about something called “Suck-Swallow-Breathe Synchrony.” At first glance, I wouldn’t have expected it to revitalize the study of math in my home, but that is exactly what has happened.
The booklet describes how the coordinating of these three actions—sucking, swallowing, and breathing—is the brain’s first major task after a baby is born. Successful “SSB Synchrony” lays the groundwork for umpteen other developmental milestones down the road. The entire discussion was fascinating, but what really jumped out at me was the description of how, later in life, the brain uses SSB synchrony as a tension reliever or to help focus on other tasks. This is why Michael Jordan sticks out his tongue when he’s playing basketball. This is why people chew on pens, mints, and fingernails. This (I now realize) is why I seem to be incapable of writing a novel without consuming vast quantities of gummy bears or gumballs. I always thought it had to do with being a sugar junkie. I now understand that it’s about the chewing—it helps my brain to concentrate on the work.
Adults, the booklet explained, quite unconsciously avail themselves of the concentration aid provided by oral stimulation. I am reminded of the editorial meetings of my past: almost everyone at the table had something to sip, munch, or chew. Kids gnaw pencils in school, but gum isn’t usually allowed, for obvious and logical reasons. But our OT told about how she used to work in a school for the deaf, and when she convinced the parents to allow the kids access to pretzels and gummy worms while they did their schoolwork, productivity skyrocketed. A child who would normally have spent 45 minutes struggling through a page of math was now finishing his work in 10 minutes.
My kids, having heard snippets of this conversation, immediately saw the possibilities.
“Let’s test the theory!” cried Jane, my junior scientist.
“Mommy, where’s some gum?” asked Rose, wasting no time. “Let’s all do some math and see if it works.”
“I want to do math too!” wailed Beanie, who, being only four, hasn’t yet climbed on the family Math-U-See bandwagon.
“Mom will make up some problems for you,” reassured practical Rose.
And so began a routine that now occurs several times a week, unprompted by me. The kids get out math books, and that’s my cue to produce some gum. They chomp contentedly and work with impressive concentration. Whether the Impressive Concentration is indeed the effect of the gum, or whether it is the effect of the desire to continue getting gum (heretofore a rare luxury), I cannot say. And I don’t much care.
Truth be told, Jane is one of those people who loves numbers and patterns and mathematical puzzles and formulas. She is working through her great-uncle’s latest college math textbook for fun. I know, I know, it seems weird to me too. But then, when I look at a window with twelve panes, I see twelve rectangles, or maybe thirteen, counting the whole window. Jane sees—oh, I don’t know how many—my brain went numb after she passed the two dozenth rectangle. (Maybe I needed some gum.) She has That Kind of Brain. So really, I’m not sure how much additional assistance the bubble gum is giving her. But what the hey. It cracks me up to hear the girls literally beg me to “let them” do some math. Gee, I’m such a nice mommy—I always say yes.