COMET • Vol. 9, No. 09 – 13 March 2008

(1) U.S. Secretary of Education Margaret Spellings Highlights Findings of the National Mathematics Advisory Panel

Source: U.S. Department of Education – 13 March 2008
URL: http://www.ed.gov/news/pressreleases/2008/03/03132008.html

Secretary of Education Margaret Spellings announced the release of the final report of the National Mathematics Advisory Panel. Created in April 2006 by President George W. Bush, the historic panel worked for more than two years reviewing the best available scientific evidence to advance the teaching and learning of mathematics. The final report and its findings were passed unanimously at the panel’s meeting yesterday at Longfellow Middle School in Falls Church, Va.

“This report represents the first comprehensive analysis of math education to be based on sound science,” said Secretary Spellings. “The National Math Advisory Panel’s findings and recommendations make very clear what must be done to help our children succeed in math. We must teach number and math concepts early, we must help students believe they can improve their math skills and we must ensure they fully comprehend algebra concepts by the time they graduate from high school. The Panel’s extensive work will benefit generations of American students.”

The experts on the National Mathematics Advisory Panel represent over six centuries of experience in their respective fields. They have received testimony from more than 200 individuals and nearly 150 organizations, and reviewed more than 16,000 research studies.

The report respects the role of teachers as those in the best position to determine how to teach a given concept or skill. Instead of defining methods for teaching, the report offers a timeline of when students must master critical topics. The panel determined that students need to develop rapid recall of arithmetic facts in the early grades, going on to master fractions in middle school. Having built this strong foundation, the panel stated students would then be ready for rigorous algebra courses in high school or earlier. Noting changing demographics and rising economic demands, Secretary Spellings stressed the significance of the panel’s findings on algebra.

“The panel’s research showed that if students do well in algebra, then they are more likely to succeed in college and be ready for better career opportunities in the global economy of the 21st century,” said Secretary Spellings. “We must increase access to algebra and other rigorous coursework if we hope to close the achievement gap between poor and minority students and their peers.”

The panel also found that the earlier children learn math, the better their chances of success.

“Just as with reading, the math knowledge children bring to school at an early age is linked with their performance in later grades,” said Secretary Spellings. “I hope parents will seize upon this finding and, just as we encourage with reading, they also spend time with their children working on numbers and core mathematics concepts.”

Adds Secretary Spellings, “It is vital that as our children continue to learn new mathematics concepts, we encourage them to believe that working harder in math will lead to achieving better results. Studies have shown that it is effort, and not just inherent talent, that makes the critical difference between success and failure. When it comes to math, it seems hard science says it is truly worth the effort!”

The Secretary will convene a national summit based on the recommendation of the National Mathematics Advisory Panel.

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(2) Final Report of the National Mathematics Advisory Panel (NMP)

Source: U.S. Department of Education – 13 March 2008
URL (NMP Main Page): http://www.ed.gov/MathPanel

On March 13, 2008, the National Mathematics Advisory Panel presented its Final Report to the President of the United States and the Secretary of Education…  Ground-breaking [Task Group, and Subcommittee] reports, rich with information for parents, teachers, policy makers, the research community, and others, are provided below.

Foundations for Success: Report of the National Mathematics Advisory Panel

== Final Report: http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

 

== Draft Task Group Reports [MS Word documents]

*  Conceptual Knowledge and Skills: http://tinyurl.com/2wajuq
*  Learning Processes: http://tinyurl.com/28a7o4
*  Instructional Practices: http://tinyurl.com/2hqtmn
*  Teachers: http://tinyurl.com/2c5tat
*  Assessment: http://tinyurl.com/ytn8us

 

== Draft Subcommittee Reports

*  Standards of Evidence: http://www.ed.gov/about/bdscomm/list/mathpanel/report/soe.pdf

*  Instructional Materials: http://tinyurl.com/2paf3w

*  National Survey of Algebra Teachers for the National Math Panel: http://www.ed.gov/about/bdscomm/list/mathpanel/report/nsat.pdf

 

== Fact Sheet: http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-factsheet.html [see below]

Paper copies of these reports may be ordered at http://EDPubs.ed.gov

If you need any of these documents in an alternative format, please contact the National Math Panel at NationalMathPanel@ed.gov

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(3) National Mathematics Advisory Panel “Fact Sheet” and “Principal Messages”

URL (Fact Sheet): http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-factsheet.html
URL (Final Report, including Executive Summary): http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

 

Text of the Fact Sheet [interspersed with portions of the Executive Summary’s “Principal Messages” within brackets]

To compete in the 21st century global economy, knowledge of and proficiency in mathematics is critical. Today’s high school graduates need to have solid mathematics skills–whether they are headed for college or the workforce. To help ensure our nation’s future competitiveness and economic viability, President George W. Bush created the National Mathematics Advisory Panel (National Math Panel) in April 2006.

The panel was charged with providing recommendations to the President and U.S. Secretary of Education Margaret Spellings on the best use of scientifically based research to advance the teaching and learning of mathematics. Expert panelists, including a number of leading mathematicians, cognitive psychologists, and educators, reviewed numerous research studies before preparing a final report containing guidance on how to improve mathematics achievement for all students in the United States.

The National Math Panel’s final report, issued on March 13, 2008, contains 45 findings and recommendations on numerous topics including instructional practices, materials, professional development, and assessments. Highlights from the report are briefly summarized below. Please visit www.ed.gov/MathPanel for the executive summary and full report.

Core Principles of Math Instruction

*  The areas to be studied in mathematics from pre-kindergarten through eighth grade should be streamlined, and a well-defined set of the most important topics should be emphasized in the early grades. Any approach that revisits topics year after year without bringing them to closure should be avoided.

* Proficiency with whole numbers, fractions, and certain aspects of geometry and measurement are the foundations for algebra. Of these, knowledge of fractions is the most important foundational skill not developed among American students.

* Conceptual understanding, computational and procedural fluency, and problem solving skills are equally important and mutually reinforce each other. Debates regarding the relative importance of each of these components of mathematics are misguided.

*  Students should develop immediate recall of arithmetic facts to free the “working memory” for solving more complex problems.

*  The benchmarks set forth by the Panel should help to guide classroom curricula, mathematics instruction, textbook development, and state assessments.

*  More students should be prepared for and offered an authentic algebra course at Grade 8.

*  Algebra should be consistently understood in terms of the “Major Topics of School Algebra,” as defined by the National Math Panel.

*  The Major Topics of School Algebra include Symbols and Expressions; linear equations; quadratic equations; functions; algebra of polynomials; and combinatorics and finite probability.

Student Effort Is Important

Much of the public’s “resignation” about mathematics education is based on the erroneous idea that success comes from inherent talent or ability in mathematics, not effort. A focus on the importance of effort in mathematics learning will improve outcomes. If children believe that their efforts to learn make them “smarter,” they show greater persistence in mathematics learning.

Importance of Knowledgeable Teachers

[Our citizens and their educational leadership should recognize mathematically knowledgeable classroom teachers as having a central role in mathematics education and should encourage rigorously evaluated initiatives for attracting and appropriately preparing prospective teachers, and for evaluating and retaining effective teachers.]

*  Teachers’ mathematical knowledge is important for students’ achievement. The preparation of elementary and middle school teachers in mathematics should be strengthened. Teachers cannot be expected to teach what they do not know.

*  The use of teachers who have specialized in elementary mathematics teaching could be an alternative to increasing all elementary teachers’ mathematics content knowledge by focusing the need for expertise on fewer teachers.

Effective Instruction Matters

[Instructional practice should be informed by high-quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers. High-quality research does not support the contention that instruction should be either entirely “student centered” or “teacher directed.” Research indicates that some forms of particular instructional practices can have a positive impact under specified
conditions.”]

*   Teachers’ regular use of formative assessments can improve student learning in mathematics.

*  Instructional practice should be informed by high-quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers.

*  The belief that children of particular ages cannot learn certain content because they are “too young” or “not ready” has consistently been shown to be false.

*  Explicit instruction for students who struggle with math is effective in increasing student learning. Teachers should understand how to provide clear models for solving a problem type using an array of examples, offer opportunities for extensive practice, encourage students to “think aloud,” and give specific feedback.

*  Mathematically gifted students should be allowed to accelerate their learning.

*  Publishers should produce shorter, more focused and mathematically accurate mathematics textbooks. The excessive length of some U.S. mathematics textbooks is not necessary for high achievement.

Effective Assessment

The National Assessment of Educational Progress (NAEP) and state assessments in mathematics should be improved in quality and should emphasize the most critical knowledge and skills leading to Algebra.

Importance of Research

The nation must continue to build the capacity for more rigorous research in mathematics education to inform policy and practice more effectively.

[Positive results can be achieved in a reasonable time at accessible cost, but a consistent, wise, community-wide effort will be required. Education in the United States has many participants in many locales–teachers, students, and parents; state school officers, school board members, superintendents, and principals; curriculum developers, textbook writers, and textbook editors; those who develop assessment tools; those who prepare teachers and help them to continue their development; those who carry out relevant research; association leaders and government officials at the federal, state, and local levels. All carry responsibilities. All can be important to success.

[The network of these many participants is linked through interacting national associations. A coordinated national approach toward improved mathematics education will require an annual forum of their leaders for at least a decade. The Panel recommends that the U.S. Secretary of Education take the lead in convening the forum initially, charge it to organize in a way that will sustain an effective effort, and request a brief annual report on the mutual agenda adopted for the year ahead.] [The President asked the Panel to use the best available scientific research to advise on improvements in the mathematics education of the nation’s children. Our consistent respect for sound research has been the main factor enabling the Panel’s joint conclusions on so many matters, despite differences of perspective and philosophy. At the same time, we found no research or insufficient research relating to a great many matters of concern in educational policy and practice. In those areas, the Panel has been very limited in what it can report.

The Panel lays out many concrete steps that can be taken now toward significantly improved mathematics education, but it also views them only as a best start in a long process. This journey, like that of the post-Sputnik era, will require a commitment to “learning as we go along.” The nation should recognize that there is much more to discover about how to achieve better results. Models of continuous improvement have proven themselves in many other areas, and they can work again for America in mathematics education.]

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(4) “Panel Calls for Systematic, Basic Approach to Math” by Sean Cavanagh

Source: Education Week – 13 March 2008
URL: http://tinyurl.com/yuydjn

A federal panel has issued a long-awaited report on how math should be taught in the early grades, a blueprint that calls for a more orderly march through the subject, with the goal of nurturing students’ effortless recall of simple procedures and helping them acquire broader problem-solving skills.

The report of the National Mathematics Advisory Panel, released March 13, echoes a theme sounded repeatedly by math researchers today: Math curricula and classroom strategies being used in states and school districts lack consistency and logic…

The panel’s report repeatedly calls for students to be able to automatically recall math procedures, such as basic addition, subtraction, multiplication, and division, quickly and effortlessly. It also cites students’ difficulty with fractions as “pervasive” and a “major obstacle” to them learning algebra.

Larry R. Faulkner, the panel’s chairman, said the group found that if students’ “working memory” is consumed with trying to perform math that they should know automatically, it hinders their ability to move to more difficult material.

“Automaticity is an important thing,” Mr. Faulkner, the former president of the University of Texas at Austin, told reporters the day before the report’s official release.

But Jere Confrey, who chaired a 2004 federal study of math curriculum, said the panel’s repeated emphasis on automatic recall and basic arithmetic implicitly, and wrongly, suggested that other methods are not as sound.

“The report seems to be unbalanced toward mastery of algorithms,” said Ms. Confrey, a professor of math education at North Carolina State University, in Raleigh, in an interview. “It has a slant to it,” she added.

Ms. Confrey also said the report emphasized fractions and geometry at the expense of other topics that could build students’ overall math understanding, such as basic statistics and probability, as well as proportions. Those other topics help “nontraditional students become intrigued and excited about mathematics,” she wrote in an e-mail.

‘Scientific Evidence’

The math panel sought to base its recommendations on “the best available scientific evidence,” as specified by the White House order. It ranked studies of math programs and strategies in categories ranging from “strong evidence” to “inconsistent” to “weak,” based on the methodology the studies used.

Ms. Confrey said the panel’s criteria were overly restrictive. Case studies and other research that did not meet the “scientific evidence” standards could provide valuable information on the true impact of math programs and interventions in the classroom, she argued. They give “short shrift to the need for multiple methods of research,” Ms. Confrey wrote.

But panel members also discovered that some areas of issues related to math education, such as cognitive studies of how children learn, have produced more high-quality research than others, such as how to prepare math educators and give them ongoing professional development, Mr. Faulkner said.

“We’re going to have to learn more about what makes a good teacher and how to instill” those abilities, Mr. Faulkner said. “Very little is known about these things,” he added, “surprisingly little, given [their] importance”…

Two agencies that are heavily involved in supporting K-12 programs in math and science research and professional development, the U.S. Department of Education and the National Science Foundation, accounted for more than half that $3 billion in spending. At a recent meeting of the math panel, U.S. Secretary of Education Margaret Spellings said she hoped the math panel’s advice would help influence federal spending across agencies.

NCTM Reaction

The math panel included a number of cognitive psychologists, researchers, and college faculty members who have studied math issues. It also included Francis M. “Skip” Fennell, the president of the National Council of Teachers of Mathematics, a 100,000-member organization that exerts a strong influence over how that subject is taught across the country.

The NCTM, based in Reston, Va., has angered some parents and members of the school and college math community who believe it has pushed a reform-style of math, focused too much on conceptual learning and not enough on automatic recall of number facts. That approach gained traction, those detractors have claimed, in voluntary national standards that the NCTM originally published in 1989.

But the organization also won praise from its critics more recently with its publication in 2006 of “Curriculum Focal Points,” a document aimed at streamlining the list of key math topics students are expected to know in grades pre-K-8.

Mr. Fennell said recently that he and other NCTM officials have visited about half the nation’s 50 states, some of which are in the process of revising their math standards, to explain and encourage them to use “Focal Points” as a resource.

The math panel relied partly on NCTM’s “Focal Points” as a reference for identifying crucial early math skills. It also drew from the math curricula used in high-performing states and top-achieving countries on international tests, including Singapore, Japan, and South Korea. In addition, the panel commissioned a survey of than 700 introductory–algebra teachers’ views on about students’ strengths and weaknesses in that subject.

James M. Rubillo, the NCTM’s executive director, said early drafts of the report had drawn both positive and negative reactions from his organization’s members. He said he was pleased with the panel’s use of “Focal Points” as a reference. He was less enthusiastic with some of the report’s language that is critical of calculators’ role in math classes, a view that he said did not reflect the technology’s potential benefits when used appropriately.

In the weeks ahead, the NCTM will “put a lens” on the report and judge whether its various recommendations are based in research or panelists’ opinions. But Mr. Rubillo also hoped the document could bridge some disagreements over math instruction.

“There’s got to be a balance between skill development and conceptual understanding,” Mr. Rubillo said. That, he said, should become “a real movement.”

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(5) “Panel Urges Schools to Emphasize Core Math Skills” by Maria Glod

Source: Washington Post – 14 March 2008
URL: http://www.washingtonpost.com/wp-dyn/content/article/2008/03/13/AR2008031301492_pf.html

…Larry R. Faulkner, chairman of the [National Mathematics Advisory Panel] and former president of the University of Texas at Austin, said the country needs to make changes to stay competitive in an increasingly global economy. He noted that many U.S. companies draw skilled workers from overseas, a pool that he said is drying as opportunities abroad improve.

“Math education isn’t just about a school subject,” Faulkner said as the panel released its final report at Fairfax County’s Longfellow Middle School. “It’s fundamentally about the chances that real people all across this country will have in life. And it’s about the well-being and safety of the nation.”

Scores from the 2006 Program for International Student Assessment showed 15-year-olds in the United States trailed peers from 23 industrialized countries in math….

The panel concluded that the math curricula and textbooks in elementary and middle schools typically cover too many topics without enough depth. It noted that countries in which children do best at math, including Singapore and Japan, emphasize core topics.

The panel identified benchmark skills that students need for a strong math foundation — for example, that students be able to add and subtract whole numbers by the end of third grade. By the time students leave fifth grade, the panel said, they should be able to add and subtract fractions and decimals.

“I think the main message of this report is simple — content is king,” said Tom Loveless, panel member and director of the Brown Center on Education Policy at the Brookings Institution.

It’s not just lessons that need to change, the panel said, but also the nation’s attitudes about math. In a culture in which parents say they “weren’t good at math either,” children assume they don’t have the talent for numbers. The panel said that research shows that practice pays off and that adults need to give students that message.

The panel also weighed in on the long-running battle between traditionalists, who favor a focus on memorization and drilling, and those who prefer stressing concepts and letting students make connections on their own. Students need to know math facts and have automatic recall, Faulkner said, but they also need “some element of discovery.”

“I think this panel has gradually evolved to the view that most members believe that most effective teachers draw from both philosophies at different times,” he said.

The panel met a dozen times, heard testimony from groups and individuals and reviewed thousands of research papers. The panel said that it is “self-evident” that teachers need to have strong math skills but that more research must be done to find the best ways to prepare them…

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(6) Pi Day, March 14, Is Party Time for Math Fans!

URL: http://www.googolpower.com/content/press-release/2008/03/14/pi-day-march-14-is-party-time-for-math-fans

Math lovers, teachers and families around the world are … [celebrating] Pi Day on March 14, or more precisely to the pi second, 3/14 (the American date format) at 1:59:26 p.m.

Pi or π, approximately equal to 3.1415926, is one of the most important mathematical constants. It represents the ratio of any circle’s circumference to its diameter. The Greek letter π, often spelled out as pi, was adopted as a symbol for the number from the Greek word for perimeter…

“If there was just one day that screams math party, March 14 would have to be it,” says Susan Jarema, founder of Googol Learning who always looks for ways to make math more exciting for children. Coincidently, March 14 is also Albert Einstein’s birthday, which offers math lovers the chance to discuss famous discoveries that have been proved through mathematics.

“To me Pi Day is not only a day to celebrate math, it also recognizes the historical progress of our universal language of mathematics,” comments Jarema. Pi dates back more than 4,000 years, when it was used by the Babylonians and Egyptians. In the third and fourth centuries B.C., great thinkers such as Archimedes, Ptolemy and Euclid came up with their own estimates and proofs. Today, supercomputers are able to estimate pi with precision to over a trillion digits.

Besides March 14, there are other days to celebrate pi. Pi Approximation Day may be observed on several dates, but the most popular is July 22 (22/7 using the European date format–just divide 22 by 7 to estimate pi). Another favorite day to observe pi is November 10 (the 314th day of the year), or November 9 in a leap year. You could also celebrate Pi in December on the 355th day of the year at 1:13 p.m., for the Chinese approximation 355/113 (divide 355 by 113 to arrive at an estimate of pi).

The first recognized Pi Day celebration was held March 14, 1988, at the San Francisco Exploratorium, where the staff and public marched around in a circle and ate fruit pies. Now, many organizations, countless websites and thousands of classrooms host celebrations. Pi enthusiasts in the math community take pride in memorizing pi and coming up with higher estimates of its digits.

Jarema created the award-winning musical Googol Power Math Series to make learning math fun for children. Since then, she has built a free-content website that shares ways to make math exciting. She offers 10 helpful ideas to make Pi Day a special celebration for your students or family…

Visit Googol Learning’s website at www.googolpower.com to check out its Pi Day resource section and for many more free resources to help increase your child’s interest in math.