Math News Archive Aug thru Dec 2009
So Turns out the hit count for math news was pretty low and (doing the math) made this a low yield low priority exercise. Focused on Learning how to make vids and so forth instead. May keep up on this a little better in 2010 but we'll see. Other stuff is higher on the list than Math News...
Back to School/Do the Math: Latest 'new math' concept: Start early and make it fun
First of a series
Sunday, August 30, 2009
By Eleanor Chute, Pittsburgh Post-Gazette
Four-year-old twins Uma and Jayanthi Simhan work on a light table with different shapes at Shady Lane School in Point Breeze.
Many American adults can't explain how to compute miles per gallon, interest paid on a loan or a 15 percent tip.
Some -- even college graduates -- aren't too embarrassed to confess: "I can't do math."
But as the school year begins, it's time to do the math.
Today's children are growing up in a world where basic math calculations can be done by a $3 calculator and the ability to earn a living and make sound consumer decisions increasingly will depend on more than simple addition and subtraction.Back to SchoolDO THE MATHThe Series
Today: Early math
They need help -- from schools and from parents, even those who are math-challenged.
And the earlier the better.
"I think all children start thinking logically and mathematically before 2 years of age," said Roberta Schomburg, associate dean in the School of Education at Carlow University and director of its graduate programs in early childhood education.
"It's not the traditional math we think of in terms of calculations and memorization of algorithms and things like that. In the early years, they're really learning concepts of number, space, passing of time, volume. They're experiencing those at a very physical level. They are building those concepts. That's very critical."
When children begin school without having learned these concepts, their teachers in kindergarten and first grade must lay that foundation, she added, "or the kids will just get further and further behind."
Just as parents have been encouraged to read to their children in the preschool years, the Committee on Early Childhood Mathematics of the National Research Council made a similar push for math with a report issued this summer, "Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity."
"The bottom line is that we are saying that little kids, starting at the age of 3 even and certainly 4, in preschools ought to be doing more math," said Herbert Ginsburg, a member of the Committee on Early Childhood Mathematics and Jacob H. Schiff Foundations professor of psychology and education at Columbia University.
Young children are good at and enjoy doing everyday math activities, he said.
"It's not at all like a lot of school math they don't enjoy," he said.
This doesn't mean the tykes are jotting down equations, but they can deal with numbers -- and talk about them -- in ways that lay the foundation for future math skills.
Talking is important. Some low-income children who didn't have opportunities to talk about math at home as preschoolers had trouble in school even though they knew some basic numbers, according to the recent early childhood study.
At Shady Lane School in Point Breeze, preschoolers learn math skills through play, naturally gravitating to making patterns with blocks, investigating how many items can fit in a circle and putting colored plastic dots in a grid to sort colors and design patterns, such as the one 4-year-old Uma Simhan called her rainbow.
"I'm putting new reds in," said Uma, who attends the school with her twin sister, Jayanthi. "I like this."
Dr. Ginsburg said children "enjoy counting as high as they can, shapes and patterns and all those kinds of things."
He said preschools usually cover counting to 10 or 20 and recognizing shapes, such as a circle, a square and a triangle.
But he said preschool teachers need to go beyond naming numbers and shapes to include concepts -- such as why a circle is a circle and why triangles can be both fat and skinny.
They also can have children count beyond 20 because that's when patterns -- a key mathematical point -- emerge and things get interesting, he said.
Dr. Ginsburg said the panel isn't talking about pushing down the fifth-grade curriculum but rather teaching preschoolers in a deep, interesting and systematic way, with lots of activities and without textbooks.
Providing children with plenty of practice in measuring and counting is important, said Alan Lesgold, dean of the School of Education at the University of Pittsburgh.
"We build knowledge on top of old knowledge," he said. "The way we learn math is we connect it to our experience."
As for what parents can do to help children learn math, Dr. Ginsburg advised "rich and interesting stimulation" at home, but not a formal curriculum.
"I know that a lot of parents are obviously concerned. They go out and they buy various materials, like workbooks at Walmart or K-Mart or whatever. A lot of these are really terrible. They're just drill-oriented kind of things.
"Research has shown board games can help. There are good television shows like 'Sesame Street' and 'Blue's Clues' and some others. There are storybooks that cover math issues, 'Anno's Counting Book' and many others," Dr. Ginsburg said.
But early math computer software needs to go beyond games of shooting down rockets, he said.
"They enjoy some of that and may learn some number facts, but it's not very deep math and they're not going to get very far with that."
Making math fun may be critical to student success, whatever the age.
Jo Boaler is Marie Curie professor of mathematics education at the University of Sussex in England and author of "What's Math Got to Do with It?" a book on how parents and teachers can help children love math.
"Math needs to be fun for children because when it is not, they disengage and their performance goes down," she said.
Her research shows that an interest in math is the most important factor in children continuing with the subject, even more so than achievement.
"When children enjoy math, they do well in the subject and they become powerful," she said.
That doesn't mean Dr. Boaler thinks math has to be easy to be enjoyable.
"Math is fun when we get to engage in the real version of the subject -- when we can ask our own interesting questions, explore patterns, make connections between different areas, solve real problems, use logic, explain reasons and discussion methods with others," Dr. Boaler said.
Her own childhood love of math grew from solving problems and puzzles, including making patterns with Cuisenaire rods -- a set of different-sized rods -- that her mother bought.
Math-challenged parents -- or anyone who has spent too much time staring blankly at math problems on a sheet of paper -- may have difficulty believing math can be fun.
"Most of us learned mathematics in ways that didn't make any sense at all," Dr. Schomburg said.
Today, she said, there is much more teaching for understanding. Some changes have been spurred by the results of the Trend in International Math and Science Study, given every four years to fourth- and eighth-graders since 1995 around the world, most recently in 2007.
The study shows that American students are behind their counterparts in some of the highest-achieving countries.
That may reflect in part different attitudes students in America and some other countries have about math.
Melissa Boston, assistant professor of mathematics education at Duquesne University, said some Americans view having math skills as they view having blue eyes: either you have them or you don't.
"In the United States, we see mathematics as an ability, where other countries which are very successful mathematically see it as an effort. As long as you try hard, you can be good at math," Dr. Boston said.
Kenneth Koedinger, a Carnegie Mellon University professor who is CMU director of the Pittsburgh Science of Learning Center, agreed.
"If you want to do it, you can. You just have to put in an effort," he said.
"It's not easy. It won't come easily to everybody, but it's a myth, 'I'm not a math person.' "
The most recent National Assessment of Adult Literacy in 2003 found nearly a quarter of adults age 16 and older scored at the below-basic level in quantitative literacy, and about a third were just at the basic level.
While the questions asked in 2003 haven't been released yet, the questions about mileage, interest and tips from the previous study in 1992 show the practical impact of such a deficit.
People learn math at different rates. But Kurt VanLehn, professor in computer science and engineering at Arizona State University, said, "There are no inherent limits. It's not like you can learn math up to a certain point and then you can't learn any more."
Even math-phobic parents can help by teaching their children good learning strategies, Dr. Koedinger said.
"That may be the best time to say, 'When I don't know how to do something, I look it up. Let's go to the Internet or to the textbook or to Google for examples.' "
Nancy Bunt, program director of the Math and Science Collaborative based at the Allegheny Intermediate Unit, said struggling is part of learning.
"Encourage [the child] to stick with it. What do you know? What don't you know? How can you find out what you don't know?"
Dr. Ginsburg said parents also can help by not conveying "the idea that learning math is awful. A lot of parents start right away with, 'Oh, math, I hate it.' "
While many young children have fun doing early math, the math achievement gap between children begins to widen around second and third grades as fractions and other more difficult concepts are introduced.
"There is evidence of a lot more math anxiety around second and third grade. The kids find it harder. They get turned off. The gap between those doing well and not so well widens," Dr. Ginsburg said.
"If they don't have the real basics in terms of what does it mean to add and subtract, what does this written math mean on a page, if it's rote, mechanical, then in math the difficulty starts to build," he said.Education writer Eleanor Chute can be reached at firstname.lastname@example.org or 412-263-1955.First published on August 30, 2009 at 12:00 am
Read more: http://www.post-gazette.com/pg/09242/994281-298.stm#ixzz0PosyhmKf
Unraveling how children become bilingual so easily
By LAURAN NEERGAARD, AP Medical Writer Lauran Neergaard, Ap Medical Writer – Tue Jul 21, 3:08 am ET
WASHINGTON – The best time to learn a foreign language: Between birth and age 7. Missed that window?
New research is showing just how children's brains can become bilingual so easily, findings that scientists hope eventually could help the rest of us learn a new language a bit easier.
"We think the magic that kids apply to this learning situation, some of the principles, can be imported into learning programs for adults," says Dr. Patricia Kuhl of the University of Washington, who is part of an international team now trying to turn those lessons into more teachable technology.
Each language uses a unique set of sounds. Scientists now know babies are born with the ability to distinguish all of them, but that ability starts weakening even before they start talking, by the first birthday.
Kuhl offers an example: Japanese doesn't distinguish between the "L" and "R" sounds of English — "rake" and "lake" would sound the same. Her team proved that a 7-month-old in Tokyo and a 7-month-old in Seattle respond equally well to those different sounds. But by 11 months, the Japanese infant had lost a lot of that ability.
Time out — how do you test a baby? By tracking eye gaze. Make a fun toy appear on one side or the other whenever there's a particular sound. The baby quickly learns to look on that side whenever he or she hears a brand-new but similar sound. Noninvasive brain scans document how the brain is processing and imprinting language.
Mastering your dominant language gets in the way of learning a second, less familiar one, Kuhl's research suggests. The brain tunes out sounds that don't fit.
"You're building a brain architecture that's a perfect fit for Japanese or English or French," whatever is native, Kuhl explains — or, if you're a lucky baby, a brain with two sets of neural circuits dedicated to two languages.
It's remarkable that babies being raised bilingual — by simply speaking to them in two languages — can learn both in the time it takes most babies to learn one. On average, monolingual and bilingual babies start talking around age 1 and can say about 50 words by 18 months.
Italian researchers wondered why there wasn't a delay, and reported this month in the journal Science that being bilingual seems to make the brain more flexible.
The researchers tested 44 12-month-olds to see how they recognized three-syllable patterns — nonsense words, just to test sound learning. Sure enough, gaze-tracking showed the bilingual babies learned two kinds of patterns at the same time — like lo-ba-lo or lo-lo-ba — while the one-language babies learned only one, concluded Agnes Melinda Kovacs of Italy's International School for Advanced Studies.
While new language learning is easiest by age 7, the ability markedly declines after puberty.
"We're seeing the brain as more plastic and ready to create new circuits before than after puberty," Kuhl says. As an adult, "it's a totally different process. You won't learn it in the same way. You won't become (as good as) a native speaker."
Yet a soon-to-be-released survey from the Center for Applied Linguistics, a nonprofit organization that researches language issues, shows U.S. elementary schools cut back on foreign language instruction over the last decade. About a quarter of public elementary schools were teaching foreign languages in 1997, but just 15 percent last year, say preliminary results posted on the center's Web site.
What might help people who missed their childhood window? Baby brains need personal interaction to soak in a new language — TV or CDs alone don't work. So researchers are improving the technology that adults tend to use for language learning, to make it more social and possibly tap brain circuitry that tots would use.
Recall that Japanese "L" and "R" difficulty? Kuhl and scientists at Tokyo Denki University and the University of Minnesota helped develop a computer language program that pictures people speaking in "motherese," the slow exaggeration of sounds that parents use with babies.
Japanese college students who'd had little exposure to spoken English underwent 12 sessions listening to exaggerated "Ls" and "Rs" while watching the computerized instructor's face pronounce English words. Brain scans — a hair dryer-looking device called MEG, for magnetoencephalography — that measure millisecond-by-millisecond activity showed the students could better distinguish between those alien English sounds. And they pronounced them better, too, the team reported in the journal NeuroImage.
"It's our very first, preliminary crude attempt but the gains were phenomenal," says Kuhl.
But she'd rather see parents follow biology and expose youngsters early. If you speak a second language, speak it at home. Or find a play group or caregiver where your child can hear another language regularly.
"You'll be surprised," Kuhl says. "They do seem to pick it up like sponges."
EDITOR's NOTE — Lauran Neergaard covers health and medical issues for The Associated Press in Washington.
FAT, DRUNK AND STUPID IS NO WAY TO GO THROUGH LIFE
“We have also arranged things so that almost no one understands science and technology. This is a prescription for disaster. We might get away with it for a while, but sooner or later this combustible mixture of ignorance and power is going to blow up in our faces.” Carl Sagan
The Ugly Numbers
Educational attainment is the single biggest determinant of lifetime income. As of 2008, 14% of Americans over 18 years old haven’t graduated high school, 31% have achieved a high school degree, 27% have earned a bachelor’s degree, and only 9% have earned an advanced degree. The median household income in the U.S. is $46,326. The median household income of Asian households is 24% higher at $57,518. The median household income of Black households is 35% lower at $30,134. Asian households have a fantastic educational achievement, with 49% of Asians achieving a bachelor’s degree or higher. Black households have a higher percentage with no high school degree (18%) than they do with a bachelor’s degree or higher (17%). Hispanic households have even more dreadful levels of educational attainment with only 12% achieving a bachelor’s degree or higher, while a full 37% of Hispanics have not graduated high school. Even though 69 million Americans have attained a high school degree, many are functionally illiterate as our public school system has just matriculated them through the system.
Somehow, despite the billions “invested” in our children, millions graduate and can’t add or subtract. Cashiers in most retail stores would not know how to give you change from a dollar if the cash register didn’t tell them. Even then, it is often times a struggle. The Mathematics literacy of our 15 year olds is well below the world average and 10% to 15% below the leading Asian countries. We did beat Russia, Italy and Mexico. Any cost benefit analysis of what we spend versus what we get would conclude that our educational system is a complete disaster. It should be clear even to a high school dropout that our government bureaucrats haven’t spent our tax money efficiently or effectively. Our public schools are either not teaching the right things or not using the right techniques.
Kathy Goodman: Basketball is not math
7:46 AM, August 12, 2009
Candace_240 I am in faculty meetings this week to get ready for the new school year starting soon, so forgive me if high school curriculum is floating through my head. Tonight, for example, as I was getting ready for our game against the New York Liberty, all I could think of was the transitive property. Everyone remembers this from Algebra I. It is the property in math that states if A is greater than B and B is greater than C, then A is greater than C.
Basketball is not math. Basketball is chemistry. Basketball is physics. Basketball may even be psychology. But basketball is not math.
A month ago, we beat the New York Liberty in Madison Square Garden by nine points without Lisa Leslie. The night before last, we beat the No. 1 team in the league by 12 points. Last night, with our full team finally healthy and available and playing at home, the transitive property says we should have won. We lost to the Liberty by four.
Rest of it:
City reading, math scores offer mixed message
By Kristen A. Graham
INQUIRER STAFF WRITER
For the seventh consecutive year, city students improved their scores on state reading and math tests, according to data released this afternoon by the Philadelphia School District.
Still, fewer than half can read at grade level, and only slightly more can perform math at grade level.
In 2008-09, 52 percent of Philadelphia schoolchildren made the grade in math, up 3 percentage points from last year. Forty-eight percent hit the mark in reading, up 2 percentage points.
If the district continues its incremental gains, it would take until 2123 for all students to reach proficiency. Under the federal No Child Left Behind law, all students must pass state reading and math tests by 2014.
Mixed? The message is simple: NOT GOOD ENOUGH. You'd think they'd want a system that guarantees success...but no...
'Increasing number of schools failed to meet goals
According to the Minnesota Department of Education, more than 45 percent of the state's schools are not making "adequate yearly progress" under the 2002 No Child Left Behind law.
There was this mathmatics teacher who was yelling at his class for not studying. He said, "I wouldn't be surprised if 50% of you flunk this math class!" One of the kids put up his hand. "But teacher," he said, "there aren't that many kids in this class."
More schools in Minnesota failed to meet state math and reading goals this year, but data released Monday about which schools are falling behind contained some bright spots for educators.
According to the Minnesota Department of Education, 1,048 out of 2,303 schools are not making "adequate yearly progress" under the 2002 No Child Left Behind law. That number is up from 931 last year and 727 in 2007.
Chevy Volt's fuzzy math
August 12, 12:27 PM Denver News Examiner
GM grabbed headlines this week with the proclamation that their Chevy Volt gets an EPA rating of 230 miles per gallon. That's a number that comes from trying to translate performance of a car that runs on electricity into terms associated with cars that run on gas. The important question is, "How much does it cost to drive this thing?".
I just heard Stewart Varney interview a GM Vice President who stated that if you were to fully charge the battery and fill the tank, you could go 340 miles before you were out of gas and out of juice.
The gas tank capacity is said to be somewhere between 6-10 gallons (they haven't decided yet). If you take the low number and assume you'll still get your 340 miles, that works out to 56 mpg. That's still very good, but not quite 230. The 56 mpg number also ignores the cost of fully charging the battery. Of course, you'll do much better if you stop and recharge rather than using the gas, but if you're on a long drive, you're probably not going to stop and recharge for 3 hours.
Bottom line, it looks to me like you might cut your gas bills in half by going with the Volt. You'll pay a $15,000 to $20,000 premium for those savings. At current gas prices, assuming you currently get 25 miles per gallon or less and drive 12,000 miles per year, you'd save about $600/year. It'll pay for itself in just 25 years or so, if you don't need to replace the batteries by then. Note: Before you start challenging this number or that, consider that if this vehicle got infinite gas milage and electricity were free, it would still take over 12 years to make up the price premium.
The good news is that there are a lot of folks who just have to have top of the line new technology regardless of the cost efficiency. These are the folks who make the third, fourth and fifth generation technology possible. If there are no severe, unforeseen problems with the technology, all electric cars could actually make fiscal sense in a few years.
The Freaky Math of Plug In Hybrids
Go go for hypertext:
Times have changed: the once-mighty GM seems to be live blogging its "game changing" Chevy hybrid electric VOLT today, claiming its $40K price is justified by its 230 mpg EPA rating. But that number, like so many numbers associated with plug in hybrids, is less impressive than it seems. The charming dorks at Environmental Economics point out that the Volt gets 230 mpg when the trip length is exactly 51.11 miles, but for a trip of 200 miles the car gets 62.5 mpg, which is not much better than my diesel VW Golf, purchased used for around $15K. Of course, there's a lot to love about Plug In hybrids, and GM's new game, but the numbers around them are vexing.
Rickety math wouldn't be a problem if it weren't for the fact that we're trying to fashion an energy policy out of the dream of having a million electric and plug in vehicles on the road by 2015. (More math: today we have only 2000 capable of sustaining freeway speeds, according to cleantechblog. So we're looking at 5000 percent growth in six years. Talk about your hockey stick inflection point!)
But the other problem with plug in hybrids, in particular, is that their gas mileage depends heavily upon the behavior of the driver. As I wrote for Forbes, one person can coax more than 99 mpg out of a modified plug in Toyota Prius, while a pedal-to-the-metal type who forgets to plug the thing in at night will get less than 40 mpg. A study by Argonne National Lab found that driving style alone can reduce the electric range of a vehicle from 40 miles to 15. The numbers get even dicier from there out, because charging a plug in Prius in a state that's got a lot of coal fired electrical generators turns out to be not much better from a greenhouse gas emissions perspective than just using gasoline.
Plug in hybrids are a great idea for Detroit, and for the rest of us too, but they are not a silver bullet for the problems of energy security and greenhouse gas emissions. And they're really not solid enough to base an energy policy around.
***Free online textbooks are now available
Ten high school math and science texts are announced. But critics say the materials fall short of standards and the real costs of using them -- in infrastructure and training -- weren't considered.
"You should be using technology when it's better than what you have now, not just because it's new technology," said Maureen DiMarco, secretary of education under Gov. Pete Wilson and a retired Houghton Mifflin Co. executive.
Let's play spot the conflict of interest...
Thomas said all students would be able to use the texts -- in varying forms. Students without computers or Internet access at home could view them in public libraries, or teachers could print chapters or the entire book, which would cost a fraction of the price of a new textbook.
2009 about freaking time...
First 10 digital textbooks for high schools named
SAN FRANCISCO - State education officials on Tuesday named the first 10 digital textbooks that meet California academic standards for high school math and science.
The electronic textbooks, available for use as soon as this fall, were among the first reviewed as part of Gov. Arnold Schwarzenegger's Free Digital Textbook Initiative.
"We have countries we look at as Third World using digital textbooks more than California."
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