http://www.npr.org/2012/04/07/150126658/fractions-curriculum-strikes-right-note-in-california&sc=fb&cc=fp
by Caitlin Esch April 7, 2012
Math teachers know that fractions can be hard for the average third-grader. Teachers at a public school in San Bruno, Calif., just south of San Francisco, are trying something new. They're teaching difficult math concepts through music, and they're getting remarkable results.
At Allen Elementary School, a roomful of third-graders sits facing music instructor Endre Balogh, their backs straight, eyes ahead, beating a mouse pad with drumsticks. As Balogh taps a rhythm, the students follow.
"What kinds of notes did you play?" Balogh asks. "Jasmine, what do you think?" Jasmine gets it right. "Eighth notes, very good."
These students are learning fractions.
"So, like two-eighths plus six-eighths, you have eight-eighths. But, since it's in the music, it equals a whole note," explains 9-year-old Donte Arevalo.
In the program, called Academic Music, students first learn the basics of reading notes. Then, they learn how to add notes, which is essentially adding fractions. Balogh is drawing the music notes on the board and adding them together.
[...]
San Francisco State University researcher Susan Courey designed the curriculum with Balogh in 2007, because as a former third-grade teacher, she knows how tricky fractions can be.
...
A recent study found that students who went through the program tested better on fractions. The average score of the Academic Music students was nearly double that of students in the regular math class. Courey says even low-performing students did better.
...
..
Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts
Sunday, April 08, 2012
Tuesday, July 26, 2011
Key Early Skills for Later Math Learning Discovered
http://www.sciencedaily.com/releases/2011/07/110711131605.htm
ScienceDaily (July 25, 2011) — Psychologists at the University of Missouri have identified the beginning of first grade math skills that teachers and parents should target to effectively improve children's later math learning.
A long-term psychology study indicates that beginning first graders that understand numbers, the quantities those numbers represent, and low-level arithmetic will have better success in learning mathematics through the end of fifth grade, and other studies suggest throughout the rest of their lives.
"Math is critical for success in many fields, and the United States is not doing a great job of teaching math," said David Geary, Curator's Professor of Psychological Sciences. "Once students fall behind, it's almost impossible to get them back on track. We wanted to identify the beginning of school knowledge needed to learn math over the next five years. We found that understanding numbers and quantity is a necessary foundation for success as the student progresses to more complex math topics. In order to improve basic instruction, we have to know what to instruct. These are the factors that make a difference in the first grade above and beyond intelligence and other abilities."
[.....]
"This study reinforces the idea that math knowledge is incremental, and without a good foundation, a student won't do well because the math gets more complex," Geary said. "The kids that can go back and forth easily and quickly in translating numerals, the number five, for example, into quantities and in breaking complex problems into smaller parts had a very good head start."
The researchers also found that first graders who understood the number line and how to place numbers on the line and who knew some basic facts showed faster growth in math skills than their counterparts over the next five years. However, the researchers found that these early math skills had no impact on future reading ability.
..
ScienceDaily (July 25, 2011) — Psychologists at the University of Missouri have identified the beginning of first grade math skills that teachers and parents should target to effectively improve children's later math learning.
A long-term psychology study indicates that beginning first graders that understand numbers, the quantities those numbers represent, and low-level arithmetic will have better success in learning mathematics through the end of fifth grade, and other studies suggest throughout the rest of their lives.
"Math is critical for success in many fields, and the United States is not doing a great job of teaching math," said David Geary, Curator's Professor of Psychological Sciences. "Once students fall behind, it's almost impossible to get them back on track. We wanted to identify the beginning of school knowledge needed to learn math over the next five years. We found that understanding numbers and quantity is a necessary foundation for success as the student progresses to more complex math topics. In order to improve basic instruction, we have to know what to instruct. These are the factors that make a difference in the first grade above and beyond intelligence and other abilities."
[.....]
"This study reinforces the idea that math knowledge is incremental, and without a good foundation, a student won't do well because the math gets more complex," Geary said. "The kids that can go back and forth easily and quickly in translating numerals, the number five, for example, into quantities and in breaking complex problems into smaller parts had a very good head start."
The researchers also found that first graders who understood the number line and how to place numbers on the line and who knew some basic facts showed faster growth in math skills than their counterparts over the next five years. However, the researchers found that these early math skills had no impact on future reading ability.
..
Friday, August 13, 2010
Students' Understanding of the Equal Sign Not Equal
http://www.sciencedaily.com/releases/2010/08/100810122200.htm
ScienceDaily (Aug. 11, 2010) — Taken very literally, not all students are created equal -- especially in their math learning skills, say Texas A&M University researchers who have found that not fully understanding the "equal sign" in a math problem could be a key to why U.S. students underperform their peers from other countries in math.
"About 70 percent of middle grades students in the United States exhibit misconceptions, but nearly none of the international students in Korea and China have a misunderstanding about the equal sign, and Turkish students exhibited far less incidence of the misconception than the U.S. students," note Robert M. Capraro and Mary Capraro of the Department of Teaching, Learning, and Culture at Texas A&M.
----- (skipping)
Students who exhibit the correct understanding of the equal sign show the greatest achievement in mathematics and persist in fields that require mathematics proficiency like engineering, according to their research.
"The equal sign is pervasive and fundamentally linked to mathematics from kindergarten through upper-level calculus," Robert M. Capraro says. "The idea of symbols that convey relative meaning, such as the equal sign and "less than" and "greater than" signs, is complex and they serve as a precursor to ideas of variables, which also require the same level of abstract thinking."
The problem is students memorize procedures without fully understanding the mathematics, he notes.
"Students who have learned to memorize symbols and who have a limited understanding of the equal sign will tend to solve problems such as 4+3+2=( )+2 by adding the numbers on the left, and placing it in the parentheses, then add those terms and create another equal sign with the new answer," he explains. "So the work would look like 4+3+2=(9)+2=11.
"This response has been called a running equal sign -- similar to how a calculator might work when the numbers and equal sign are entered as they appear in the sentence," he explains. "However, this understanding is incorrect. The correct solution makes both sides equal. So the understanding should be 4+3+2=(7)+2. Now both sides of the equal sign equal 9."
One cause of the problem might be the textbooks, the research shows.
The Texas A&M researchers examined textbooks in China and the United States and found "Chinese textbooks provided the best examples for students and that even the best U.S. textbooks, those sponsored by the National Science Foundation, were lacking relational examples about the equal sign."
Parents and teachers can help the students. The two researchers suggest using mathematics manipulatives and encourage teachers "to read professional journals, become informed about the problem and modify their instruction."
..
ScienceDaily (Aug. 11, 2010) — Taken very literally, not all students are created equal -- especially in their math learning skills, say Texas A&M University researchers who have found that not fully understanding the "equal sign" in a math problem could be a key to why U.S. students underperform their peers from other countries in math.
"About 70 percent of middle grades students in the United States exhibit misconceptions, but nearly none of the international students in Korea and China have a misunderstanding about the equal sign, and Turkish students exhibited far less incidence of the misconception than the U.S. students," note Robert M. Capraro and Mary Capraro of the Department of Teaching, Learning, and Culture at Texas A&M.
----- (skipping)
Students who exhibit the correct understanding of the equal sign show the greatest achievement in mathematics and persist in fields that require mathematics proficiency like engineering, according to their research.
"The equal sign is pervasive and fundamentally linked to mathematics from kindergarten through upper-level calculus," Robert M. Capraro says. "The idea of symbols that convey relative meaning, such as the equal sign and "less than" and "greater than" signs, is complex and they serve as a precursor to ideas of variables, which also require the same level of abstract thinking."
The problem is students memorize procedures without fully understanding the mathematics, he notes.
"Students who have learned to memorize symbols and who have a limited understanding of the equal sign will tend to solve problems such as 4+3+2=( )+2 by adding the numbers on the left, and placing it in the parentheses, then add those terms and create another equal sign with the new answer," he explains. "So the work would look like 4+3+2=(9)+2=11.
"This response has been called a running equal sign -- similar to how a calculator might work when the numbers and equal sign are entered as they appear in the sentence," he explains. "However, this understanding is incorrect. The correct solution makes both sides equal. So the understanding should be 4+3+2=(7)+2. Now both sides of the equal sign equal 9."
One cause of the problem might be the textbooks, the research shows.
The Texas A&M researchers examined textbooks in China and the United States and found "Chinese textbooks provided the best examples for students and that even the best U.S. textbooks, those sponsored by the National Science Foundation, were lacking relational examples about the equal sign."
Parents and teachers can help the students. The two researchers suggest using mathematics manipulatives and encourage teachers "to read professional journals, become informed about the problem and modify their instruction."
..
Fun With Mortality Tables
http://krugman.blogs.nytimes.com/2010/08/13/fun-with-mortality-tables/
August 13, 2010, 5:50 pm
Hoo boy, if Social Security is the big thing in the next few months — which is starting to look possible — it’s going to be like old times again, shooting down all the usual fallacies one more time.
So: one thing you’re going to hear is something along the lines of, “In 1950 life expectancy was only 68 years, so hardly anyone was collecting Social Security; now it’s 78 years — the problem is obvious”.
Does anyone know what’s wrong with this? You over there in the corner?
That’s right: a life expectancy of 68 years doesn’t mean that a lot of people toddle along then suddenly keel over over after threescore and eight birthdays. Mostly it meant much higher child mortality than we have now, which has no relevance one way or the other to Social Security.
Much more to the point is the number of years people could expect to live after reaching 65: 14 years in 1950, 18.5 years now. Not so impressive a change, is it? And the retirement age is already 66 for my cohort, and scheduled to rise to 67 on current law.
Oh, and by the way, rising life expectancy was built into Social Security planning from the beginning. The big surprise has, if anything, been stagnating life expectancy among less affluent Americans.
=========================================================
Paul Krugman has a series of posts about facts about Social Security.
http://krugman.blogs.nytimes.com/
..
August 13, 2010, 5:50 pm
Hoo boy, if Social Security is the big thing in the next few months — which is starting to look possible — it’s going to be like old times again, shooting down all the usual fallacies one more time.
So: one thing you’re going to hear is something along the lines of, “In 1950 life expectancy was only 68 years, so hardly anyone was collecting Social Security; now it’s 78 years — the problem is obvious”.
Does anyone know what’s wrong with this? You over there in the corner?
That’s right: a life expectancy of 68 years doesn’t mean that a lot of people toddle along then suddenly keel over over after threescore and eight birthdays. Mostly it meant much higher child mortality than we have now, which has no relevance one way or the other to Social Security.
Much more to the point is the number of years people could expect to live after reaching 65: 14 years in 1950, 18.5 years now. Not so impressive a change, is it? And the retirement age is already 66 for my cohort, and scheduled to rise to 67 on current law.
Oh, and by the way, rising life expectancy was built into Social Security planning from the beginning. The big surprise has, if anything, been stagnating life expectancy among less affluent Americans.
=========================================================
Paul Krugman has a series of posts about facts about Social Security.
http://krugman.blogs.nytimes.com/
..
Friday, October 30, 2009
Pandemic flu vaccine campaigns may be undermined by coincidental medical events
http://www.eurekalert.org/pub_releases/2009-10/cchm-pfv103009.php
Public release date: 30-Oct-2009
Contact: Nick Miller
Cincinnati Children's Hospital Medical Center
Pandemic flu vaccine campaigns may be undermined by coincidental medical events
Lancet paper stresses importance of accounting for background rates of adverse events
CINCINNATI – The effectiveness of pandemic flu vaccination campaigns – like that now underway for H1N1 – could be undermined by the public incorrectly associating coincidental and unrelated health events with the vaccines.
This is the conclusion of a paper published online Oct. 31 by the Lancet and authored by an international team of investigators led by Cincinnati Children's Hospital Medical Center.
"Regardless of whether someone gets the vaccine, bad things happen to people every day and generally occur at fairly predictable rates," said Steven Black, M.D., lead author and a physician in the Center for Global Health and Division of Infectious Diseases at Cincinnati Children's. "Identifying real safety concerns with new vaccines means we have to untangle actual safety signals from background medical events, which are those that would happen without vaccination."
The team of investigators from 13 global medical institutions and health agencies reviewed medical data from prior studies and from hospital databases to identify background rates of health events that occurred without any vaccine. Their review showed the rates of adverse events varied by year, country, age and sex of the population.
The problem the authors identified is that public concern regarding medical events can interfere with important vaccine programs, even if the vaccine is not the cause. One example they cited is the interruption of a 2006 seasonal influenza campaign in Israel, where four deaths occurred within 24 hours of immunization. The clustering of fatalities and close timing of vaccination resulted in global news coverage, public trepidation and compromised the inoculation campaign.
In actuality, the four patients who died all were in a group already at high risk for sudden death from age and underlying medical conditions. Their deaths were consistent with a cardiac cause of death, and the number of deaths was lower than would be expected normally for such a high risk population. Further analysis of the fatalities in Israel showed death normally occurs in this high risk group at a rate greater than one per 1,000 individuals in the same time period. Based on this, the researchers said 20 coincidental deaths among that group could be expected to occur by chance within 24 hours of an immunization.
The authors also revisited one of the concerns raised during the 1976-77 swine flu vaccination program. The vaccine in that campaign was associated with an increased number of Guillian-Barre Syndrome cases, in which the body's immune system mistakenly attacks part of the nervous system. Guillian-Barre normally affects about one out of every 100,000 people a year. Based on this Guillian-Barre background rate, if 100 million people in the United States are inoculated in a pandemic flu vaccination campaign, the researchers said one would expect 215 new cases of the disease within six weeks of vaccine. These cases would be expected to occur whether or not the vaccine had been given.
"The reporting of even a fraction of such a large number of case as adverse events following immunization, with attendant media coverage, would likely give rise to high levels public concern, even though the occurrence of such cases was completely predictable and would have happened in the absence of a mass campaign," according to the paper.
To help address these concerns, the U.S. Centers for Disease Control and Prevention (CDC) and other health agencies have been creating systems to gather and accurately assess data on background health events when evaluating vaccine safety. The current paper presents some new data but also puts existing data into context for the public, said Dr. Black, who also serves as a pandemic flu vaccine safety consultant to the National Vaccine Program Office at the Department of Health and Human Services.
"In the heat of the moment of a pandemic vaccination campaign, the public isn't good at evaluating comparative risk or realizing that obviously some people die or develop serious illnesses every day," Dr. Black said. "By putting background rate data into proper context, we want to help people make an informed decision about pandemic flu vaccinations."
Public release date: 30-Oct-2009
Contact: Nick Miller
Cincinnati Children's Hospital Medical Center
Pandemic flu vaccine campaigns may be undermined by coincidental medical events
Lancet paper stresses importance of accounting for background rates of adverse events
CINCINNATI – The effectiveness of pandemic flu vaccination campaigns – like that now underway for H1N1 – could be undermined by the public incorrectly associating coincidental and unrelated health events with the vaccines.
This is the conclusion of a paper published online Oct. 31 by the Lancet and authored by an international team of investigators led by Cincinnati Children's Hospital Medical Center.
"Regardless of whether someone gets the vaccine, bad things happen to people every day and generally occur at fairly predictable rates," said Steven Black, M.D., lead author and a physician in the Center for Global Health and Division of Infectious Diseases at Cincinnati Children's. "Identifying real safety concerns with new vaccines means we have to untangle actual safety signals from background medical events, which are those that would happen without vaccination."
The team of investigators from 13 global medical institutions and health agencies reviewed medical data from prior studies and from hospital databases to identify background rates of health events that occurred without any vaccine. Their review showed the rates of adverse events varied by year, country, age and sex of the population.
The problem the authors identified is that public concern regarding medical events can interfere with important vaccine programs, even if the vaccine is not the cause. One example they cited is the interruption of a 2006 seasonal influenza campaign in Israel, where four deaths occurred within 24 hours of immunization. The clustering of fatalities and close timing of vaccination resulted in global news coverage, public trepidation and compromised the inoculation campaign.
In actuality, the four patients who died all were in a group already at high risk for sudden death from age and underlying medical conditions. Their deaths were consistent with a cardiac cause of death, and the number of deaths was lower than would be expected normally for such a high risk population. Further analysis of the fatalities in Israel showed death normally occurs in this high risk group at a rate greater than one per 1,000 individuals in the same time period. Based on this, the researchers said 20 coincidental deaths among that group could be expected to occur by chance within 24 hours of an immunization.
The authors also revisited one of the concerns raised during the 1976-77 swine flu vaccination program. The vaccine in that campaign was associated with an increased number of Guillian-Barre Syndrome cases, in which the body's immune system mistakenly attacks part of the nervous system. Guillian-Barre normally affects about one out of every 100,000 people a year. Based on this Guillian-Barre background rate, if 100 million people in the United States are inoculated in a pandemic flu vaccination campaign, the researchers said one would expect 215 new cases of the disease within six weeks of vaccine. These cases would be expected to occur whether or not the vaccine had been given.
"The reporting of even a fraction of such a large number of case as adverse events following immunization, with attendant media coverage, would likely give rise to high levels public concern, even though the occurrence of such cases was completely predictable and would have happened in the absence of a mass campaign," according to the paper.
To help address these concerns, the U.S. Centers for Disease Control and Prevention (CDC) and other health agencies have been creating systems to gather and accurately assess data on background health events when evaluating vaccine safety. The current paper presents some new data but also puts existing data into context for the public, said Dr. Black, who also serves as a pandemic flu vaccine safety consultant to the National Vaccine Program Office at the Department of Health and Human Services.
"In the heat of the moment of a pandemic vaccination campaign, the public isn't good at evaluating comparative risk or realizing that obviously some people die or develop serious illnesses every day," Dr. Black said. "By putting background rate data into proper context, we want to help people make an informed decision about pandemic flu vaccinations."
Statisticians reject global cooling
http://news.yahoo.com/s/ap/20091026/ap_on_bi_ge/us_sci_global_cooling;_ylt=AtzAhJxjs5HF0X1LWeb8lVWs0NUE;_ylu=X3oDMTFlMG04OHRoBHBvcwMxMTUEc2VjA2FjY29yZGlvbl9zY2llbmNlBHNsawNhcGltcGFjdHN0YXQ-
By SETH BORENSTEIN, AP Science Writer Seth Borenstein, Ap Science Writer – Mon Oct 26, 5:12 pm ET
WASHINGTON – Have you heard that the world is now cooling instead of warming? You may have seen some news reports on the Internet or heard about it from a provocative new book. Only one problem: It's not true, according to an analysis of the numbers done by several independent statisticians for The Associated Press.
The case that the Earth might be cooling partly stems from recent weather. Last year was cooler than previous years. It's been a while since the super-hot years of 1998 and 2005. So is this a longer climate trend or just weather's normal ups and downs?
In a blind test, the AP gave temperature data to four independent statisticians and asked them to look for trends, without telling them what the numbers represented. The experts found no true temperature declines over time.
"If you look at the data and sort of cherry-pick a micro-trend within a bigger trend, that technique is particularly suspect," said John Grego, a professor of statistics at the University of South Carolina.
Yet the idea that things are cooling has been repeated in opinion columns, a BBC news story posted on the Drudge Report and in a new book by the authors of the best-seller "Freakonomics." Last week, a poll by the Pew Research Center found that only 57 percent of Americans now believe there is strong scientific evidence for global warming, down from 77 percent in 2006.
Global warming skeptics base their claims on an unusually hot year in 1998. Since then, they say, temperatures have dropped — thus, a cooling trend. But it's not that simple.
Since 1998, temperatures have dipped, soared, fallen again and are now rising once more. Records kept by the British meteorological office and satellite data used by climate skeptics still show 1998 as the hottest year. However, data from the National Oceanic and Atmospheric Administration and NASA show 2005 has topped 1998. Published peer-reviewed scientific research generally cites temperatures measured by ground sensors, which are from NOAA, NASA and the British, more than the satellite data.
The recent Internet chatter about cooling led NOAA's climate data center to re-examine its temperature data. It found no cooling trend.
"The last 10 years are the warmest 10-year period of the modern record," said NOAA climate monitoring chief Deke Arndt. "Even if you analyze the trend during that 10 years, the trend is actually positive, which means warming."
The AP sent expert statisticians NOAA's year-to-year ground temperature changes over 130 years and the 30 years of satellite-measured temperatures preferred by skeptics and gathered by scientists at the University of Alabama in Huntsville.
Statisticians who analyzed the data found a distinct decades-long upward trend in the numbers, but could not find a significant drop in the past 10 years in either data set. The ups and downs during the last decade repeat random variability in data as far back as 1880.
Saying there's a downward trend since 1998 is not scientifically legitimate, said David Peterson, a retired Duke University statistics professor and one of those analyzing the numbers.
Identifying a downward trend is a case of "people coming at the data with preconceived notions," said Peterson, author of the book "Why Did They Do That? An Introduction to Forensic Decision Analysis."
One prominent skeptic said that to find the cooling trend, the 30 years of satellite temperatures must be used. The satellite data tends to be cooler than the ground data. And key is making sure 1998 is part of the trend, he added.
It's what happens within the past 10 years or so, not the overall average, that counts, contends Don Easterbrook, a Western Washington University geology professor and global warming skeptic.
"I don't argue with you that the 10-year average for the past 10 years is higher than the previous 10 years," said Easterbrook, who has self-published some of his research. "We started the cooling trend after 1998. You're going to get a different line depending on which year you choose.
"Should not the actual temperature be higher now than it was in 1998?" Easterbrook asked. "We can play the numbers games."
That's the problem, some of the statisticians said.
Grego produced three charts to show how choosing a starting date can alter perceptions. Using the skeptics' satellite data beginning in 1998, there is a "mild downward trend," he said. But doing that is "deceptive."
The trend disappears if the analysis starts in 1997. And it trends upward if you begin in 1999, he said.
Apart from the conflicting data analyses is the eyebrow-raising new book title from Steven D. Levitt and Stephen J. Dubner, "Super Freakonomics: Global Cooling, Patriotic Prostitutes and Why Suicide Bombers Should Buy Life Insurance."
A line in the book says: "Then there's this little-discussed fact about global warming: While the drumbeat of doom has grown louder over the past several years, the average global temperature during that time has in fact decreased."
That led to a sharp rebuke from the Union of Concerned Scientists, which said the book mischaracterizes climate science with "distorted statistics."
Levitt, a University of Chicago economist, said he does not believe there is a cooling trend. He said the line was just an attempt to note the irony of a cool couple of years at a time of intense discussion of global warming. Levitt said he did not do any statistical analysis of temperatures, but "eyeballed" the numbers and noticed 2005 was hotter than the last couple of years. Levitt said the "cooling" reference in the book title refers more to ideas about trying to cool the Earth artificially.
Statisticians say that in sizing up climate change, it's important to look at moving averages of about 10 years. They compare the average of 1999-2008 to the average of 2000-2009. In all data sets, 10-year moving averages have been higher in the last five years than in any previous years.
"To talk about global cooling at the end of the hottest decade the planet has experienced in many thousands of years is ridiculous," said Ken Caldeira, a climate scientist at the Carnegie Institution at Stanford.
Ben Santer, a climate scientist at the Department of Energy's Lawrence Livermore National Lab, called it "a concerted strategy to obfuscate and generate confusion in the minds of the public and policymakers" ahead of international climate talks in December in Copenhagen.
President Barack Obama weighed in on the topic Friday at MIT. He said some opponents "make cynical claims that contradict the overwhelming scientific evidence when it comes to climate change — claims whose only purpose is to defeat or delay the change that we know is necessary."
Earlier this year, climate scientists in two peer-reviewed publications statistically analyzed recent years' temperatures against claims of cooling and found them not valid.
Not all skeptical scientists make the flat-out cooling argument.
"It pretty much depends on when you start," wrote John Christy, the Alabama atmospheric scientist who collects the satellite data that skeptics use. He said in an e-mail that looking back 31 years, temperatures have gone up nearly three-quarters of a degree Fahrenheit (four-tenths of a degree Celsius). The last dozen years have been flat, and temperatures over the last eight years have declined a bit, he wrote.
Oceans, which take longer to heat up and longer to cool, greatly influence short-term weather, causing temperatures to rise and fall temporarily on top of the overall steady warming trend, scientists say. The biggest example of that is El Nino.
El Nino, a temporary warming of part of the Pacific Ocean, usually spikes global temperatures, scientists say. The two recent warm years, both 1998 and 2005, were El Nino years. The flip side of El Nino is La Nina, which lowers temperatures. A La Nina bloomed last year and temperatures slipped a bit, but 2008 was still the ninth hottest in 130 years of NOAA records.
Of the 10 hottest years recorded by NOAA, eight have occurred since 2000, and after this year it will be nine because this year is on track to be the sixth-warmest on record.
The current El Nino is forecast to get stronger, probably pushing global temperatures even higher next year, scientists say. NASA climate scientist Gavin Schmidt predicts 2010 may break a record, so a cooling trend "will be never talked about again."
By SETH BORENSTEIN, AP Science Writer Seth Borenstein, Ap Science Writer – Mon Oct 26, 5:12 pm ET
WASHINGTON – Have you heard that the world is now cooling instead of warming? You may have seen some news reports on the Internet or heard about it from a provocative new book. Only one problem: It's not true, according to an analysis of the numbers done by several independent statisticians for The Associated Press.
The case that the Earth might be cooling partly stems from recent weather. Last year was cooler than previous years. It's been a while since the super-hot years of 1998 and 2005. So is this a longer climate trend or just weather's normal ups and downs?
In a blind test, the AP gave temperature data to four independent statisticians and asked them to look for trends, without telling them what the numbers represented. The experts found no true temperature declines over time.
"If you look at the data and sort of cherry-pick a micro-trend within a bigger trend, that technique is particularly suspect," said John Grego, a professor of statistics at the University of South Carolina.
Yet the idea that things are cooling has been repeated in opinion columns, a BBC news story posted on the Drudge Report and in a new book by the authors of the best-seller "Freakonomics." Last week, a poll by the Pew Research Center found that only 57 percent of Americans now believe there is strong scientific evidence for global warming, down from 77 percent in 2006.
Global warming skeptics base their claims on an unusually hot year in 1998. Since then, they say, temperatures have dropped — thus, a cooling trend. But it's not that simple.
Since 1998, temperatures have dipped, soared, fallen again and are now rising once more. Records kept by the British meteorological office and satellite data used by climate skeptics still show 1998 as the hottest year. However, data from the National Oceanic and Atmospheric Administration and NASA show 2005 has topped 1998. Published peer-reviewed scientific research generally cites temperatures measured by ground sensors, which are from NOAA, NASA and the British, more than the satellite data.
The recent Internet chatter about cooling led NOAA's climate data center to re-examine its temperature data. It found no cooling trend.
"The last 10 years are the warmest 10-year period of the modern record," said NOAA climate monitoring chief Deke Arndt. "Even if you analyze the trend during that 10 years, the trend is actually positive, which means warming."
The AP sent expert statisticians NOAA's year-to-year ground temperature changes over 130 years and the 30 years of satellite-measured temperatures preferred by skeptics and gathered by scientists at the University of Alabama in Huntsville.
Statisticians who analyzed the data found a distinct decades-long upward trend in the numbers, but could not find a significant drop in the past 10 years in either data set. The ups and downs during the last decade repeat random variability in data as far back as 1880.
Saying there's a downward trend since 1998 is not scientifically legitimate, said David Peterson, a retired Duke University statistics professor and one of those analyzing the numbers.
Identifying a downward trend is a case of "people coming at the data with preconceived notions," said Peterson, author of the book "Why Did They Do That? An Introduction to Forensic Decision Analysis."
One prominent skeptic said that to find the cooling trend, the 30 years of satellite temperatures must be used. The satellite data tends to be cooler than the ground data. And key is making sure 1998 is part of the trend, he added.
It's what happens within the past 10 years or so, not the overall average, that counts, contends Don Easterbrook, a Western Washington University geology professor and global warming skeptic.
"I don't argue with you that the 10-year average for the past 10 years is higher than the previous 10 years," said Easterbrook, who has self-published some of his research. "We started the cooling trend after 1998. You're going to get a different line depending on which year you choose.
"Should not the actual temperature be higher now than it was in 1998?" Easterbrook asked. "We can play the numbers games."
That's the problem, some of the statisticians said.
Grego produced three charts to show how choosing a starting date can alter perceptions. Using the skeptics' satellite data beginning in 1998, there is a "mild downward trend," he said. But doing that is "deceptive."
The trend disappears if the analysis starts in 1997. And it trends upward if you begin in 1999, he said.
Apart from the conflicting data analyses is the eyebrow-raising new book title from Steven D. Levitt and Stephen J. Dubner, "Super Freakonomics: Global Cooling, Patriotic Prostitutes and Why Suicide Bombers Should Buy Life Insurance."
A line in the book says: "Then there's this little-discussed fact about global warming: While the drumbeat of doom has grown louder over the past several years, the average global temperature during that time has in fact decreased."
That led to a sharp rebuke from the Union of Concerned Scientists, which said the book mischaracterizes climate science with "distorted statistics."
Levitt, a University of Chicago economist, said he does not believe there is a cooling trend. He said the line was just an attempt to note the irony of a cool couple of years at a time of intense discussion of global warming. Levitt said he did not do any statistical analysis of temperatures, but "eyeballed" the numbers and noticed 2005 was hotter than the last couple of years. Levitt said the "cooling" reference in the book title refers more to ideas about trying to cool the Earth artificially.
Statisticians say that in sizing up climate change, it's important to look at moving averages of about 10 years. They compare the average of 1999-2008 to the average of 2000-2009. In all data sets, 10-year moving averages have been higher in the last five years than in any previous years.
"To talk about global cooling at the end of the hottest decade the planet has experienced in many thousands of years is ridiculous," said Ken Caldeira, a climate scientist at the Carnegie Institution at Stanford.
Ben Santer, a climate scientist at the Department of Energy's Lawrence Livermore National Lab, called it "a concerted strategy to obfuscate and generate confusion in the minds of the public and policymakers" ahead of international climate talks in December in Copenhagen.
President Barack Obama weighed in on the topic Friday at MIT. He said some opponents "make cynical claims that contradict the overwhelming scientific evidence when it comes to climate change — claims whose only purpose is to defeat or delay the change that we know is necessary."
Earlier this year, climate scientists in two peer-reviewed publications statistically analyzed recent years' temperatures against claims of cooling and found them not valid.
Not all skeptical scientists make the flat-out cooling argument.
"It pretty much depends on when you start," wrote John Christy, the Alabama atmospheric scientist who collects the satellite data that skeptics use. He said in an e-mail that looking back 31 years, temperatures have gone up nearly three-quarters of a degree Fahrenheit (four-tenths of a degree Celsius). The last dozen years have been flat, and temperatures over the last eight years have declined a bit, he wrote.
Oceans, which take longer to heat up and longer to cool, greatly influence short-term weather, causing temperatures to rise and fall temporarily on top of the overall steady warming trend, scientists say. The biggest example of that is El Nino.
El Nino, a temporary warming of part of the Pacific Ocean, usually spikes global temperatures, scientists say. The two recent warm years, both 1998 and 2005, were El Nino years. The flip side of El Nino is La Nina, which lowers temperatures. A La Nina bloomed last year and temperatures slipped a bit, but 2008 was still the ninth hottest in 130 years of NOAA records.
Of the 10 hottest years recorded by NOAA, eight have occurred since 2000, and after this year it will be nine because this year is on track to be the sixth-warmest on record.
The current El Nino is forecast to get stronger, probably pushing global temperatures even higher next year, scientists say. NASA climate scientist Gavin Schmidt predicts 2010 may break a record, so a cooling trend "will be never talked about again."
Monday, June 29, 2009
Claims that the demonstrations are caused by outside forces, such as the CIA, are insulting to the Iranian people, implying that they don't have the strength to fight oppression on their own. When voiced by people in the U.S., it is itself a form of the low esteem toward other countries that they accuse the U.S. of.
http://www.newscientist.com/article/mg20227144.000-statistics-hint-at-fraud-in-iranian-election.html
24 June 2009 by Stephen Battersby Magazine issue 2714
ALLEGATIONS that Iran's presidential election on 12 June was rigged are being followed up by statisticians in the US and elsewhere who are studying published voting figures for signs of irregularities. They say they have found "moderately strong" evidence that the figures are not genuine, though all are careful to emphasise that maths alone can't prove fraud.
Opponents of the incumbent, Mahmoud Ahmadinejad, who was declared to have won by a landslide, have pointed to his wide margin of victory, the speed of the announcement and some unexpected results, such as Mehdi Karroubi's poor showing in his home state of Lorestan.
One suggested anomaly - that Ahmadinejad's proportion of the vote remained almost constant as the results were announced in six stages - was soon debunked by New York-based statistician and political pundit Nate Silver. He says this is not surprising when votes are reported in large slabs, and that the same effect would have occurred during last year's US presidential election if the results had been reported this way.
To dig deeper, Boudewijn Roukema of Nicolaus Copernicus University in Torun, Poland, used a mathematical tool called Benford's law. In many random sets of data, numbers are more likely to begin with 1 than any other digit. The next most frequent starting digit is 2, then 3 and so on, in a precise relationship. The law applies to any set of numbers scattered randomly on a logarithmic scale.
Any deviation from this pattern could suggest that figures have been manipulated. This has been used to uncover tax fraud and false expenses claims, and Roukema now says it points to fraud in the Iranian election. He analysed the vote counts reported for the four candidates in 366 districts. Votes for three of the candidates fit expected patterns, but Karroubi has an unexpectedly large number of counts beginning with the digit 7. The chance of such a large deviation from Benford's law happening without foul play is only 0.7 per cent, Roukema says. "The simplest interpretation would be that someone interfered in the overall counts per district."
Political scientist Walter Mebane of the University of Michigan, Ann Arbor, has found another anomaly. Based on figures from Iran's presidential election in 2005, when Karroubi was also among Ahmadinejad's rivals, he built a statistical model to predict how each would be expected to do in various districts in 2009.
The model assumes that the 2005 votes were based on regional differences in policy preferences, ethnicities and demographics that should still show up in 2009. Yet in around 200 of the 366 districts voting numbers were inconsistent with the model - and in two-thirds of these, Ahmadinejad's vote was higher than predicted. "It is moderately strong evidence in favour of the idea that there was fraud," says Mebane.
This is far from proof, however. "It is also compatible with the idea that the model is no good," Mebane admits. "I've never said that statistics alone can prove fraud." What it can do is identify places where there may be fraud, so that other investigations - such as studying the ballot papers themselves - can follow.
Monday, March 02, 2009
3/3/09: Math fans to celebrate Square Root Day
How neat. This is the first time I've heard of this.
http://news.yahoo.com/s/ap/20090303/ap_on_fe_st/odd_square_root_day;_ylt=Al2cs_SAONqgzPcm_uSJ9wes0NUE;_ylu=X3oDMTFpZXI4a2g1BHBvcwMyNARzZWMDYWNjb3JkaW9uX21vc3RfcG9wdWxhcgRzbGsDMzMwOW1hdGhmYW5z
Mon Mar 2, 7:32 pm ET
REDWOOD CITY, Calif. – Dust off the slide rules and recharge the calculators. Square Root Day is upon us.
The math-buffs' holiday, which only occurs nine times each century, falls on Tuesday — 3/3/09 (for the mathematically challenged, three is the square root of nine).
"These days are like calendar comets, you wait and wait and wait for them, then they brighten up your day — and poof — they're gone," said Ron Gordon, a Redwood City teacher who started a contest meant to get people excited about the event.
The winner gets, of course, $339 for having the biggest Square Root Day event.
Gordon's daughter even set up a Facebook page — one of a half-dozen or so dedicated to the holiday — and hundreds of people had signed up with plans to celebrate in some way. Celebrations are as varied: Some cut root vegetables into squares, others make food in the shape of a square root symbol.
The last such day was five years ago, Feb. 2, 2004, which coincided with Groundhog Day. The next is seven years away, on April 4, 2016.
http://news.yahoo.com/s/ap/20090303/ap_on_fe_st/odd_square_root_day;_ylt=Al2cs_SAONqgzPcm_uSJ9wes0NUE;_ylu=X3oDMTFpZXI4a2g1BHBvcwMyNARzZWMDYWNjb3JkaW9uX21vc3RfcG9wdWxhcgRzbGsDMzMwOW1hdGhmYW5z
Mon Mar 2, 7:32 pm ET
REDWOOD CITY, Calif. – Dust off the slide rules and recharge the calculators. Square Root Day is upon us.
The math-buffs' holiday, which only occurs nine times each century, falls on Tuesday — 3/3/09 (for the mathematically challenged, three is the square root of nine).
"These days are like calendar comets, you wait and wait and wait for them, then they brighten up your day — and poof — they're gone," said Ron Gordon, a Redwood City teacher who started a contest meant to get people excited about the event.
The winner gets, of course, $339 for having the biggest Square Root Day event.
Gordon's daughter even set up a Facebook page — one of a half-dozen or so dedicated to the holiday — and hundreds of people had signed up with plans to celebrate in some way. Celebrations are as varied: Some cut root vegetables into squares, others make food in the shape of a square root symbol.
The last such day was five years ago, Feb. 2, 2004, which coincided with Groundhog Day. The next is seven years away, on April 4, 2016.
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