Efforts to improve math instruction and achievement must move beyond the single- minded debates over how the subject should be taught to a more comprehensive view of what students need to become proficient, a long-awaited report from the National Research Council recommends.
"Adding It Up: Helping Children Learn Mathematics" calls for an overhaul of instruction, curricula, and testing for elementary and middle school students. The report, released last week, also urges investment in more rigorous and ongoing professional development for teachers and further research on successful mathematics programs.
While both computational skills and a deep understanding of math concepts are essential parts of a complete math education, it concludes, other elements--including problem-solving and reasoning abilities, as well as an awareness of the relevance of math in everyday life--are also necessary for mathematical proficiency.
"We wanted to get away from the debates about teaching skills or teaching understanding," said Jeremy Kilpatrick, a mathematics professor at the University of Georgia and the chairman of the Mathematics Learning Study Committee, which produced the report. "It's not a question of teaching one or the other. It's about teaching skills and understanding, and much more."
Essential for All Students
The 16-member committee, composed of mathematicians, math educators, cognitive psychologists, teachers, and a business representative, maintains that all students can and should acquire a deep knowledge and understanding of math in order to succeed in an increasingly technological world. But U.S. students' performance on state and national tests, as well as in international comparisons--viewed as disappointing by many educators and policymakers--has forced a re-examination of how the subject is taught.
While test scores of 4th and 8th graders on the National Assessment of Educational Progress in math have been rising, just two-thirds of those students demonstrated basic skills on the test given in 1996. Results from the latest test, administered in 2000, are due out this spring.
The Third International Mathematics and Science Study, first conducted in 1995 and repeated for 8th graders only in 1999, found that American students were about average in math achievement compared with their counterparts in more than three dozen other nations. Moreover, the U.S. performance tended to drop off by 8th grade. The TIMSS report points to a shallow curriculum, inadequate instructional materials, and a lack of math expertise among most elementary and middle school teachers as barriers to improving math education.
Those findings have fueled recent debates over whether instruction should emphasize skill-building or deeper understanding of math concepts--arguments that draw parallels with the long-standing "reading wars."
The National Research Council, a division of the congressionally chartered National Academy of Sciences, modeled "Adding It Up" after the NRC's influential report on reading written by a panel of experts in 1998. ("NRC Panel Urges End to Reading Wars," March 25, 1998: http://edweek.org/ew/vol-17/28read.h17)
Similar to the reading panel, the math-committee members represented varying perspectives on how math should be taught and how students learn the subject. Beginning in 1999, the committee reviewed research on teaching and learning in the subject before making its recommendations.
The 444-page report presents a portrait of mathematics learning, using examples of how students acquire proficiency in whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. It also describes how the relationship between teachers and students, as well as their attitudes toward the subject, affect how the material is taught and how well students learn it.
Vignettes included in the report show how different instructional strategies can lead to students' proficiency, according to Deborah Loewenberg Ball, a professor of math education at the University of Michigan and a member of the panel.
"Our review of the research makes plain that the effectiveness of mathematics teaching and learning does not rest in simple labels," the report says. "Rather, the quality of instruction is a function of teachers' knowledge and use of mathematical content, teachers' attention to and handling of students, and students' engagement in and use of mathematical tasks."
In addition to its primary recommendations, the committee came to a number of other conclusions for improving teaching and learning in the subject:
* While algebra for all middle school students is a worthwhile and attainable goal, the report says, simply moving Algebra 1 from 9th grade to 8th is a formula for failure. Instead, the panel suggests, algebraic principles should be built into the curriculum beginning in the early grades.
* A sufficient amount of time--at least an hour a day--should be allotted for teaching math, beginning in prekindergarten.
* The use of calculators and computers can benefit students, though further investigation is needed into how they can be used to improve learning.
* Textbooks and assessments should better reflect the strands of mathematical proficiency students need and should gauge how well students are learning them.
* Teacher education and professional development should not simply require teachers to take more math courses, but should stress courses that reflect the complex interplay between mathematical knowledge and effective teaching.
The initial reaction to "Adding It Up" was positive among math educators, who see it as a unifying document amid the often-fierce "math wars."
"There were a lot of people on the committee who brought very different perspectives, and they were able to come to consensus," said John Thorpe, the executive director of the National Council of Teachers of Mathematics.
How much immediate influence the report might have in shaping education policy or improving classroom practice is hard to gauge, some observers said. Most states have already set--and some are already in the process of revising--the standards that are meant to drive instruction. The textbooks intended to help teachers meet those standards are either ready for sale or in the latter stages of development.
California, the most profitable state for publishers, adopted its K-8 mathematics textbooks earlier this month, and its next adoption is not scheduled for six years.
Committee members hope the report influences national initiatives that may come out of President Bush's education agenda.
The report, sponsored by the Department of Education and the National Science Foundation, will also have a long "shelf life," according to Michael Feuer, the director of the NRC's Center for Education. As states and districts continue their work to improve math instruction, he said, it can provide guidance.
In the meantime, a sustained and comprehensive effort is needed, said Mr. Kilpatrick, the committee's chairman. "We have never done well in this country in teaching mathematics to elementary and middle school children," he said. "But that is not an excuse for complacency. It is time to take action."
Among the underlying causes for the poor performance of U.S. students in the areas of math and science, three problems must be addressed -- too many teachers teaching out-of-field; too few students taking advanced coursework; and too few schools offering a challenging curriculum and textbooks.
The Higher Education Community recognizes that it has a vested interest in working to improve elementary and secondary math and science achievement. More than twenty states have begun to form partnerships with colleges and universities for the purpose of raising math and science standards for students, providing math and science training for teachers, and creating innovative ways to reach underserved schools.
The Math and Science Partnership program provides funds for states to join with institutions of higher education in strengthening K-12 math and science education. States that access these funds will be required to establish partnership agreements with state colleges, universities and community colleges and school districts, with the goal of strengthening K-12 math and science education. These funds could be used by the states to defray the cost of the partnerships and to involve other colleges and community colleges in their math and science initiatives.
The success of partnerships between states and institutions of higher education will be linked to accountability goals that measure important indicators such as student performance on state assessments, increasing participation of students in advanced courses in math and science and passing advanced placement exams, and increasing the numbers of teachers that major in math or science.
Summary of Proposals
Establishes Math and Science Partnerships. States and local districts would be eligible to receive new federal funds to help fund partnerships with the math and science departments of institutions of higher education. Partnerships would focus on strengthening the quality of math and science instruction in elementary and secondary schools and could include such activities as making math and science curricula more rigorous, improving math and science professional development, attracting math and science majors to teaching, and aligning high school math and science standards to foster college placement.
Involves Major Research Institutions. Research universities will be encouraged to participate fully in these state partnerships in order to strengthen K-12 math and science education.
President Bush and Senate Democrats offered their own proposals to hold the nation's schools more accountable Tuesday, each promising the other they would work together to find common ground. Mr. Bush weighed in first during a morning meeting in the Oval Office with a handful of Republican and Democratic congressional leaders who help manage education issues on Capitol Hill...
At the crux of the new president's education reforms is his call for annual state testing in math and reading in the elementary schools. He opposes national testing, he said, because it would undermine local control. But he made clear that without annual testing by the states, "we don't know who is falling behind and who needs help"...
Under his plan, disadvantaged students at schools that continued to fail after three years of special assistance could use public funds to transfer to better public or private schools, or receive additional help.
Assuming a far more activist role than his Republican predecessors, Mr. Bush also wants to expand charter schools, increase money for technology, cut red tape and school bureaucracies and provide more flexibility in the use of federal funds, particularly to improve the quality of teachers.
Senate Democrats have similar goals for better teachers and more flexibility but no voucher programs. "We believe that there is a lot of room for collaboration," Mr. Leiberman said, noting that both the Democrats and the new Republican president were committed to closing the achievement gap. "We also share a commitment to strengthening accountability, broadening flexibility for local schools, spurring innovation and public school choice"...
The sweeping education plan proposed by President Bush last week reflects a growing political consensus that the federal government should step up the pressure on states and school districts to improve academic achievement, especially for disadvantaged children, observers say.
While the details of how that pressure should be applied are sure to be the subject of debate in the coming months, Mr. Bush's plan has struck a chord among members of both major political parties who believe that federal funding should be tied to student performance...
Linked to the president's demand for more accountability is the promise of greater flexibility in spending federal aid. And both of those elements were infused in a proposal offered the same day by a group of centrist Democrats...
Under the president's plan, accountability for achievement would be enforced by a proposed requirement that states test 3rd through 8th graders in Title I schools every year in reading and mathematics. Only 15 states, including Mr. Bush's Texas, currently do so.
The plan would penalize states that failed over time to close the achievement gaps between students of different races and family-income levels by reducing a portion of the states' Title I administrative funds. It would offer financial rewards to schools and states that closed those gaps.
"I believe strongly in local control of schools," Mr. Bush said last week. "But educational excellence for all is a national issue, and at this moment is a presidential priority"...
Current federal law also contains some accountability demands. The 1994 reauthorization of the Elementary and Secondary Education Act, which includes the $8.6 billion-a-year Title I program for disadvantaged students, requires states to set up systems of standards and aligned assessments and demonstrate yearly progress. Some states are still struggling to comply with that mandate. That law also requires states and districts to intervene in poor-performing schools.
But the Bush plan would go further. In addition to the emphasis on more testing, coupled with rewards and penalties, it would pose a new threat for persistently failing schools: the loss of substantial federal aid. And, in the most controversial provision of the accountability package, some of the federal money could eventually go to private schools.
If, after one year, a poor-performing Title I school showed no improvement, it would receive extra financial and technical assistance. After two years, the district would have to take corrective action and offer the school's pupils public school choice. Ultimately, after three years, parents of students in failing Title I schools could take a portion of the federal dollars, matched by state funds, to spend on tutoring or on tuition at another school, whether public, private, or religious...
But Democrats have made clear that an insistence on using federal money for private school vouchers would kill the deal. And given the razor-thin hold that Republicans now have in Congress, many political observers predict that the voucher element will eventually fall by the wayside.
Mr. Bush's plan would also consolidate most federal K-12 programs into a much smaller and more flexible set of funding sources. In addition, it would create a few new programs, including a K-2 reading initiative and a plan to improve math and science instruction...
The so-called New Democrats--a centrist group affiliated with the Democratic Leadership Council--insist that more federal spending is critical if the federal government is to expect more from schools. "We want to give states and local districts the resources they need to help every student learn at a high level," said Sen. Lieberman, the 2000 Democratic vice presidential nominee, who has often worked with Republicans on education issues.
In addition to committing to more spending, the bill Mr. Lieberman and Sen. Evan Bayh, D-Ind., put forward would consolidate most federal K-12 programs into five, goal-oriented titles, demand measurable progress from states, and increase the targeting of federal aid to the neediest students. Rep. Dooley, the lead sponsor of the House companion to the Senate bill, said the New Democrats' plan differs from that of the Bush administration in that it would direct more aid to poor students...
President Bush's drumbeat for testing and accountability in education could require more than half the states to greatly expand their testing programs and spell major changes for the federal assessment now used to gauge student progress nationally.
Some educators embraced Mr. Bush's school proposals announced last week, including annual testing in grades 3-8, while others worried about an avalanche of assessments...
President Bush is...proposing financial rewards for schools and states that make significant progress in closing the achievement gap between students of different racial and economic groups. Progress on state tests would be confirmed by expanding the National Assessment of Educational Progress, the federal testing program, to assess a sample of 4th and 8th graders in each state in reading and mathematics every year...
Some educators last week welcomed the call for annual testing, saying it would provide a better gauge of student progress and more useful information for teachers and schools, such as the ability to pinpoint teachers' strengths and weaknesses...
But Mr. Payzant, a former assistant secretary of education in the Clinton administration, said he worried that the cost to states of writing such tests "could result in a backing away" from more rigorous, curriculum-driven exams.
"The big question mark to me about this is how testing every kid every year would affect our own state assessment system, which is measuring at a much higher level," said Robert F. Sexton, the director of the Prichard Committee for Academic Excellence, a Kentucky citizens' group. His state uses a mix of multiple-choice, short-answer, extended-response, and portfolio exams...
Others said they had nothing against the annual testing of students, as long as it didn't result in excessive testing and was not used as the sole measure of student or school performance...
State reactions last week depended, in part, on what each state already has in place. Fifteen states now test students in grades 3-8 in reading and math. But of those, only seven use a criterion-referenced test, meaning it is aligned with the state's standards. Six rely primarily on norm-referenced, off-the-shelf exams that are intended to compare the performance of students against others nationally. And two states use a combination of tests that differ by grade level...
Under Mr. Bush's proposal, federal money would help cover the costs of creating the assessments, but the administration has not yet cited a specific amount. States would have three years after the plan was enacted to implement the tests, and the states that did so before the end of the second year would be eligible for a one-time financial bonus...
Most states, meanwhile, have yet to meet the existing testing and accountability requirements under the federal Title I program, which were supposed to be in place this school year. And educators said last week it was unclear how Mr. Bush's plans would mesh with those rules.
"A lot of states have a long way to go to meet their final assessment responsibilities," said William L. Taylor, the acting chairman of the Washington-based Citizens' Commission on Civil Rights, a private watchdog group. "Testing is necessary, but right now, we ought to be concentrating on getting the kinds of assessments that we can have some confidence in, rather than engaging in a kind of testing mania"...
But Mr. Jennings of the Center on Education Policy argued that President Bush was offering "weak accountability, not strong accountability," because states would be able to pick their own definitions of acceptable student achievement, and the worst penalties states would face for failing to make progress would be losing a portion of their administrative funds under Title I.
"The issue before was, how the heck do you make sure that state standards and state tests are good enough in order to make these rewards and impose these consequences?" said Jeanne Allen, the president of the Washington- based Center for Education Reform, which promotes school choice. "And I think the Bush proposal answers these questions very nicely."
Mr. Bush has proposed verifying state test-score gains by comparing them with NAEP results. To make that work, however, more states would have to participate in the national assessment. In 1999-2000, 48 states signed up for NAEP, but only 40 had their students take the tests because the others could not persuade enough schools to volunteer.
Moreover, NAEP math and reading tests are administered only every two to four years.
Mark D. Musick, the chairman of the governing board that sets policy for the assessment, said he believes in NAEP as one measure to confirm states' progress.
But, he said, the Bush plan would mean big changes. The total NAEP budget for national and state testing is currently $38 million. "As a rough rule of thumb, to do what is being proposed would certainly double or triple that," said Mr. Musick, who is also the president of the Atlanta-based Southern Regional Education Board. Enticing schools to participate in NAEP by paying them or underwriting all test administration would push the figure still higher.
Educators also expressed concern that testing alone wouldn't produce changes in student achievement and that, despite a promise of some money to help low-performing schools, too little attention was being paid to students' opportunity to learn.
"We know how much intervention and help you have to give schools. Just having the standards and assessments doesn't get the job done," said Mr. Sexton of Kentucky...
...In mid-December the 106th Congress finally agreed on an FY 2001 appropriations bill for Labor, Health and Human Services, and Education.
The final agreement was considered a victory for education, with a $6.5 billion (18 percent) increase above last year's allotment for the Department of Education.
Funding for the Eisenhower professional development state grants for FY 2001 was set at $485 million (which includes the mandated $250 million set aside for science and math educators' professional development.)
Language added to the appropriations bill now allows Local Education Agencies to use funds in excess of the allocation to improve teacher quality by reducing the number of teachers teaching out of field, implementing mentoring programs, and providing opportunities for teachers to attend multi-week institutes. Specific funds may also be used to help the state become an Ed-Flex state, and to continue the Troops to Teachers program...
For more information on these and other federal education appropriations, visit the Department of Education website at www.ed.gov.
The Bush Education Plan
Last week, President George W. Bush released a blueprint of his Administration's education reforms. As expected, his plan streamlines Education Department K-12 programs into broad funding streams, permitting states and local school districts to decide how to use the federal funds. It is anticipated that this plan will be introduced as legislation by the Republican leadership.
The Administration's plan focuses on seven performance-based titles (Title II, Part B is Improving Teacher Quality, Improving Science and Math Instruction)...
Three R's Introduced in the Senate
Also last week, Senator Joseph Lieberman (D-CT) again introduced the Public Education Reinvestment, Reinvention, and Responsibility Act (Three R's). Last year the Three R's was introduced and defeated as a substitute for S. 2, the Senate ESEA bill. The New Democrat Coalition, a moderate group that worked to refocus national education policy by bringing together ideas from both Republicans and Democrats, created it.
This legislation also block grants existing federal programs (including the Eisenhower professional development program) into five funding streams to states and LEAs...
Specifically in the area of teacher quality, the Three R's would combine the Eisenhower program and the Goals 2000 program and increase annual funding to $3.6 billion to improve the quality of teachers, principals and administrators. Funding to states would be based on formula based on 50 percent poverty, 50 percent on student population. It requires states to have all teachers fully qualified by the year 2006, and requires LEAs to provide professional development. The Three R's encourages innovative training and mentoring partnership programs between schools, universities, non-profits, corporations and business groups, and preserves the class size reduction program in the early grades...
Rep. John Boehner (R-OH) has been named chair of the House Education and Workforce Committee, replacing retiring chair William Goodling. Rep. Boehner is in his sixth term in Congress; during the 106th Congress, he chaired the Employer-Employee Relations Subcommittee, which led the efforts to reform health care and modernize the nation's retirement and pension system. He was Republican Conference Chair during the 104th and 105th Congresses. Rep. Ralph Regula (R-OH) will serve as the new chair of the House Appropriations Subcommittee on Labor, Health and Human Services, and Education.
The Senate, divided 50-50 as a result of the election, has forged a historic power sharing agreement. Senators have agreed to have a 50-50 ratio on all committees and to attain an equal balance of the interests of both parties.
New Democratic Senators to the Senate Health, Education, Labor, and Pensions (HELP) Committee include New York Senator Hillary Rodham Clinton and North Carolina Senator John Edwards. They will join these Senators, who will continue on the HELP Committee: Kennedy (ranking member, MA), Dodd (CT); Harkin (IA); Mikulski (MD); Bingaman (NM); Wellstone (MN); Murray (WA); and Reed (RI).
Republican Senators on the HELP Committee include Jeffords (chair, VT); Gregg (NH); Frist (TN); Enzi (WY); and Hutchinson (AR), Collins (ME) and Sessions (AL) New members to the HELP committee include Virgina Sen. John Warner; Missouri Senator Christopher (Kit) Bond; and Kansas Senator Pat Roberts. Departing the Senate HELP Committee are DeWine (OH), Brownback (KS), and Hagel (NE)...
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