“They lied to me,” says Madalyn McDaniel of Atascadero, California. “They completely betrayed me.” At a parents’ night at the local high school, McDaniel was told about a great opportunity for her son: the Interactive Mathematics Program, in which he would learn everything taught in traditional math courses — only in a more effective way. But after signing him up, McDaniel realized the program was not at all what was advertised. Instead of learning rules and formulas, her son and his classmates were presented with problems and expected to invent their own ways of solving them. “He was very frustrated,” McDaniel says. “I’d say, ‘Look in the book, it will explain.’ He’d say, ‘Mom, there is no book.'”
McDaniel had encountered “whole math.” Also known as fuzzy math or new-new math, whole math is an instructional scheme based on the idea that knowledge is only meaningful when we construct it for ourselves.
Trying to understand what was going on, McDaniel spent three weeks in a class using the Interactive Mathematics Program. As a member of a cooperative learning group along with three 15-year-olds, she joined in activities like cutting out pieces of graph paper, some two units by two, others three by three, all the way up to 15 by 15. The group then played a game that involved forming triangles with the edges of their graph-paper squares (known as ” manipulatives” in the whole-math trade). The object of the game was to see when two sides of the triangle would “win” (that is, the number of units in the squares forming the two sides would be greater than the number of units in the squares forming the third side), when one side would win, and when there would be a tie. Since it turned out that ties always involved right triangles, the class, after two days, had developed a right-triangle rule: a<2> + b<2>= c<2>. Having thus “discovered” the Pythagorean theorem, students were given a single homework problem — which, McDaniel reports, only two students managed to get right.
“This could have been a great exercise,” McDaniel observes, “if it had reinforced a concept students had understood and practiced.” But among whole- math advocates, she notes, there’s a belief that “if you work with these manipulatives, you’ll arrive at knowledge that you so truly understand that you don’t have to practice.” This view fits rather neatly, she says, with student inclinations, and with the realities of the whole-math classroom. Reinventing all of mathematics doesn’t leave much time for practice, particularly since whole-math enthusiasts feel driven to link classroom math to real-world concerns and thus have students spend a good deal of time writing about subjects such as traffic congestion and oil spills. One Interactive Mathematics Program unit titled “Leave Room for Me” begins by assigning a two- to five-page essay on the world population explosion. The student might choose “pros and cons to birth control,” for example.
Seeing danger ahead, McDaniel got her son out of the Interactive Mathematics Program and into traditional math courses. Others were not so farsighted. Debby Arnold, also of Atascadero, believed the teachers who told her that, although the program might seem strange, she shouldn’t be alarmed. It was the college-track program, after all, and it was going to work. But when, after three years of getting As and Bs in math, her son Joey went off to college, he, like many of his classmates in the program, was diagnosed as significantly below grade level and put in a remedial program. Arnold subsequently took her daughter, an eleventh-grader also enrolled in the program, to a private tutoring center, where she was diagnosed as having second-grade math skills. “She couldn’t accurately and with reasonable speed add single digits,” Arnold says. After a year of expensive private tutoring, Michelle Arnold is now at the ninth-grade level, and her mother hopes that by the time she graduates, she’ll have caught up. “We’re upset,” she says. ” We’re mad. Where is the common sense?”
The lack of candor that these parents encountered is not unique to whole- math instruction. Many parents have been told that whole language, a teaching approach that discounts phonics, is not being used in their schools, only to discover later that it is. But the whole-math people are taking a giant step beyond offering false reassurances at parents’ night. With help from the Clinton administration, they are working to pull the wool over the entire country’s eyes about the most ambitious mathematical assessment the nation has ever undertaken: the national test in mathematics to be administered annually to eighth-graders starting in 1999.
The whole-math disaster began in 1989 when the National Council of Teachers of Mathematics issued a set of standards declaring a new approach to be in order. No more “drill and kill,” as whole-math people like to call traditional teaching. Instead, from kindergarten on, there would be a calculator in every hand so that young minds would be free of irksome chores like addition and multiplication and thus able to take on higher-order tasks – – such as inventing their own personal methods of long division. No more teacher as “sage on the stage,” instructing a class of students; a teacher would serve instead as a “guide on the side,” offering non-judgmental questions and comments to groups of students working out their own mathematical meanings.
The national council’s standards have influenced teaching in many states, but nowhere more than in California, and as various whole-math curricula have entered the schools — “Mathland” in Davis and Petaluma, “Quest 2000” in Brea, “College Preparatory Math” in El Segundo — parents have rallied in opposition. The most sophisticated protest was mounted out of San Diego, where a small group of parents established a Web site titled Mathematically Correct (http://ourworld.compuserve.com/homepages/mathman/). Advocates of math reform themselves — they strongly favor teaching algebra in eighth grade, for example — the group’s members came together out of concern that whole math would deprive the next generation of crucial skills. “We were worried,” says Mike McKeown, a molecular biologist and one of the founders, ” that our kids wouldn’t be able to do the jobs we do.”
Mathematically Correct is a virtual history of the advance of whole math in California and beyond. A report from Stockton tells of school administrators throwing out traditional textbooks so that teachers would be forced to use the Mathland curriculum. Parents in Illinois describe how they have been advised to let their son work with a school counselor because he “values correct and complete answers too much.” There are also success stories: the school board in Sonoma Valley that has banned calculators in grades K-3; the school board in Hemet that is requiring individual grades rather than the group grades characteristic of many whole-math classrooms; parents in Cottage Grove, Oregon, who have gotten traditional math courses reinstated.
As Mathematically Correct demonstrates, the way math is taught has become a matter of profound controversy. But this is apparently too awkward a fact for an administration bent on national testing to be honest with the public about At a February meeting held in Washington, D.C., Reuben Carriedo of the San Diego schools had a question for Mike Cohen, the White House point man on education. What was all this talk about widely accepted math standards? Specifically, what was this about a consensus surrounding the views of the National Council of Teachers of Mathematics? “There are many battles being fought right now,” Carriedo observed.
Cohen responded: “We’ve got a situation in math . . . where you can assert that there is pretty wide agreement on the kinds of stuff that kids ought to learn . . . and then act as though it’s true and then use an assessment . . . that will help make it more true in the future than it is now.” Pretend that everyone agrees with the whole-math approach, in other words, and then build a test that makes sure they do.
The February meeting at which Cohen spoke was one of a half-dozen gatherings to plan the national test that the Department of Education held between January and June. Apparently concerned about being accused of favoritism in awarding contracts to develop the tests, the department has posted transcripts of these meetings on the Internet (www.ed. gov/nationaltests), where they testify to another kind of bias: favoring the controversial approach to math instruction that the math teachers’ council represents.
Consider the fate of the Third International Math and Science Survey. When the president first announced his plan for national tests in his January 1997 State of the Union address, the math assessment was to be based on the international survey, which had been much in the news since it had shown U.S. eighth-graders performing below average in mathematics in comparison with other nations. The president called the survey “a test that reflects the world-class standards our children must meet for the new era.” Pascal Forgione, commissioner of education statistics in the Department of Education, said it was “a benchmark for what world-class performance is in math and science.”
But the survey is a test that pays attention to whether students know how to multiply fractions and do long division As a result, Thomas Romberg, a University of Wisconsin education professor who led the development of the math-teachers’-council’s standards, let Department of Education representatives know that he did not think much of the international assessment. To build a national test on the international survey, Romberg said at a February 19 meeting this year, is to base it “on a test that most of us four or five years ago said, Hey, this really isn’t what’s important.” Later, he declared, “I don’t want to get boxed into a framework that I am less than happy with.”
At the conclusion of the February meeting, Mike Smith, acting deputy secretary of education, made sure that representatives of the math teachers’ council understood how important their views were to the administration. “We want to make you as close partners as you’ll take us,” he said. Within a week, Smith was explaining to potential developers of the national test that the math section would not be based on the international survey after all, but on the National Assessment of Educational Progress (NAEP), which is, he said, “a little more appropriate for the United States.”
The administration subsequently named a committee to oversee the math assessment. Its chair, John Dossey, is a past president of the National Council of Teachers of Mathematics; its vice-chair, Gail Burrill, is the current president of the council; and its membership is thoroughly supportive of the council’s views. In their discussions, committee members have made clear that although the NAEP is better than the international survey, they still regard it as a hindrance. It “measures what’s the status quo in the classroom,” says Dossey, instead of measuring “where our students should be.” It carries “long sets of items that are . . . curriculum dependent” — i.e., that judge what a student has learned in the classroom — “rather than [evaluating] students’ mathematical thinking.”
Thus while Mike Smith of the Department of Education assures the public that the math test “will be based on the National Assessment of Educational Progress,” math-committee members are working to see how, within that framework, they can manipulate the exam to reflect their views. They’ve discussed at length, for example, targeting certain topics and subtopics so that test developers will have to give them high priority. Since one consequence of this will be to give low priority to basics like whole-number computation (described by a committee member as “the stuff that the man in the street expects that most of us think is just a waste of time”), members have even put forth a proposal to counter charges that they are opposed to basic skills: a preamble to the exam stating that basic skills aren’t tested for because those skills are assumed.
While test supporters are selling national assessments as a way to let parents and teachers know how students are doing, math-committee members are intent on creating a test that will encourage teachers to adopt the ways of the National Council of Teachers of Mathematics. The council’s president, Gail Burrill, who is a math teacher, concluded early in deliberations that making the exam a more powerful lever for change was in large part a matter of molding perceptions. At the February 19, 1997, meeting, she said to Gary Phillips, who heads the national testing project in the Department of Education:
It would be very easy to help me move beyond [the NAEP framework] because I know that my superintendent will not go to look for this document. What he will read is the document that you send that comes with the test. So if we put forth some of the expectations that are not conflicting but maybe above or different in a sense than what’s in here, that would be fine because that would be sending the message that I want to send to the teachers and to the administration. But it wouldn’t necessarily reflect the exact test they were going to get.
Burrill’s suggestion has been translated by the Department of Education into a requirement that the developer of the math test send to teachers in advance of the exam a booklet of the extended open-ended problems that the teachers’ council favors. Teachers will thereby be duped into teaching more in the whole-math mode.
Administration representatives at math-committee meetings encourage committee members to think of the test as something that will continue to evolve in their favor. In a May meeting, Gary Phillips told the math committee that the math test is “consistent with what the [National Council of Teachers of Mathematics] wants us to do. . . . If we can’t get there 100 percent in 1999, we need — you need to feel and to be committed and to state that we are moving in that direction.”
Phillips’s words are no doubt of special solace in the matter of calculators. The public tends to think that classroom calculators hinder the development of mental math skills. In a recent survey, 86 percent opposed their early use. And so the math committee has concluded it must proceed incrementally: a section on the first exam where calculators will be useful but not necessary; then the next year a section where they are essential; and finally the nirvana where any student can use any machine on any part of the exam. Observes John Dossey, the most enthusiastic calculator advocate on the committee: “We know at this level, in a balanced program, that calculators cause no harm to what are traditional basic skills.”
He should tell that to Debby Arnold, who is convinced that her eleventh- grader couldn’t add because she’d never had to without a calculator. Or to Marianne Jennings, an Arizona mother and businessschool professor, who reports her eighth-grader using a calculator to figure 10 percent of 470. Even during the math panel’s deliberations, one committee member told about ” students coming into university courses who, when confronted with numerical problems, frequently have recourse to the calculator where it’s literally right on the surface.”
Whole-math advocates have a penchant for making it sound as though their ideas are based on a solid body of research, but as Frank B. Allen, a former president of the math-teachers’ council, points out, “Most of the major recommendations in the [council’s] standards have nothing to support them other than the consensus of the authors and the conventional wisdom harbored by some of our more vocal mathematics educators.” Allen is appalled at what his old organization has done. “How dare these writers,” he asks about the authors of the council’s standards, “propose sweeping changes including a complete restructuring of the school mathematics curriculum on such flimsy evidence?”
The reason that whole-math advocates declaim with such confidence seems to be that they work in an environment where no one questions their assumptions. Skeptics of whole math are as rare in colleges of education as opponents of postmodernism in English departments. Indeed, as in English departments, those most loyal to the prevailing mode of thought are most rewarded. John Dossey was chosen to be the author of one textbook and is credited as ” conceptualizer” for another in Addison-Wesley’s whole-math series. This second book, Focus on Algebra, has been dubbed “Rainforest Math” by Marianne Jennings, who observes that environmentalism and Third-World concerns seem to loom larger in it than equations. Thomas Romberg, the education professor who is so disapproving of the international math and science survey, is the author of Math in Context, a whole-math program recently published by the Encyclopedia Britannica Education Corporation. Romberg received $ 1,702,780 from the National Science Foundation to develop the Math in Context curriculum. The developers of the Interactive Mathematics Program, which Madalyn McDaniel and Debby Arnold encountered, have received $ 9,059,941 in federal funds and more on top of that from the state of California.
One can understand why the whole-math people behave as they do, but what about the Clinton administratlon? Perhaps it is inevitable when a president has reaped significant political benefit from aligning himself with organized education for his administration to line up with a group like the National Council of Teachers of Mathematics. But Bill Clinton will not be running again, which ought to allow him and his appointees to put a certain distance between themselves and the teachers’ council. Moreover, the politics of the whole-math controversy follow no party line. Although the education establishment is given to calling those who oppose its ideas stooges of the far Right, there are, in fact, liberals as well as conservatives leading the charge against whole math. The most dramatic example is the group that organized the Mathematically Correct Web site. Most of its members are liberal Democrats.
But the administration seems to have decided that it needs the enthusiastic support of the National Council of Teachers of Mathematics. Mike Smith talks repeatedly about the great campaigns that will be waged to encourage participation in national testing. The president will talk up the tests for two years, the Department of Education will launch initiatives. The Urban League will help stir up excitement — and so will education groups like the teachers’ council. “This is going to be a test,” Smith declared early in the year, “unlike any other test that there has ever been.”
The plan may succeed. Once the test is ready and students can take it for free, it may be difficult for governors to explain why they aren’t signing up their states’ eighth-graders. And Congress, which should be the first line of defense, seems to have little energy for taking the president on about anything, even something as important as whether taxpayer dollars are going to be spent, probably to the tune of $ 100 million, to produce and deliver an examination that will, in the opinion of many, accelerate the decline of American education.
Meanwhile, out in California, Madalyn McDaniel and Debby Arnold continue the battle against whole math. Even though the math curriculum of Atascadero High School is no longer a matter of concern to their kids, they know it’s important to others. They’re still going to parents’ nights, and, armed with experience and information, they try to make sure that the truth is told.
Too bad they’re not in Washington, D.C.
Lynne V. Chaney is a senior fellow at the American Enterprise Institute.
