Feature

Math Wars: Tradition vs. Real-World Applications

The contentiousness over the direction of math reform plays out fitfully in local schools by RICHARD LEE COLVIN


The message to the educators in Escondido, Calif., could not have been clearer: Parents, not math teachers, would decide what kind of math classes high school students would take.

By a unanimous vote last January, the trustees in the 18,000-student suburban San Diego County district agreed to phase out the most experimental of its high school curricula, a project-based program known as Interactive Math.

Students taking those classes, which featured weeks-long explorations of complicated, real-world problems but little practice with formulas, had performed poorly on a traditional standardized test given by the school district. The trustees retained another experimental program, known as Core Plus Mathematics. But only those students whose parents deliberately chose to enroll them in it could participate. All others were to be in traditional math--algebra, geometry and algebra II, the time-tested (some say time-worn) staples of American secondary school education.

To ensure schools didn't lobby parents on behalf of Core Plus, the trustees stipulated that parents had to select a math program before conferring with a counselor.

"Parents who very sincerely thought that integrated math was not the way to go felt locked in," says David Jenkins, Escondido’s interim superintendent who was in charge of business operations at the time. "Fortunately, we had a board that was sympathetic to parents and had great concern that parents were not being given the option and the necessary information to make a sound decision as to where they wanted their children."

Not surprisingly, 70 percent of the students wound up in the traditional math courses. Math reform--which stressed real-world situations and de-emphasized mastering the factoring, procedures and geometric proofs of traditional courses--had taken it on the chin. Again.


Contentious Debate
The past four years have not been easy for California math reformers who in the 1980s and early 1990s were considered national leaders. The state adopted a framework for math education in 1985 that presaged many of the positions taken in 1989 by the National Council of Teachers of Mathematics. NCTM's standards then ignited a heated debate over and passionate re-examination of math education in America.

In California, the standards prompted another rewrite of the framework that many say, in retrospect, went beyond what NCTM envisioned. That may have been the last clear victory for the educators who believe that traditional math courses have been elitist, abstract, too focused on error-free calculation and obsessed with mind-numbing repetition--besides being ineffective for many students. Ever since, they've been on the losing end of many state and local decisions, handed defeats by parents and policymakers who say the strategies devised to fix those problems are too radical.

Taught traditionally, many students failed to learn math well enough to use it as a tool in their daily lives. The proposed solution to that problem--having students ponder real-world dilemmas--didn't necessarily teach them much math.

The string of setbacks began in 1994 when the state Board of Education added to its list of approved curriculum materials three series of elementary and middle school textbooks previously rejected by an advisory panel of educators. The added textbooks, though influenced by the NCTM standards, also included an emphasis on drill and practice. Then, in 1995, a panel of educators and outsiders appointed to rethink the state's approach to math concluded that basic skills had been neglected.

Rather than simply revise the state's framework, the state board ordered it rewritten and then stacked a panel to do the job with critics of NCTM-type reforms. Finally, in 1997, the state board adopted state academic standards that prompted protests from scores of math teachers. The standards are detailed--critics say too detailed--and leave no doubt that math knowledge should be acquired step-by-step with an emphasis on numbers and skills.

The use of calculators is downplayed in the elementary grades. Multiplication facts are to be memorized. Practice is praised. Understanding, in this view, comes from skilled use of math, not from trial and error.

Dual Approaches
Yet even though the issue over math has been settled at the state level in California, controversies continue to erupt across the state and country. Things became so heated last year that U.S. Secretary of Education Richard W. Riley called for a "cease-fire." Sometimes, he said, "people seem to be hunting for ways to disagree. … This unhealthy habit of thinking in dogmatic ways does our children little good."

For administrators, that debate often comes down to whether to allow parents and students to choose between the approaches or to dictate a single path. Choice is more difficult to offer in elementary schools, but it can be done in middle and high school.

That's what parents in the San Fernando Valley area of Los Angeles asked for. They won assurances that all middle and high schools would provide a traditional course sequence as well as the reform-oriented integrated courses. In those courses, the problems drive the curriculum and students draw on algebra, geometry, probability, statistics and other strands of mathematics in searching for solutions.

In most schools, the math teachers willingly offer both approaches, thereby avoiding conflicts with skeptical parents. That was what the teachers tried to do at Rosemead High School, east of Los Angeles. For a few years, it was possible to see distinctly different classes right down the hall from one another.

In an Interactive Math class, the students became presenters and worked in groups, reporting on homework to their peers while their teacher coached them from the back of the room. Down the hall, the teacher stood at the front of the room, going over homework and answering questions.

Interactive Math is used in more than 100 schools across the country. In trials, those students have done no worse, but no better, on college entrance exams than students taught traditionally. IMP's developers, however, cast that record in a positive light, saying that IMP spends relatively little time on algebra and geometry, the topics most dominant on the SAT. Besides, IMP students tend to take more math. That's especially true for weaker students who have not succeeded in traditional classes in the past.

But after several years of trying to make that arrangement work, the teachers at Rosemead have returned to an all-traditional curriculum. Melody Martinez, an enthusiastic supporter of IMP, says her approach never attracted enough strong students. The parents of college-bound students wanted their kids in traditional classes. That meant that IMP classes were dominated by weaker students. "It's hard to change some people's minds once they are made up," she says.

Paul Sacco, a counselor at San Lorenzo Valley High School south of San Jose, does not believe in giving parents a choice. In a newsletter distributed by the Interactive Math Program, he explains. When a school has both programs, parents and students "can choose one and then blame that math program for a student's failure. At San Lorenzo Valley, we feel that IMP is the better program. We don't even consider the traditional sequence as a possibility."

The elimination of traditional algebra in his daughter's middle school in the Valley Center district, which feeds into the Escondido district, made a math activist out of a quiet software engineer named Larry Gipson. He went to the superintendent to ask for restoration of a traditional class. Two weeks later he had what he wanted. But he realized his victory was only partial.

Gipson discovered that the high schools in the Escondido district already had eliminated the traditional course sequence. He wrote an essay criticizing that decision for the local newspaper. That caused like-minded parents to contact him. Together they formed a group they called "Parents for Math Choice."

For the next nine months, Gipson and fellow parents packed school board meetings, only getting on the formal agenda once. Finally, however, they got what they wanted--the right to choose which math their kids would take. Then they analyzed the comparative performance of the programs and they used that to achieve another victory: The traditional courses became the norm while the newer approach became an option.

"I didn't want my kids experimented on," Gipson told The Los Angeles Times. "I went and looked at the curriculum and said, 'This isn't going to work.' There were no practice problems--none of the traditional algorithms such as quadratic equations."

As a result of the conflict, the curriculum director and the superintendent in the K-8 district in Gipson's hometown moved on. So did two curriculum directors in the high school district. Rather than argue with administrators over the merits of the mathematical or educational merits of their approach, Gipson said, "My tactic was more about beating the district politically."

A Century of Oscillation
Math instruction in the United States has oscillated between the same poles that shape and reshape our culture, politics and even our morality. We are torn between discipline and liberation, between demanding performance and handing out praise--a two-step dance that in education causes us to fixate on facts and formulas and then to turn around and complain that rote learning undermines understanding.

Whatever the pushes and pulls, what goes on behind most classroom doors has remained much the same for the past 100 years even though most Americans wind up with little usable mathematics knowledge.

Sherman K. Stein, a math professor at University of California at Davis, considered the history of math reform in his book, Strength in Numbers. He plumbed the angst of math teachers dating back to 1908, quoting a teacher who wrote to the first edition of the Mathematics Teacher journal to complain about his "general dissatisfaction" with how the subject was being taught.

In a lament that might be heard today, a teacher charged in a 1958 letter to the same publication that "the traditional curriculum is meaningless, and by heading for abstract mathematics, the modernists are moving further away from reality."

In the 1950s, math instruction drilled and killed. Some university scholars tried to devise new lessons that would expose students to math's underlying theory. The Russians' 1957 launch of Sputnik gave those efforts a sudden boost. Thus was born "New Math," which tried to teach calculating in bases other than 10, number sets, number theory and the commutative and associative principles.

This was math for mathematicians, not for carpenters and engineers, critics said. Even so, enthusiastic teachers flocked to crash courses during the summer and plunged right in.

By 1960, however, dissent was growing. Stein quotes a letter signed by 65 mathematicians that blasted New Math. Its designers, the letter said, "stress content at the expense of pedagogy" and "assume that all young people should like what present-day mathematicians like."

By 1973, the movement was grinding to a halt and the bestseller Why Johnny Can't Add by Morris Kline finished it off.

Another round of "back to basics" was followed in the 1980s by an emphasis on problem-solving and in the 1990s by the National Council of Teachers of Mathematics' standards, which stressed the importance of students working together in cooperative groups.

The NCTM standards have another objective--addressing the large gap in math performance between white and minority students, except for Asian Americans. That means that many schools have eliminated ability grouping for math classes. Lessons in the Interactive Math program, for example, do not follow the traditional sequence of starting with easy operations and building to more difficult ones. All students gain exposure to a wider range of mathematical concepts, even those who in the past might have taken only low-level business math. Many question, however, whether mere exposure is enough to facilitate learning.

Growing Backlash
For all of the back and forth, math achievement in the United States remains mixed. SAT scores this year hit an all-time high, even as more minority students are taking them. Even so, the gap between white and minority scores remains wide.

According to the National Assessment of Educational Progress, 17-year-olds today are not performing differently than 20 years ago, before the advent of reform mathematics. Only six of 10 high school seniors can compute with decimals, fractions and percentages. Fewer than one in 10 can use beginning algebra. And in California, 54 percent of the freshmen entering the state university system must take remedial courses.

"Things the average students would know backward and forward 12 years ago, these students don't know at all," says Jerry Rosen, a professor of math at California State University at Northridge. Today, he says, students use calculators even to manipulate single-digit numbers.

The backlash seems to be gaining momentum, with negative articles appearing in Time, Investor’s Business Daily, The New York Times, The Wall Street Journal and the New York Review of Books.

No one believes that the problems the curricular acrobatics were meant to address--the fact that most American adults are illiterate mathematically and proud of it--have gone away. And these days, employers expect employees to be able to use geometry, probability, statistics and even the dreaded algebra on the job.

NCTM's Reassessment
Had Americans needed any further proof of the inadequacy of math education, they received it in the results of the Third International Math and Science Study that have been released over the past two years. Although U.S. 4th graders did relatively well in math, 8th graders slipped to below average and 12th graders plunged to near the bottom.

Those results are now influencing the math debate. The discussion is moving beyond curricula to questions of textbooks, teacher training, expectations and focusing instruction on fewer topics. The clearest lesson from TIMSS was that the curriculum in the United States was a "a mile wide and an inch deep," meaning that teachers skate superficially over too many mathematical topics. Other countries tend to focus their efforts better, imparting to students a deeper understanding.

That was one of the concerns raised by the NCTM when it lashed out against California's state board of education soon after it adopted academic standards that, though highly demanding, focused on skills rather than thinking and understanding. The board defended itself, saying the new standards are easy to assess using objective tests. Then-NCTM president Gail Burrill, a researcher at University of Wisconsin-Madison, wrote to the state board, saying, "Today's children cannot be prepared for tomorrow's increasingly technological world with yesterday's content."

But the NCTM now is rethinking its standards. For several years, the NCTM has worked with major professional mathematics groups, asking them to address shortcomings of the present document. A discussion draft of the standards was distributed in October, which will lead to a new document in 2000.

NCTM's current president, Glenda Lappan, a professor of education at Michigan State University, helped write the current version of the standards but says they were often misunderstood. Some have interpreted them to mean, for example, that correct answers don't matter. But Lappan says that is a "gross misinterpretation" of their intent. The point, she says, is to get teachers to listen to children as they explain their thinking in solving a math problem. That way, the teachers can check on how well the students understand what they're doing.

In an interview published last year by the Council for Basic Education, Lappan says the "next version of the standards will be more explicit about the need for students to develop deep understanding of algorithms and proficiency and comfort in using them."

Even as the NCTM has worked to rewrite the standards, it has begun a series of publications that address key issues in mathematics education. To foster discussion, the organization has brought in mathematicians who have been critical of the standards to serve as guest editors for those documents.

Lappan says a sense of cooperation between the two sides is growing, although much contentiousness still exists. "I'm beginning to see places where people understand that this isn't about winning," she says. "It's about educating kids."

Avoiding Divisiveness
States and districts across the country have tried to learn from California’s intense struggles over math.

"California scared us to death," says Uri Treisman, a math professor at the University of Texas who managed the creation of Texas' math standards. To avoid such a divisive struggle, Texas tried to isolate those who held extreme positions. The state conducted focus groups with parents and teachers, asking them to discuss what they wanted in a math program.

As it turned out, Treisman says, no disagreements emerged. "Everybody wanted the basics and everybody wanted more," he says. "Everybody wanted their kids to know the facts accepted by history and everybody wanted them to be able to use them."

Rather than identify which programs or textbooks were acceptable, the state found high-performing schools to use as models. Some of those schools used materials from Saxon Publishers, which place emphasis on practice and review to develop mastery. But some successful schools used methods aligned with the NCTM standards.

"In certain communities parents want a very structured curriculum and there is a deep sense of order," Treisman says. So the schools are fighting a losing battle if they try to adopt a curriculum that is entirely at odds with that, he says. "The last thing you want to do is get caught up in ideological fights that have nothing to do with the people you are serving."

Texas is but one of a number of states where math reform is gaining momentum. Ohio, Arkansas, South Carolina, New Jersey and others have managed to avoid controversy. Several years ago, the public schools in Scarsdale, N.Y., were set to choose a new math series for its elementary schools. Ann Schaeffer, a consulting teacher in the district, first formed a committee of teachers and administrators to come up with a list of criteria for the new books. The original list of 120 items was pared down significantly and then shared with parents. They added two elements the educators had neglected--homework and computation. The series the district was replacing had not focused on computation, and the parents objected.

"Nothing gets by parents here," Schaeffer says.

The books the district wound up selecting, Math Trailblazers, have a "terrifically strong computational strand that children keep visiting and revisiting throughout the year," she says.

Montana received a National Science Foundation grant to develop new lesson plans in line with the NCTM standards. The NSF money, along with matching state funds, was enough to hire about 200 math teachers to work on the project. They created new, real-world lessons such as one requiring students to learn linear programming to make business decisions.

The new approach met resistance, however. In Great Falls, the school board had to eliminate it and purchase a traditional textbook series. Larry Kaber, chair of the math department at Flathead High School in Kalispell, Mont., says many of the state's math teachers have altered their teaching methods as a result of the NSF grant. But most of the lessons are not in regular use because of parent resistance.

Kaber, one of the leaders of that effort, believes in retrospect that the project faltered because teachers were too insular. If he had it to do over again, he says, he would "make sure to spend a lot more time with parent groups." He also says he would find people likely to be the biggest critics of math reform and get them involved.

He says he does not think the math teachers' efforts will go to waste. But adding the new lessons into the curriculum will take time. As with many of the reform-type programs, Kaber says, "the algebra structure was not as strong as it should have been."

Lingering Impact
In Escondido, Calif., the scars from the math conflict remain. Parents now have a majority vote on the district's curriculum committee. Some teachers, who had originally recommended adoption of the Interactive Math program, remain bitter.

"They feel that their traditional input and knowledge and expertise has been disregarded," says Jenkins, the interim superintendent.

Assistant Superintendent Jayme B. Arner, the Escondido administrator who was in charge of curriculum during the math battle there, says the lesson is that times have changed. No longer, she says, are educators the unchallenged experts. When schools want to make major changes in instruction, they need to first listen carefully to the community with an open mind.

Second, she says, administrators need to do their homework. They need to research the math battles in other communities, including Escondido. That, she adds, "seems professionally pro-active and wise."

Finally, administrators need to read the research on various math issues. That way, she says, "you can as an educator provide and reference information rather than referencing your own feelings."

Richard Lee Colvin is an education writer for The Los Angeles Times. E-mail: Richard.Colvin@latimes.com