Friday, March 21, 2008


Really Says it ALL!

Presidential Math Panel Vows to Increase Learning Disabilities
Tuesday, March 18, 2008 5:17 AM
Gary Stager

In the last year of his term, the President of the United States and the
Department of Education are now trying to do for math what they did for
reading. The notable achievements of Reading First include massive fraud,
profiteering, junk science, federal control over classroom practice, fear
and hysteria. While the National Reading Panel was stacked with ideologues
sharing the same educational philosophy, the National Math Panel co-opted
the National Council of Teachers of Mathematics (NCTM) by appointing the
organization’s President to serve on the committee.

The National Council of Teachers of Mathematics, never known for its
radicalism, swung hard towards “the basics” last year in its Curriculum
Focal Points and now finds itself in the uncomfortable position of having
to disagree with NCTM’s President and the President of the United States.
“Skip” Fennell did neither his members nor millions of American school
kids any favors by participating in this unnecessary process.
These federal education expeditions seek to narrow both the range of
content and pedagogy permissible in public schools. The private and
religious schools the GOP wants to support with taxpayer-funded vouchers
are immune from these intrusions. The one-size-fits-all prescriptions for
what ails public education are justified by claiming that schemes are

The rigid definition of “scientific evidence” enforced by Department of
Education may be fine in testing remedies for restless leg syndrome, but
is ill-suited for the complexities of education. But hey, these are the
folks who have mangled the English language to imply that theory is merely
an unproven guess.

There is a lot wrong with the recent math report, but making Algebra the
holy grail of K-8 mathematics is wrong-headed and goes unquestioned.
Stressing the importance of fractions as critical prerequisites for
Algebra adds insult to injury.

In a world-class display of side-splitting math teacher humor, panel
member Frances “Skip” Fennell told the New York Times , “Just as
“plastics” was the catchword in the 1967 movie The Graduate, the catchword
for math teachers today should be ‘fractions.’“ What Fennell doesn’t realize is that the person who said, “Plastics,” in The Graduate was emblematic of everything wrong with society. “Plastics,” was a metaphor for a shallow, superficial, inauthentic culture focused on
the wrong values. The National Math Advisory Panel’s greater focus on
fractions represents a “plastic” version of mathematics that will do more
harm than good.

It’s easy to see how someone might think that several years worth of
fraction study prepares a child for Algebra. Fractions have numerators
over denominators, separated by a horizontal line. Many algebraic
equations have something over something else, also separated by a line.
That’s all you need to know. Right?

Not only is the progression from arithmetic manipulation of fractions to
Algebra tenuous, but neither of the assumptions underlying the value of
teaching fractions or Algebra are ever questioned. The President’s Math
Panel, like most of the math education community maintains a Kabbalah-like
belief in an antiquated scope and sequence. Such curricular superstition
fuels a multigenerational feud in which educators fight over who has the
best trick for forcing kids to learn something useless, irrelevant or

Despite the remarkable statement in the 1989 National Council of Teachers
of Mathematics Standards, “Fifty percent of all mathematics has been
invented since World War Two,” the NCTM has been in full retreat ever
since. Although much of this “new” mathematics is playful, practical,
beautiful or capable of being visualized via the computer, little new
content has made its way into the curriculum. Against this backdrop of
unimaginative heuristics and a leadership vacuum, math class has become
increasingly torturous for too many students.

Children who struggle to manipulate fractions do so because the skills are
taught absent a meaningful context in a culture where fractions are rarely
ever used. Fraction fans might argue that fractions are important in
following a recipe, but little cooking is done during fraction
instruction. Even if kids did get to learn fractions by cooking, they
might add, subtract or even multiply fractions, but one hardly ever
divides fractions. The fact that there are four arithmetic functions
doesn’t justify drilling kids for several grade levels. I wonder how many
members of the Presidential panel can coherently explain how division of
fractions works beyond repeating the trick – multiply the first fraction
by the reciprocal of the second fraction?

The Report of the National Mathematics Advisory Panel
does not dispute that teachers spend lots of time teaching fractions. The
report merely urges that teachers do even more of the same while hoping
for a different result. A definition of insanity comes to mind.
It would be bad enough if wasted time was the only consequence of the
fanatical fraction focus, but too many students get the idea that they
can’t do math. This damages their inclination towards learning other forms
of mathematics. Given the importance of mathematics and the widespread
mathphobia sweeping the land, students can ill afford to a diminution in
their self-image as capable mathematicians.

Educators should not be complicit in creating learning disabilities
regardless of what the President or his friends say.

Thursday, March 13, 2008


Fractions, Fractions and More Fractions

Fixate on Fractions, Says Math Panel
The Associated PressThursday, March 13, 2008; 2:40 PM
WASHINGTON -- Schools could improve students' sluggish math scores by hammering home the basics, such as addition and multiplication, and increasing the focus on fractions and some geometry, a presidential panel recommended Thursday.
"Difficulty with fractions (including decimals and percents) is pervasive and is a major obstacle to further progress in mathematics, including algebra," the panel, appointed by President Bush two years ago, said in a report.
Because success in algebra has been linked to higher graduation rates and college enrollment, the panel focused on improving areas that are the foundations of algebra. Average U.S. math scores on a variety of tests drop around middle school, when algebra coursework typically begins. That trend also led the panel to focus on what's happening before kids take algebra.
A major goal for students should be mastery of fractions, since that is a "severely underdeveloped" area and one that's important to later algebra success, the report states.
"Students don't know how to translate fractions into decimals or into percentages and they can't locate fractions on a number line," said panelist Tom Loveless, a senior fellow and education expert at the Brookings Institution, a Washington-based think tank.
The report also says other critical topics _ such as whole numbers and aspects of geometry and measurement _ should be studied in a more in-depth way.
When it comes to whole numbers, the report states that students must have a clear grasp of the meaning of basic operations of addition, subtraction, multiplication and division, among other things.
With geometry and measurement, students should be able to find unknown lengths, angles and areas, the report says.
"By building on a strong foundation of skills, students will be ready for rigorous courses in high school or earlier," said Education Secretary Margaret Spellings, praising the report.
Spellings and the panelists emphasized the need to boost U.S. students' math performance because of the increasing need for high-level math skills in today's workplace and because of the need to compete with workers from other countries for global jobs.
U.S. students do particularly poorly on international tests. On one recent exam given to 15-year-olds in 30 industrialized countries, U.S. students posted an average score that was lower than the average in 23 of the other countries.
In general, U.S. math curricula ought to be streamlined, according to the report.
"There is I think a tendency in American curricula to cover too many things too shallowly," Larry Faulkner, the panel's chair and the former president of the University of Texas, said.
The report takes a diplomatic stance when it comes to taking a position on the best methods to teach math to kids.
In recent years, there has been a dispute over whether children should learn a sequence of basic skills in math, including multiplication tables and some memorization, or should understand the theory behind math problems and come up with solutions on their own.
The report says both quick and effortless recall of facts and conceptual understanding of math are beneficial.
In addition, the back-to-basics camp has tended to favor "teacher-directed" instruction, in which teachers do all the explaining, while the opposing side has backed "student-centered instruction," in which students have the main responsibility for learning math _ often through working with peers.
The panel found students can benefit from both styles.
"You need some element of discovery to allow kids to secure concepts in their minds, and you need to be able to have a reasonably efficient approach to be able to cover the material," Faulkner said.
Teachers need to emphasize that effort pays off, because too many kids feel that they are just not good at math and give up too early, according to the report.
Faulkner said much more research is needed to understand why certain teachers are able to boost their students' math skills. "Very little is known about these things, surprisingly little I think to this panel _ given the importance of that question," Faulkner said.
The report did note that elementary- and middle-school teachers need more math preparation.
It took aim at math textbooks, saying they are too long and lack coherence.
Textbook publishers say they are trying to cover all the things in various state standards. Like for other subjects, each state sets its own math standards dictating what students should learn and when. Many critics say students would be better off with a single national standard, but the panel didn't weigh in on that.
The math panel's report comes several years after another presidential panel outlined what ought to be done to improve reading performance. That panel stressed the importance of phonemic awareness in reading instruction and emphasized the need to combine a variety of reading approaches into teaching strategies. It also led to the creation of a federal reading program for schools serving low-income students.
Spelling said she hoped Thursday's report would lead to the creation of a similar math program. "I think, like the reading panel, this can be a seminal moment in math education," Spelling said.


Read the Final Report of the National Math Panel


The Wall Street Journal Weighs In

Education Panel Lays Out Truce In Math Wars
Effort to Fix 'Broken' System Sets Targets for Each Grade, Avoids Taking Sides on Method
By JOHN HECHINGERMarch 5, 2008; Page D1

A presidential panel, warning that a "broken" system of mathematics education threatens U.S. pre-eminence, says it has found the fix: A laserlike focus on the essentials.
The National Mathematics Advisory Panel, appointed by President Bush in 2006, is expected to urge the nation's teachers to promote "quick and effortless" recall of arithmetic facts in early grades, mastery of fractions in middle school, and rigorous algebra courses in high school or even earlier. Targeting such key elements of math would mark a sharp departure from the diverse priorities that now govern teaching of the subject in U.S. public schools.

The panel took up its work amid widespread alarm at the sorry state of math achievement in America. In the most recent testing by the Program for International Student Assessment, released late last year, U.S. 15-year-olds achieved sub-par results among developed nations in math literacy and problem-solving, behind such countries as Finland, South Korea and the Netherlands. "Without substantial and sustained changes to the educational system, the United States will relinquish its leadership in the twenty-first century," reads a draft of the final report, due to be released next week by the Department of Education.

Unlike most countries that outperform the U.S., America leaves education decisions largely to state and local governments and has no national curriculum. School boards and state education departments across the country are likely to pore over the math panel's findings and adjust their teaching to make sure it aligns with the nation's best thinking on math instruction. The federal government could also use the report to launch a national program in math instruction, as the government did for literacy after findings from a similar advisory panel on reading in 2000.
The math panel's draft report comes amid the so-called math wars raging in the nation's public classrooms. For two decades, advocates of what has come to be known as "reform math" have promoted conceptual understanding over drilling in, say, multiplication and division. For example, to solve a basic division problem, 150 divided by 50, students might cross off groups of circles to "discover" that the answer was three. Some parents and mathematicians have complained about "fuzzy math," and public school systems have encountered a growing backlash.
The advisory panel's 19 members include eminent mathematicians and educators representing both sides of the math wars. The draft of the final report declines to take sides, saying the group agreed only on the content that students must master, not the best way to teach it.
The group said it could find no "high-quality" research backing either traditional or reform math instruction. The draft report calls a rigid adherence to either method "misguided" and says understanding, which is the priority of reform teachers, and computation skills, emphasized by traditionalists, are "mutually supported."

Larry Faulkner, the panel's chairman and president of the Houston Endowment, a philanthropic foundation, said in an interview that the group had "internal battles" but decided "it's time to cool the passions along that divide." The panel held 12 meetings around the country, reviewed 16,000 research publications and public-policy reports and heard testimony from 110 individuals.

The advisory group also doesn't take a position on calculator use in early grades, a contentious issue among educators and parents. The draft says the panel reviewed 11 studies that found "limited to no impact of calculators on calculation skills, problem-solving or conceptual development." But the panel, noting that almost all the studies were more than 20 years old and otherwise limited, recommended more research on whether calculators undermine "fluency in computation."

Still, the draft report says calculators shouldn't be used on tests used to assess computation skills. Some states allow disabled children to use calculators on tests of arithmetic.
The draft report urges educators to focus on "critical" topics, as is common in higher-performing countries. The panel's draft report says students should be proficient with the addition and subtraction of whole numbers by the end of third grade and with multiplication and division by the end of fifth. In terms of geometry, children by the end of sixth grade should be able to solve problems involving perimeter, area and volume.

Students should begin working with fractions in fourth grade and, by the end of seventh, be able to solve problems involving percent, ratio and rate. "Difficulty with fractions [including decimals and percents] is pervasive and is a major obstacle to further progress in mathematics, including algebra," the draft report says.

These benchmarks mirror closely a September 2006 report by the National Council of Teachers of Mathematics, which many viewed as a turning point in the math wars because it recognized the importance of teaching the basics after the group for years had placed more emphasis on conceptual understanding.

Francis Fennell, president of the math teachers group and a panel member, said the group's specific recommendations could help parents determine whether their kids are on the right track.

The draft report recommends a revamp of the National Assessment of Educational Progress, a widely followed test administered by the Education Department, to emphasize material needed for the mastery of algebra, especially fractions. The draft calls for similar changes to the state tests children must take under the federal No Child Left Behind Law.

The document urges publishers to shorten elementary and middle-school math textbooks that currently can run on for 700 to 1,000 pages and cover a dizzying array of topics. Publishers say textbooks often must cover a patchwork of state standards.


How the Report Plays in the NYTimes

March 13, 2008
Panel Proposes Streamlining Math
American students’ math achievement is “at a mediocre level” compared with that of their peers worldwide, according to a new report by a federal panel. The panel said that math curriculums from preschool to eighth grade should be streamlined to focus on key skills — the handling of whole numbers and fractions, and certain aspects of geometry and measurement — to prepare students to learn algebra.
“The sharp falloff in mathematics achievement in the U.S. begins as students reach late middle school, where, for more and more students, algebra course work begins,” said the report of the National Mathematics Advisory Panel, appointed two years ago by President Bush. “Students who complete Algebra II are more than twice as likely to graduate from college, compared to students with less mathematical preparation.”
The report, to be released Thursday, spells out specific goals for students. For example, it says that by the end of the third grade, students should be proficient in adding and subtracting whole numbers; two years later, they should be proficient in multiplying and dividing them. By the end of sixth grade, it says, students should have mastered the multiplication and division of fractions and decimals.
The report tries to put to rest the long and heated debate over math teaching methods. Parents and teachers in school districts across the country have fought passionately over the relative merits of traditional, or teacher-directed, instruction, in which students are told how to solve problems and then are drilled on them, as opposed to reform or child-centered instruction, which emphasizes student exploration and conceptual understanding. The panel said both methods have a role.
“There is no basis in research for favoring teacher-based or student-centered instruction,” said Dr. Larry R. Faulkner, the chairman of the panel, at a briefing for reporters on Wednesday. “People may retain their strongly held philosophical inclinations, but the research does not show that either is better than the other.”
Districts that have made ‘’all-encompassing decisions to go one way or the other,” he said, should rethink those decisions, and intertwine different methods of instruction to help students develop a broad understanding of math.
“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. These capabilities are mutually supportive, .”
The president convened the panel to advise on how to improve math education for the nation’s children. Its members include math and psychology professors from leading universities, a middle-school math teacher and the president of the National Council of Teachers of Mathematics.
Closely tracking an influential 2006 report by the National Council of Teachers of Mathematics, the panel said that the math curriculum should include fewer topics, and then spend enough time on each of them to make it is learned in depth and need not be revisited in later grades. This is how top-performing nations approach the curriculum.
After a similar advisory panel on reading made its recommendations in 2000, the federal government used the report as a guide for awarding $5 billion in federal grants to promote reading proficiency.
The new report does not call for a national math curriculum, or for new federal investment in math instruction. It does call for more research on successful math teaching, and recommends that the Secretary of Education convene an annual forum of leaders of the national associations concerned with math to develop an agenda for improving math instruction.
The report cites a number of troubling international comparisons, including a 2007 assessment finding that 15-year-olds in the United States ranked 25th among their peers in 30 developed nations in math literacy and problem solving.
The report says that Americans fell short, especially, in handling fractions. It pointed to the National Assessment of Educational Progress, standardized-test results that are known as the nation’s report card, which found that almost half the eighth graders tested could not solve a word problem that required dividing fractions.
After hearing testimony and comments from hundreds of organizations and individuals, and sifting through 16,000 research publications, the panelists shaped their report around recent research on how children learn.
For example, the panel found that it is important for students to master their basic math facts by heart.
“For all content areas, practice allows students to achieve automaticity of basic skills — the fast, accurate, and effortless processing of content information — which frees up working memory for more complex aspects of problem solving,” the report said.
Dr. Faulkner, a former president of the University of Texas at Austin, said the panel “buys the notion from cognitive science that kids have to know the facts.”
“In the language of cognitive science, working memory needs to be predominately dedicated to new material in order to have a learning progression, and previously addressed material needs to be in long-term memory,” he said.
The report also cites recent findings that students who depend on their native intelligence learn less than those who believe that success depends on how hard they work. Dr. Faulkner said the current “talent-driven approach to math, that either you can do it or you can’t, like playing the violin” needed to be changed.
“Experimental studies have demonstrated that changing children’s beliefs from a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turn improves mathematics outcomes,” the report says “When children believe that their efforts to learn make them ‘smarter,’ they show greater persistence in mathematics learning.”
The report makes a plea for shorter and more accurate math textbooks. Given the shortage of elementary teachers with a solid grounding in math, the report recommends further research on the use of math specialists to teach several different elementary grades, as is done in many top-performing nations.
The report also recommends a revamping of the math content on the national assessment test, to focus on the same skills that the report emphasizes.
Here are the panel’s recommended benchmarks for elementary school math education:
Benchmarks in Math Education Fluency With Whole Numbers
1 By the end of Grade 3, students should be proficient with the addition and subtraction of whole numbers.
2 By the end of Grade 5, students should be proficient with multiplication and division of whole numbers.
Fluency With Fractions
1 By the end of Grade 4, students should be able to identify and represent fractions anddecimals, and compare them on a number line or with other common representations offractions and decimals.
2 By the end of Grade 5, students should be proficient with comparing fractions and decimalsand common percents, and with the addition and subtraction of fractions and decimals.
3 By the end of Grade 6, students should be proficient with multiplication and division offractions and decimals.
4 By the end of Grade 6, students should be proficient with all operations involving positiveand negative integers.
5 By the end of Grade 7, students should be proficient with all operations involving positiveand negative fractions.
6 By the end of Grade 7, students should be able to solve problems involving percent, ratio,and rate and extend this work to proportionality.
Geometry and Measurement
1 By the end of Grade 5, students should be able to solve problems involving perimeter andarea of triangles and all quadrilaterals having at least one pair of parallel sides (i.e.,trapezoids).
2 By the end of Grade 6, students should be able to analyze the properties of two-dimensional shapes and solve problems involving perimeter and area, and analyze the properties of three dimensional shapes and solve problems involving surface area and volume.
3 By the end of Grade 7, students should be familiar with the relationship between similar triangles and the concept of the slope of a line.
Source: National Mathematics Advisory Panel, 2008.


First of several responses to the Report

Several Observations of Steven Rasmussen, Publisher and CEO of Key Curriculum Press, after reading the Final Report of the NMAP

A colleague of ours in mathematics education pointed out that the panel should be the “National Arithmetic Advisory Panel” because they have developed guidelines for an arithmetic curriculum, not a modern mathematics curriculum. I wholeheartedly agree. The over-emphasis in the report of a narrow set of skills and procedures leading to algebra, including a set of procedures the panel has inappropriately named as “the” standard algorithms, limits the mathematical horizons of U.S. students and reduces the likelihood that they will be prepared for the mathematics that will drive scientific research and economies Ant the report’s definition of algebra is date and could have been written for the 19th Century. in the 21st Century. For instance, data analysis and statistics--basic skills of both the scientific and economic workforce—are completely ignored in the report. Mathematical modeling and problem solving are only given lip service.

This report of the Bush administration fails to recognize that the greatest impediment to progress in the mathematical achievement of our children is the underfunding of education in the U.S., especially scientific education and especially scientific education in our urban centers. Just as the next generation is likely to witness the extinction of many species in our habitats, without a major increase in resource commitment, the next generation is likely to witness the extinction of mathematics and science teachers in their classrooms. Working conditions are too poor and support is too inadequate to motivate young people to dedicate themselves to teaching mathematics and science. The narrowing of the mathematical field as advocated in the NMAP Final Report only exacerbates this problem. If I were charged with summarizing “what is known that could support a major national effort that could succeed in improving mathematics achievement,” I would have focused on the need to commit resources at the federal and state levels to scientific education.

While the report claims to have examined 16,000 research publications and policy reports in its examination of mathematics education, the report makes many claims that fly in the face of scientific evidence. The report is highly opinionated, subjective, and political. For instance in its claim that “high school students enrolled in courses using textbooks featuring an integrated approach may not be in a position to take more advanced coursework in their senior year,” the panel cites “an analysis of high school mathematics standards, and one state’s standards in particular,” not research. Much research has, in fact, been undertaken in this area and the scientific evidence points in the direction that students using integrated curricula study more advanced mathematics, not less. In its findings on the use of technology, the report ignores mention of the most researched and widely used classes of technology for mathematics, open-ended investigative and modeling tools like our own software, The Geometer’s Sketchpad, or graphing calculators.

The NMAP Final Report seems to believe that a targeted, magic “algebra pill” can address the crisis in mathematics education in the U.S. And they attempt to support a highly subjective and narrow definition of mathematical knowledge as the direction our field should move in. This narrowing of mathematics education will further undermine the interests of our children in pursuing scientific careers and under-prepare them for the economy of the future. It will drive good teachers out of the teaching profession and discourage young people from entering the profession.

Nothing in the report points to ways to create more engagement of students in the study of mathematics. In fact, if one were to follow its mandate, I believe that we would interest fewer, not more, citizens in the pursuit of mathematical careers. One of the central problems in our mathematical classrooms is shear boredom—and that applies to teachers as well as students. A rich curriculum, even if focused, can motivate children to study more mathematics, not less. Teaching and learning, are after all, are voluntary pursuits, and we have to be aware that the subjects must be inviting if we are going to attract new recruits to our field.

This passage below typically blames the abused and neglected for their problems, not pointing to the discriminatory application of national educational resources and the “opportunity gap” that exists in U.S. Schools.

Children’s goals and beliefs about learning are related to theirmathematics performance. Experimental studies have demonstrated thatchanging children’s beliefs from a focus on ability to a focus on effortincreases their engagement in mathematics learning, which in turnimproves mathematics outcomes: When children believe that their effortsto learn make them “smarter,” they show greater persistence inmathematics learning. Related research demonstrates that the engagementand sense of efficacy of African-American and Hispanic students inmathematical learning contexts not only tends to be lower than that ofwhite and Asian students but also that it can be significantly increased.
Teachers and other educational leaders should consistently help studentsand parents to understand that an increased emphasis on the importanceof effort is related to improved mathematics performance. This is acritical point because much of the public’s self-evident resignation aboutmathematics education (together with the common tendencies to dismissweak achievement and to give up early) seems rooted in the erroneousidea that success is largely a matter of inherent talent or ability, not effort.

The section of the report regarding textbooks talks about length and accuracy, two important (and obvious) aspects of textbooks, but hardly the most important factors in curriculum. The absence of any comment or analysis of pedagogy, instructional design, levels of depth, etc., in this section of the report is appalling.

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