Education Panel Lays Out Truce In Math Wars
Effort to Fix ‘Broken’ System Sets Targets for Each Grade, Avoids Taking Sides on Method
Wall Street Journal By JOHN HECHINGER March 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.
The National Mathematics Advisory Panel is expected to call for the following “critical foundations” or benchmarks for U.S. school children.
Fluency with whole numbers:
- By the end of grade three, students should be proficient with the addition and subtraction of whole numbers.
- By the end of grade five, students should be proficient with multiplication and division of whole numbers.
Fluency with fractions:
- By the end of grade four, students should be able to identify and represent fractions and decimals, and compare them on a number line or with other common representations of fractions and decimals.
- By the end of grade five, students should be proficient with comparing fractions and decimals and common percents, and with the addition and subtraction of fractions and decimals.
- By the end of grade six, students should be proficient with multiplication and division of fractions and decimals.
- By the end of grade six, students should be proficient with all operations involving positive and negative integers.
- By the end of grade seven, students should be proficient with all operations involving positive and negative fractions.
- By the end of grade seven, students should be able to solve problems involving percent, ratio and rate and extend this work to proportionality.
Geometry and measurement:
- By the end of grade five, students should be able to solve problems involving perimeter and area of triangles and all quadrilaterals having at least one pair of parallel sides (i.e. trapezoids).
- By the end of grade six, 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.
- By the end of grade seven, students should be familiar with the relationship between similar triangles and the concept of the slope of a line.
Source: Draft of National Mathematics Advisory Panel final report
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.