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In a small room deep within the Salt Palace Convention Center, about 70 teachers from across the nation spent Friday morning learning how to better teach fractions.
They folded long, narrow strips of paper in half and then in half again. They used raisins, pretzels and graham crackers to add and subtract numbers with decimals. Both were exercises they'll try with their elementary school students to teach them about fractions.
"Math builds on itself all the time," said Bonnie Clark, a teacher from West Haven's Kanesville Elementary School who attended the National Council of Teachers of Mathematics workshop. "They've got to know multiplication, division and fractions, for sure, to know algebra."
A recent, landmark report couldn't agree more. A National Mathematics Advisory Panel, created by President Bush, spent two years examining research and talking to parents and teachers about how to improve math education in America. The panel ultimately came up with 45 main findings and recommendations ideas that could subtly or drastically change the way educators teach math.
The report's key recommendations include, for grades PreK-8, spending more time teaching fewer concepts and focusing more on basic skills critical to learning algebra such as whole numbers, fractions and aspects of geometry and measurement.
"It has a lot of implications for math instruction not just in Utah but throughout the country," said Brenda Hales, Utah state associate superintendent.
Putting ideas into action: This week, a month after the national panel released its findings, 10,000 math teachers from across the country and several panel members gathered in Salt Lake City and discussed the panel's recommendations as part of the annual math teachers' conference.
Some educators said they might not be able slow down and teach fewer topics more in-depth as the report recommends because states and the federal government require them to teach and test on a certain number of topics each year under No Child Left Behind.
Others are optimistic they can incorporate at least some of the findings, such as the need to focus more on fractions, into their lessons.
"It's going to help give us some direction," Gloria Vincent, a Jordan School District elementary math specialist, said of the report.
Camille Baker, president of the Utah Council of Teachers of Mathematics and a Jordan math teacher specialist, said the report highlights many things teachers already know.
"It's not anything we haven't known," Baker said. "Do we need to come together and strategize about how we can best accomplish these things? Yes."
In fact, many of the recommendations might seem downright obvious to an outsider.
The importance of fractions, the idea that topics shouldn't be revisited year after year without closure and the concept that students should both memorize and understand what they're learning don't seem dramatic on the surface.
But the ideas aren't as obvious as they seem. Many have been issues of contention within math education for years, including in Utah.
Utah rewrote its entire math curriculum this year after battles over whether it's best to teach "fuzzy" conceptual math or "kill and drill" computational math.
The national panel found a combination is best.
"To prepare students for algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills," the report said. "Debates regarding the relative importance of these aspects of mathematical knowledge are misguided."
Deborah Loewenberg Ball, a National Mathematics Advisory Panel member, said its one of many issues the panel tried to help resolve.
"There's been so much argument about this that it's actually distracted us from making progress," Ball said. "Now we can move on."
Getting started: In some ways, Utah is already following some of the math panel's recommendations, and in other ways, it's not.
The state's new math curriculum, for example, is more streamlined than the old curriculum but "probably not as much as it needs to be," Hales said.
The report also found that "research on teacher incentives generally supports their effectiveness" but that there are still so many unknowns that policy about teacher incentives should be "carefully evaluated."
Gov. Jon Huntsman Jr. recently signed bills to pay math and science teachers more and provide $20 million for pay for performance this year. Legislative and Utah State Board of Education groups also will study the issue further.
Hales said she and education officials from every state plan to meet soon to discuss where to go next with the panel's recommendations.
"If there are any kinds of changes that need to be made to the math program . . . we'll do it as fast as we need to," she said.
Baker said Utah teachers don't need to wait for the state or federal governments to move before acting on some of the panel's recommendations. She said schools can start having conversations now about the importance of fractions and computational and conceptual understanding in order to form strategies.
Carol Thompson, an education consultant and former teacher, thinks teachers nationwide can start improving math education now.
"It's now up to our community of math people to implement these and figure out how in each school district they're going to do that," Thompson said.
Other findings from the final report of the National Mathematics Advisory Panel:
U.S. math textbooks are much longer than in many nations with higher mathematics achievement than the U.S. "thus demonstrating that the great length of our textbooks is not necessary for high achievement," according to the report.
More research is needed on the uses of calculators. Only one of the studies the panel reviewed was less than 20 years old.
Research should be performed on the use of full-time math teachers in elementary schools. Now, most elementary school teachers teach one class a variety of subjects all day.
Teachers and others should help students and parents to understand that effort, not just ability or talent, leads to mathematical achievement.
Research supports the idea that teachers' knowledge of math affects their students' achievement.
"Difficulty with fractions (including decimals and percents) is pervasive and is a major obstacle to further progress in mathematics, including algebra."