Asserting that mathematics educators have “led the way” in establishing a national consensus on what students should learn in the subject, some 500 math educators, business leaders, and policymakers--including President Bush--met here last week to begin outlining a vision for measuring progress.
The officials noted that the mathematics profession has come to a virtual agreement on new standards for the curriculum and professional training of math teachers. But to put such changes into effect, they said, tests must change to reflect the new standards.
“You’ve labored for years to reach a consensus on standards for math performance,” President Bush told the group. “But you can’t blaze a trail for the future until we know where we stand.”
Mr. Bush and Secretary of Education Lamar Alexander said the math educators’ efforts represent a perfect example of what they expect all subject-matter groups to undertake as part of their newly announced “America 2000" strategy. That proposal called for the development of “world class” standards for each of five core subjects, including math, and new American Achievement Tests to measure students’ performance against the standards.
But many of the educators here suggested that it may be impossible to develop a single test that could provide information to help improve teaching and learning that at the same time could provide data to compare schools, school districts, and states. And even if such an assessment could be developed, they said, it would take years to put together, far longer than many policymakers want.
President Bush said in announcing his plan, for example, that the first achievement test, for 4th graders, should be in place in the fall of 1993, with tests for 8th and 12th graders to follow.
“I’m very skeptical about having an assessment serving [accountability needs] by 1994,” said Robert L. Linn, co-director of the National Center for Research on Evaluation, Standards, and Student Testing at the University of Colorado at Boulder.
But Mr. Alexander, while acknowledging that the effort will take years to perfect, said educators should aim for the President’s target date.
“We need to get on with it,” he said. “We don’t want to just ponder it forever. We’re saying, ‘Give us the best you’ve got beginning in 1993.”’
Though more than a year in planning, last week’s meeting, billed as the “national summit on mathematics assessment,” comes at a time of a growing debate over national standards and assessment.
In addition to President Bush, at least four groups--including the National Education Goals Panel, which held a public forum as part of the conference--have considered or called for some form of national test or examination system.
Participants noted that, long before the President’s call, the math community had moved toward a consensus on standards for the profession.
In a report issued in 1989, the National Council of Teachers of Mathematics outlined curriculum standards that reflect widespread agreement among math educators about changes in the way the subject should be taught.
The document argues that mathematics is “something human beings do to make sense of the world,” according to Thomas A. Romberg, director of the National Center for Research in Mathematical Sciences Education at the University of Wisconsin at Madison. By contrast, he said, most schools now teach “eight years of 18th-century arithmetic, followed by a year of 17th-century algebra, followed by a year of 3rd-century-B.C. geometry.”
A similar report, issued in March, outlines standards for teacher training in math. (See Education Week, March 13, 1991.)
Mr. Alexander, who chaired the steering committee for last week’s summit, said the math educators’ efforts represent a model for other disciplines.
“We are fortunate math teachers got out this far ahead,” the Secretary said. “They are setting an example for other subjects.”
But Shirley A. Hill, former chairman of the Mathematical Sciences Education Board, the arm of the National Academy of Sciences that sponsored the summit, noted that the experience of math teachers suggests that other disciplines may not have such an easy row to hoe in their efforts to set standards.
“I think it is generally acknowledged among our colleagues in other disciplines that we have our act together,” said Ms. Hill, the Curator’s Professor of Mathematics and Education at the University of Missouri at Kansas City. “However, if anyone thinks that this coordination and consensus is an overnight phenomenon, I have the historical facts and the scars to disabuse you of that notion.”
Moreover, said Lauren B. Resnick, director of the Learning Research and Development Center at the University of Pittsburgh, other disciplines are more contentious than math. Achieving a national consensus on a literary canon, for example, may prove extremely difficult, she said.
“It’s going to be very difficult in this country to deal with a concept of a canon, to say which knowledge and pieces of the culture are going to be considered the national culture,” Ms. Resnick said.
But Roger B. Porter, President Bush’s domestic-policy adviser, said the potential pitfalls should not deter educators from undertaking the task.
“The fact that it is difficult does not mean it is not important,” he said. “We should step back and say, ‘What is it students ought to know, what skills ought they possess?”’
As part of their deliberations last week, conference participants began discussing a set of standards for assessment in the field, to complement the profession’s standards for curriculum and professional training.
In many ways, Ms. Hill said, the assessment standards are the most important of the three. Since testing tends to drive curriculum, she noted, high-quality assessments that match goals for proper instruction could help spur needed curricular change.
“There is a growing gap between the objectives of today’s reform in mathematics and our tests of student performance,” she said. “But assessment that matches what we value, what will be of value to our students in the future, is attainable.”
The proposed standards are expected to emphasize that the primary purpose of assessment is improving teaching and learning, according to Ray C. Shiflett, executive director of the math board.
At the same time, he said, they are expected to stress that tests must be aligned with the curricular and professional-training standards.
“All three elements must work together,” he said.
In offering his recommendations, President Bush proposed that the guidelines also emphasize that assessments should also raise the performance level of every student.
Rather than determine simply that the top students are performing well, he said, “tests should ensure that average students achieve at world-class status.”
But other participants suggested that the proposed standards may conflict with the goals of policymakers who are developing new forms of national assessments.
For example, said Nancy Cole, executive vice president of the Educational Testing Service, tests to improve classroom instruction should be separate from those used to monitor school districts’ and states’ performance.
“An assessment should be designed to fit the purpose to which it is put,” she said. “Students and teachers don’t need a national test. They need assessment devices that will help them think about what math is. That’s a very different kind of thing than policymakers need to assess the overall progress of the nation.”
Richard Peters, director of school assessment for the Indiana Department of Education, added that “tests for all seasons and all reasons” would also be unwieldy and expensive. The curricular goals demand alternative forms of assessments, such as portfolios and performance-based assessments, which are time-consuming to administer and evaluate, he noted.
“To get a reliable measure of how Johnny is doing takes several questions and performances,” he said. “It’s not a one-shot deal.”
In addition, he said, testing every student is not necessary to determine the overall progress of the nation.
“It’s like doing quality control with every piece down the line,” Mr. Peters said. “It’s very costly. The money would be better spent on better classroom assessment, rather than getting the national government into every house.”
But Gov. Roy Romer of Colorado, chairman of the National Education Goals Panel, responded that a new assessment system is needed to provide both data to policymakers and to help boost the level of student achievement.
“I’m not spending time on the panel so that we only give a statistical report to the nation,” he said. “That doesn’t turn me on.”
“I do not understand,” he added, “why we can’t focus on a new assessment instrument that raises the level of reach of individual students, and find a way to siphon off from that a report” to policymakers.
Mr. Romer maintained that he does not favor a single test that would be administered to every student. Rather, he said, groups of states could develop assessments that would be calibrated to the national standard.
Such a grouping “would accelerate the time line by several years if we start now,” Governor Romer said.
But conference participants warned that changing the assessment system, and the way math is taught, will be difficult and will require massive amounts of public support, resources, and time.
“We should take the long view, and not rush into changing math assessment overnight,” Mr. Shiflett said. “Ten years would not be surprising.”
