It is “math choice’’ time in Jane Fulkerson’s combined kindergarten and 1st-grade class here, and there is an audible buzz in the air.

From Risk to Renewal:
About This Series

Part 1

February 10, 1993

• • Charting a Course to Reform: The Next 10 Years
• • Mission Impossible? Educators Confront Tough Task of Rethinking Goals
• • Obstacle Course: Barriers to Change Thwart Reformers at Every Twist and Turn
• • The Future of School

Part 2

February 24, 1993

• • Intro: The Balance of Power
• • Time and Space
• • The Coherent Curriculum
• • States Move From ‘Inputs’ to ‘Outcomes’ in Effort to Regulate Schools
• • Basic Training
• • Dollars and Sense
• • Signing Up the Public

Part 3

April 21, 1993

• • Charting a Course: The Next 10 Years
• • Kentucky Moves To Enact Reform Plan
• • Policymakers, Educators Seek Strategy

Children are sprawled around the room as they engage in a wide range of carefully chosen activities. In one corner, tiny hands spin a number on a cardboard spinner and count out colorfully painted beans. On the floor, two small girls connect colored plastic cubes to make patterns repeat. Three children at a table nearby color in rows of seven blocks each on a worksheet.

“You have to make different patterns,’' explains one of the three, a pigtailed girl in a spotless pink sweatsuit. “But they all equal seven.’'

Ms. Fulkerson herself is working with a group of children as they move the hands on a clock and discuss the time of day they go to school and then the time they go to bed.

As the children become excited, their voices rise and then fall again. The buzzing sound resumes.

To Ms. Fulkerson and other teachers like her here at Elizabeth Freese Elementary School, that buzz is the sound of children learning.

“I think,’' the veteran teacher says, “that this is the right way to teach.’'

The “right way,’' to Ms. Fulkerson’s way of thinking, means giving students plenty of hands-on learning opportunities and helping them begin to think critically and to talk with one another and work together to solve problems. She wants to expose her students early on to a wide variety of mathematical elements--patterns, measurement, even some geometry. And she wants to instill in her pupils a basic sense of what numbers mean and how they feel.

A teacher for 18 years, Ms. Fulkerson has come to this new view of teaching through the California mathematics framework.

One Piece of the Puzzle

California’s subject-matter frameworks--there are now eight in all--are the focus of a pioneering effort in this state to improve schooling for every child in every classroom.

Unlike most state reforms, which tinkered around the edges of schooling, California started by aiming directly at the heart of the educational enterprise: the teaching and learning that goes on in the classroom every day. And the frameworks lay out the blue-print for a fundamental overhaul in curriculum.

Where state curriculum guidelines have traditionally been lists of topics schools should cover at each grade level, California’s curriculum frameworks seek to articulate a more comprehensive--yet, at the same time, less specific--view of what teaching in a particular subject should look like.

Rather than simply specify content, the frameworks call for changes in the way subjects are taught. They urge educators to move away from the traditional “drill and skill’’ approaches to teaching and to stress, instead, teaching children to think critically and to problem-solve. They advocate teaching fewer topics in greater depth. And, rather than lay out topics by grade level, they only broadly state the concepts, themes, or “big ideas’’ students should master in, for example, grades 3 through 6.

To be sure, officials here recognize that reforming the curriculum alone won’t improve schools, and they see reform as a complex jigsaw puzzle that also includes the kinds of tests students are given, the quality and availability of training for teachers, and the kinds of educational materials available to schools. But the key piece of the puzzle is the curriculum.

“The whole reform effort needs to be driven by what you want to teach and how you want to teach it,’' says Bill Honig, who spearheaded the frameworks as the state’s superintendent of public instruction. “Some of the other reforms never get to that.’'

While California led the way, a number of other states--Connecticut, Maine, Rhode Island, and South Carolina, among them--have also begun to use curriculum documents to anchor their school-reform efforts.

Similar efforts are under way at the national level as well. In 1989, the National Council of Teachers of Mathematics published national curriculum standards.

Now, national standards for what students should know and be able to do at key points in their schooling are also being hammered out in seven other subjects.

Most of these new standards-setting efforts came after President Bush and the nation’s governors, in a historic “education summit’’ nearly 3 years ago, agreed that one goal for education should be that American students meet “world class’’ standards for learning in major academic subjects.

Reformers are also hoping to convince federal lawmakers that a national system of examinations is needed to reinforce those standards.

Local Control’s Waterloo

All of this activity is remarkable for a nation that has long cherished the notion that control of the content of schooling belongs largely in the hands of local communities.

“Local control met its Waterloo at the October 1989 education summit of the President and the governors,’' says Allen R. Odden, an education professor at the University of Southern California.

“Ten years ago, this would never have happened,’' he continues. “Now we’re saying, ‘Yes, it’s possible to have national standards, and it is desirable.’ ''

Those efforts, however, are still new, and disagreements remain about how to proceed.

While California and the national efforts seek to define the curriculum subject by subject, other states and some educators argue for a more holistic view that would look at the full range of student learning and foster interdisciplinary instruction.

Educators in Maine, for example, point out that learning is naturally interdisciplinary, and that what students learn in one subject is inextricably linked to what they learn in another. Part of educators’ task, they say, is to help pupils see the connections. Thus, that state’s curriculum-reform document divides learning into much broader areas, such as “communication’’ and “personal and global stewardship.’'

And as California’s experience shows, putting the entire puzzle together is a daunting enterprise. If there is a lesson here for other, similar efforts nationwide, it is that change is complicated and it moves at a glacial pace.

Although California has been working at curriculum-centered reform for eight years now, the effort has reached, at most, only two-thirds of the teachers in the state. The state’s assessment system, which many say drives instruction, is only this year fully implementing a redesign that more closely matches the frameworks. And efforts to provide professional development for teachers to help them reorient instruction along the lines of the frameworks--particularly pre-service education for prospective teachers--have fallen far short of the need.

“The framework is the push, and then you have to ask yourself, ‘How do you get that done?’ '' Mr. Honig says. “How you get that done is a very difficult, very complex question.’'

Nevertheless, the experience here has provided a beacon for educators nationwide. If the largest and most diverse state can define what it is students ought to know and be able to do, many say, surely other states and the nation as a whole can do the same.

Curriculum Reforms From Sputnik to Basics

To a degree, the curriculum has always figured in efforts to improve schooling. In the 1950’s, Americans’ fear of losing the space race led to the “Sputnik revolution.’' Schools nationwide beefed up math and science teaching. But education historians say those changes weren’t widely implemented and had all but disappeared from schools by the mid-1970’s.

In more recent decades, the “back to basics’’ movement fueled a renewed emphasis on basic arithmetic and reading skills. States also began to require “minimum competency’’ tests as a condition of high school graduation.

That movement achieved one of its central aims: It made strides in closing the achievement gap that separates African-American students from their white peers.

But there were also drawbacks.

“I think it created an artificial ceiling for children and teachers, and when the minimum becomes the ceiling, it doesn’t allow for stretching all children,’' says Barbara S. Nielsen, the state superintendent of schools in South Carolina. Her state, one of the first to adopt a basic-skills curriculum, is now working to develop frameworks modeled on the California approach.

The emphasis on basic academic skills also reinforced what many claimed was wrong with education in the first place. There was too much “drill and skill,’' too much emphasis on rote learning, and too few opportunities for students to learn to think.

Throughout most of the current education-reform era, however, few efforts have dealt directly with what is taught in schools.

A Nation at Risk, the landmark report that spawned the reform movement in 1983, called only for students to take more courses--four years of English, three of math, three of science, and so on--without saying what should make up the content of those courses.

“As if,’' George Leonard writes in The Atlantic magazine, “four rather than three years of English for students already turned off by the present system would make much of a difference.’'

By the end of the 1980’s, however, 42 states had raised high school graduation requirements in response to the report.

“In fact, what happened was that people took the same courses they were teaching anyway and retitled them,’' says Diane S. Ravitch, a former U.S. assistant secretary for educational research and improvement.

Where Do You Start?

By contrast, Ms. Ravitch says, reform should start with a definition of what students should know and be able to do, and work backward from there to redesign the system to achieve those ends.

And no place took that idea more seriously than the Golden State, she notes. “California led with the key to systemic reform,’' Ms. Ravitch says. “That is, if you want to change curriculum, where do you start?’'

The answer, she says, is “with the curriculum.’'

In addition to leading by example, California has also had a direct influence on national efforts to redefine curricula.

Ms. Ravitch, for example, who as assistant secretary sponsored the national standards-setting projects, was the co-author of California’s history and social-sciences framework. And her co-author, Charlotte Crabtree, is directing the national history-standards project.

Moreover, Ms. Ravitch’s deputy, Francie M. Alexander, oversaw the development of California’s frameworks as the state’s deputy superintendent of public instruction.

Dean of Instruction Leads the Crusade

Educators in California credit Mr. Honig, the exuberant and outspoken former superintendent, with having spearheaded the state’s crusade to overhaul the content of schooling.

“He really has been the dean of instruction here in California,’' says Michael Kirst, an education professor at Stanford University.

In the early 1980’s, when he was elected superintendent for the first time, Mr. Honig set out almost immediately to remake the state’s curriculum frameworks. He has been an aggressive advocate for them ever since and has taken a direct hand in their development. At times, Mr. Honig says, he sent drafts of the frameworks back for revision up to nine times.

Although curriculum commissions were set up to put together the frameworks, Mr. Honig had a substantial say in choosing the teachers, subject-matter experts, and business people who were appointed to the panels.

Mr. Honig’s continued participation in the frameworks process, however, appears unlikely.

He was removed from his job in February following his conviction on four felony conflict-of-interest charges. Mr. Honig has said he will contest those convictions.

‘Philosophical Edge’

As a result of Mr. Honig’s stewardship, however, almost all of the frameworks have “a philosophical edge,’' Mr. Kirst says.

The superintendent’s leadership enabled the state to “get a document with specific content and pedagogical philosophies without watering it down to satisfy every special interest,’' he says. “Some groups are happy with that, and some are not happy.’'

One of Mr. Honig’s specifications for the frameworks was that they have what he calls “pitch.’'

“You want them to be not too general so that there is no focus and not so specific that everybody can’t buy into it,’' he says. Members of the curriculum committees said that balance was often difficult to strike.

That, coupled with the guiding principle that “less is more,’' also meant that tough decisions had to be made about what to keep in the frameworks and what to throw out. Much of what was cut or de-emphasized were topics that were once commonly taught in schools.

In math, computational skills were played down in favor of exposing students to what the document calls the “strands’’ of mathematics--geometry, statistics and probability, logic, measurement, algebra, patterns and functions, and number sense.

Documents Remain Controversial

Some educators still contend that the emphasis in the language-arts framework on having young children read literature and whole texts came at the expense of instruction in phonics.

And the history-social sciences framework remains controversial among educators in that field partly because some social-studies educators contend its emphasis on history shortchanges economics, political science, sociology, and other subjects that traditionally fall under that umbrella.

Moreover, when it came time to choose textbooks reflecting the history-social sciences framework, a heated debate erupted over the proper emphasis on the history of various racial and ethnic groups. While the books, in keeping with the framework, attempted to strike a balance between stressing diversity and the common heritage, some argue that they didn’t go far enough in presenting the multicultural view. In Oakland, for example, school officials refused to purchase any of the textbooks adopted under the framework.

Some of those philosophical shifts remain controversial.

In the math framework, for example, parents still question the diminishing emphasis on drilling addition, multiplication, subtraction, and division skills into children.

“I still hear stories about people going into McDonald’s, and the kids there can’t make change,’' says Susan Braun, a school board member in San Diego. “People are very concerned their children won’t be able to add.’'

And parents and teachers alike worry that their children won’t learn phonetic skills in classrooms where literature is emphasized.

Indeed, these concerns highlight one of the fundamental conflicts in standards-setting and curriculum reform--the issue of depth over breadth. As teachers begin to stress long-term projects and deeper understandings for children, they touch on fewer topics. Why, parents who have become familiar with the curriculum through older children ask, does my younger child seem to be learning less in school?

In San Diego, Transforming a Vision

Of the eight visionary frameworks created so far, the math document was the first. Since then, reform-minded frameworks have been completed in language arts, science, health, history and the social sciences, foreign languages, the arts, and physical education. Completed in 1985 and updated again in 1992, the math framework brings the state’s framework process full cycle.

The second revision, math educators say, was largely a fine-tuning aimed at making the state framework more compatible with national math standards. The 1985 framework, in contrast, marked a significant leap from traditional classroom instruction practices.

In San Diego--Ms. Fulkerson’s district--administrators began to acquaint teachers with the coming changes a year before the frameworks were released.

“The frameworks are not something you can just give out to teachers and forget about it,’' says Vance Mills, the district’s instructional-team leader for math, science, and education technology.

Teacher workshops and in-service sessions were held. The district also made an effort to link the frameworks with other reform efforts already going on there. San Diego is a district noted for its willingness to experiment with educational reforms, and many of those projects, such as the New Standards Project, a privately funded effort to develop what could become a national system of standards and assessments, were compatible with the changes called for in most of the frameworks.

District officials also have begun in recent years to take steps to make sure teachers have the equipment they need to teach in the new ways called for in the framework.

For example, in an effort to move students beyond arithmetic and into mathematics, the framework recommends extensive use of calculators in school. Now, every time the district buys a textbook, it buys a calculator as well.

“I can’t say that ... you’re going to see these in 100 percent of the classrooms,’' Mr. Mills says. “But what we’ve done is take away the excuse that we don’t have the equipment.’'

‘Selling’ the Approach

The district also began “selling’’ the new approach to parents at every opportunity. San Diego schools have a “family math’’ program aimed at helping parents and children work together to improve their math skills. And many schools used the program as a vehicle to explain the framework to parents.

“Few parents were taught in these ways, and they think their kids are playing,’' says Susan Manning, a resource teacher at Ms. Fulkerson’s school, where the “family math’’ program was used to great advantage.

In other districts, such as those in surrounding San Diego County, administrators have begun to hold “fairs’’ where examples of students’ work are displayed to ease parents’ concerns.

Despite the San Diego district’s efforts, implementation of the frameworks at the classroom level has been uneven--as it is, observers say, across the state.

“You find that one-third of teachers are willing to go to volunteer sessions and look to make changes,’' Mr. Mills says. “Another one-third are not necessarily willing to volunteer, but they’re willing to make changes, and you have to conduct the in-service [training] during school hours.’'

“The last third are the ones who will never change, and you just have to hope they’ll retire,’' Mr. Mills says.

Statewide, even Mr. Honig estimates that no more than 7 percent of teachers have fully adapted their teaching styles to the frameworks.

He adds, however, “I met a teacher, a guy in Los Angeles, who told me that in the last three years he has really shifted his teaching in the classroom to give a lot more problem-solving.’'

“Is he teaching the full framework? Probably not,’' Mr. Honig says. “Are his kids getting some benefit? Yes.’'

Signs of Progress

Ms. Fulkerson is a teacher who might fall in the first two-thirds of teachers described by Mr. Mills. She requested a copy of the math framework when it was published, and she uses it when she plans her course of instruction for the year.

Elsewhere at her school, there is evidence that other teachers are making similar efforts to transform the frameworks’ philosophies into practice.

In one 1st-grade classroom, students have compiled a bar graph comparing all the sunny days of the year to the rainy days. In every class, there are boxes of manipulatives--interlocking plastic cubes, and beans, barrettes, and buttons to count--all tools intended to help students feel and see the math concepts they are learning.

Students in a 4th-grade classroom use calculators to work out story problems. Then, they put them aside to do some “mental math,’' figuring out methods to make computations quickly in their heads.

The problem they are given is 30 x 4 + 5. When a boy volunteers an answer, the teacher, Kristina Wenger, replies: “I want to know what Jared did in his mind to figure that out.’' Several methods for solving the equation are suggested.

As is called for in the framework, one lesson implicit in this exercise is that there is no one “right’’ way to solve a problem.

The Status Quo

In a high school in another part of the city, however, the intractable nature of more traditional instructional practices is plainly evident.

One of the biggest changes for high schools in the math framework is the introduction of a course of study known as Math A. The course is meant to replace such traditional courses as general mathematics or consumer mathematics and to serve as a bridge between arithmetic and algebra.

Among its features are an emphasis on giving students authentic problems, rooted in real-life experiences. It recommends long-term projects for students to undertake collaboratively, and it incorporates some “higher mathematics,’' such as algebra and geometry.

The state provides five days of specialized training--more than is usually the case--for teachers of Math A and its successor course, Math B, for students who don’t immediately go on to algebra.

In this high school, however, students are seated at individual desks in neat rows. They work alone on worksheets that keep them busy only as long as the 45-minute class period.

The worksheets depict household items with three prices listed above them. The task for students is to guess which of the prices would have been correct in 1900.

To find out if their guesses are correct, the students are told to find the mean of an unrelated group of numbers listed in a corner near each picture.

While the exercise employs some practical information, it is hardly the kind of real-life problem that students might encounter outside school.

“We’re trying a lot of things, and we’re trying to learn from them, but we don’t have it all figured out yet,’' says Thomas W. Payzant, the district’s superintendent of schools.

Enough Training and The ‘Right Kind’ of Training

Like many observers of the California effort, Mr. Payzant believes the biggest obstacle to implementing the frameworks is the lack of professional development to support the kinds of fundamental changes teachers must make to teach in the ways the frameworks intended.

The state allows schools to set aside eight noninstructional days each year for training. The 1992 math framework, however, suggests that teachers need at least 10 days of in-service training just to teach it correctly.

Moreover, funds to pay the cost of such training or for the wages of substitute teachers are scarce.

“It’s hard when you get into budget-cutting, and if you have to make tough decisions,’' Mr. Payzant says. “Very typically, staff-development time is the first thing that goes.’'

San Diego has had to make some of those tough decisions. The school system’s budget declined by $22 million last year and is expected to decrease by up to $9 million more this year, Mr. Payzant says.

The budget cuts force schools such as Freese to pick and choose among the professional-development opportunities available to their teachers. The question for Freese’s staff this year was: Should teachers attend a countywide language-arts conference or go to a similar two-day event in mathematics? The school opted for the former.

The same kinds of financial pressures are working against schools statewide.

Hit hard by the recession and cuts in federal spending on defense, state spending for education deteriorated sharply in the late 1980’s. The state has slipped from 31st in the nation in 1982-83 to around 43rd in per-pupil expenditures, according to Mr. Kirst.

It isn’t, however, just a matter of getting enough time or money for professional development. Having the right kinds of training opportunities is equally important.

“Even the best skill-training workshops are insufficient for the kind of major changes we want to get out of the frameworks,’' says Mr. Odden, who, with Mr. Kirst, directs Policy Analysis for California Education, a state policy-research consortium.

What is also needed, says Milbrey W. McLaughlin, the director of the National Research Center on the Context of Secondary School Teaching at Stanford University, are “learning communities’’ that support teachers as they attempt to unlearn old methods and construct new practices for themselves.

Training Projects Under Way

Ms. McLaughlin conducted research comparing California teachers with teachers in Michigan, where little state-level reform activity was taking place.

In schools where teachers could observe their colleagues’ classrooms or meet to talk about practice, she found, the frameworks were “strong stuff that forced productive, good discussions around issues of content and pedagogy.’' In both states, however, such discussions never took place in schools where those kinds of opportunities were unavailable.

To address some of those concerns, a handful of comprehensive professional-development programs are now under way throughout the state.

The California Math Project, for example, operates at 17 sites across the state and links teachers with university math educators for three to four weeks of training. The teachers then return to their schools to provide support and training for their colleagues. Those “teacher leaders’’ also receive follow-up attention over a period of three to four years, according to Nicholas Branca, who directs the effort.

“Teachers need to take the time to understand the mathematics involved,’' Mr. Branca says. “It’s almost like having a different mindset about what mathematics is and how you’re teaching it.’'

Most elementary school math teachers, he adds, have had little--or no--training in the subject before becoming teachers.

The California Mathematics Project was launched in the early 1980’s, even before the 1985 framework was in place. Two years ago, similar projects were put in place in the seven other subject areas.

Another program, which is supported by a grant from the National Science Foundation, draws teachers together from middle schools to discuss ways to improve math education. The program, known as the Mathematics Renaissance Project, has so far provided support for more than 200 teachers statewide.

Experts point out, however, that those numbers are still very small, representing only a small portion of the more than 200,000 teachers who could benefit from them.

Moreover, at the college level, state officials concede, there is no mechanism for making sure that education-school students are exposed to the frameworks’ concepts and philosophies before they become teachers. Those universities and colleges that are providing such training for students--and there are some--are doing so on their own.

Testing for Thinking

Efforts by states to implement curricular standards are also thwarted by standardized tests that bear little or no resemblance to the kind of teaching called for in standards-setting or curricular-reform efforts.

In 1987, California began an ambitious redesign of its assessment that was aimed at matching the tests to the frameworks’ goals and at measuring, for the first time, what students are able to do with what they know.

That effort came to an abrupt halt in 1990, however, when then-Gov. George Deukmeijian, embroiled in a feud with Mr. Honig, cut off funding for the California Assessment Program, known less formally as CAP.

Some schools across the state that had adapted their teaching to the frameworks saw their students’ test scores dip--particularly in the area of language arts.

This spring, however, the state is finally poised to put that puzzle piece in place. The state’s newly redesigned assessments will be administered to nearly every student in reading, writing, and math in grades 4, 8, and 10. The assessments are also expected to be expanded to include history and science in grades 5, 8, and 10 next year.

“If anything drives the curriculum in California,’' Mr. Mills says, “it is the CAP.’'

“School-by-school results are published, and they get a lot of attention,’' he adds. “When we get that CAP in place, I think you’ll see a major change.’'

Pressuring for Change

Textbooks and curricular materials--another piece in the state’s systemic reform effort--have also been slow to change.

California is the second-largest market among the 22 states that approve textbooks at the state level for use in classrooms; only Texas buys more books. Most states permit local districts to choose their own textbooks.

The state hoped to use its considerable clout with the textbook-publishing industry to pressure publishers to produce materials that would complement its frameworks.

In math, the state board of education set out to make those intentions known early on by rejecting all of the textbooks submitted by publishers after the 1985 framework was adopted. Publishers were permitted to try again but, Mr. Honig says, their next efforts “were still only about 20 percent there.’'

As a result, teachers went for years with either old texts or new ones that didn’t match up with the framework.

“All of the new books are really heavily into the manipulatives, but they don’t do the business of teaching math,’' said David Crum, a bilingual 2nd-grade teacher at Euclid Elementary School in San Diego. “I actually keep my framework in my room to refer to because the books are so weird.’'

For other teachers, administrators say, it was easier to simply rely on whatever textbooks were at hand.

To plug the gap in textbooks and materials, the state has been developing curriculum units that teachers could insert into their teaching. That effort, however, is far from complete.

There are signs, however, that the next round of math textbooks may represent a significant improvement over the previous generation.

The Glencoe division of Macmillan/McGraw-Hill just this year published the first textbook designed for California’s Math A course. Designed as a resource book for students, the new book contains suggestions for long-term projects and activities and, in appendices at the back, lists the concepts, applications, formulas, weights, and measures students will need to know to carry out the suggested activities.

Noting, for example, that a person of average metabolism will gain a pound of weight after consuming 3,500 calories more than normal, one such activity asks students to work with a partner and keep track of the calories they consume each day. Then, pupils are asked to find their average daily calorie consumption and to determine how many calories they must consume to gain or lose weight.

For City Schools, ‘Pie in the Sky’?

Even if they support curricular frameworks, classroom teachers face practical problems in implementing them--problems, they contend, that were never anticipated in systemic reform efforts.

Patricia Climes, who teaches Math A at Crawford High School in San Diego, points out that, on average, one-third of her students are absent from class on any given day. The high absentee rate, she says, prevents her from assigning long-term projects to her students.

Often, Ms. Climes and other teachers say, the students in Math A classes are those who have the most difficulties in school. Many are poor, and some are also recent immigrants with poor command of English. The teachers contend that many of the students have become indifferent to their efforts.

“Sometimes, I feel many of us in the city schools feel some of these materials are a little ‘pie in the sky’ for our kids,’' she says.

But, if the frameworks are to be truly successful, district administrators say, they must work with all students.

Moreover, other teachers say, they may not undertake cooperative-learning tasks with their students simply because the desks in their classrooms are not suited for that purpose. The desks vary in height, for example, or books tend to slide onto the floor.

The Long View

For the most part, however, California educators say, the pieces of the puzzle are beginning to fall into place.

“What has not been the biggest complaint has been the unwillingness of the system to respond,’' Mr. Kirst says.

“There’s widespread recognition of the frameworks,’' he says. “A lot of districts are briefing teachers on them, and a lot of teachers are trying them.’'

Among those who are trying them, many say the new content and methods are making a difference.

“I think it’s making a difference in their self-concepts, in their risk-taking, and in their math,’' Ms. Fulkerson, the kindergarten and 1st-grade teacher in San Diego, says. “In my classroom this year, I’m not seeing kids who are feeling bad about themselves in math.’'

Ms. Fulkerson’s students, it should be noted, come from what the district calls a “minority isolated’’ school. More than 43 percent of the students at Freese are African-American; another 22 percent are Hispanic, and 15 percent are Filipino. Between 65 percent and 75 percent come from families poor enough to qualify for the federal free and reduced-price lunch program.

It has also helped California’s curriculum project, educators say, that the state’s math framework and the N.C.T.M.'s national standards share some common philosophies.

“We’re all moving in the same direction,’' Jack Price, the co-director of the Center for Science and Math Education at California State Polytechnic University in Pomona, says. “In fact, all of the subject areas are all singing out of the same hymnbook.’'

The existence of the national standards, he adds, may have been the primary reason publishers of math textbooks are beginning to make major changes in their materials.

The national standards have now been incorporated into curriculum guidelines of one sort or another in 40 states and the District of Columbia, says Mary Lindquist, the current president of the math teachers’ group.

Perhaps more important, in a nationwide survey conducted last year, 48 percent of high school teachers and 22 percent of elementary school teachers said they were “well aware’’ of the national math standards.

However, real classroom-by-classroom change may still be years away. Mr. Price predicts it may not come until the turn of the century.

And, all the while, new discoveries are being made in the sciences, history is growing longer each day, and new works of literature are becoming classics. The definition of what students should “know and be able to do’’ may necessarily grow and change as a result.

“One half of the mathematics we know today,’' says Iris Carl, a former president of the N.C.T.M., “has been invented since World War II.’'

California updates its frameworks every seven years. And educators in this state warn that national standards-setting efforts also must insure that their standards are fluid while, at the same time, working to put them into common practice.

However, until real change begins to occur at the classroom level, Mr. Payzant says, “everyone has to be vigilant on keeping the focus on improving teaching and learning for all students.’'

“If not,’' he says, “this will run the risk of being viewed as one more misguided reform effort in the history of American education.’'