It's been a bad autumn for public school leaders in the state of Washington, a battleground in the nation's reemergent math wars. First, a whopping 52 percent of seventh graders and 41 percent of fourth graders failed the statewide math test. That dismal news further energized a new parents' group already lobbying to ditch the state's Reform Math curriculum, which favors estimation and kid-invented solutions to problems and downplays basics like long division and multiplication tables. Worst of all from the point of view of the public education establishment, the original champion of Reform Math--the National Council of Teachers of Mathematics--did an about-face in September and called for a nationwide return to basics.
By the beginning of October, Washington's besieged school administrators were circling the wagons: The state superintendent of public instruction announced she stood by the existing standards. One of their principal architects, math-education expert Virginia Warfield, compared the call for change to book burning. Criticism of the way math is taught in the state is a "smear and sneer campaign," Warfield added in an email newsletter on October 8. And she warned Washingtonians that Stanford mathematician James Milgram, one of the leaders of the return-to-basics movement, is "Rush Limbaugh with a Ph.D."
The fight will move to the legislature in January, when dueling math bills are due to be introduced. But whatever the outcome of that local controversy, its existence is indicative of a renewed struggle over math teaching coast to coast.
There's little dispute about the underlying predicament: U.S. public schools--rich ones, poor ones--have been failing math for decades. It was way back in 1965 that a musical spoof blasted the then-popular New Math, forebear of today's Reform Math, as "so very simple that only a child can do it." Eleven years ago, American eighth graders were revealed to be near the bottom of the international mathematics heap, just above their peers in Iran and Cyprus. And since at least 1990, the proportion of middle-class American high school sophomores proficient at "low level mathematical concepts, such as simplifying an algebraic expression," has languished around 45 percent.
The National Council of Teachers of Mathematics has been leading this downhill march. After the federal government sounded the alarm with the report A Nation at Risk in 1983, which warned of a "rising tide of mediocrity" in the schools, the NCTM developed a plan to put things right. In 1989 it published Curriculum and Evaluation Standards for School Mathematics, a 258-page document that would define the prevailing wisdom for a generation.
Drills and memorization, it said, were the problem with American math teaching. Where once the student was required to master skills as prescribed by the teacher, under the new regime the student "discovers or creates math knowledge." Some math problems "should be open-ended with no right answer," and for "complex calculations" such as "column addition, long division," a "calculator should be used." Standards advocated communicating math in words and pictures while deemphasizing basic algorithms. This would make math more accessible, the argument ran, not just improving students' math performance, but ultimately "creating a just society in which women and various ethnic groups enjoy equal opportunities and equitable treatment."
Standards was quickly criticized by traditionalists such as Caleb Nelson in the American Spectator. But state departments of education and school districts already gripped by the "constructivist" fad ("A conceptual approach enables children to acquire clear and stable concepts by constructing meanings in the context of physical situations and allows mathematical abstractions to emerge from empirical experience."--Standards, p. 17) lapped it up. New texts, supported by over $50 million from the National Science Foundation, swept the country: Investigations in Number, Data and Space by the math program developer TERC and distributed by Pearson Scott Foresman; MathScape, by the Education Development Center and published by Glencoe/McGraw-Hill; and Everyday Mathematics, by the University of Chicago School Mathematics Project and published by Wright Group/McGraw-Hill. By 2005 half the states were no longer requiring children to master the multiplication tables.
The effects of the Reform Math cure were worse than the poor-performance disease. Where in 1990 some 33 percent of college-bound sophomores had been proficient at "multi-step solutions . . . such as drawing an inference based on an algebraic expression," by 2002 the figure had dropped to 28 percent. Sophomores in "general" high school programs had similarly regressed. The reforms didn't even advance the fashionable goal of attracting girls to math: There were fewer women studying college math in 2004 than in 1989 when the Reform Math standards were published. Fewer men, too.
Reform Math, while not the sole cause of American students' poor performance, bears much of the blame. Says University of Rochester mathematician Ralph Raimi, "A student could take essentially no mathematics at all except for the bare bones of arithmetic until the 9th grade and be better off than today's kids who have reform programs."
So this September, when the NCTM reversed course and published Curriculum Focal Points, calling for a return to basics, the move was heartily welcomed in certain quarters. The 41-page document "makes no bones about the fact that algorithms (such as long division and the concept of borrowing in subtraction) should be taught," says Harvard mathematician Wilfried Schmid, a critic of Reform Math and a member of a new math-education panel appointed by President Bush. Curriculum Focal Points argues for the kinds of practices in use in the countries where children score high on international math tests, such as Singapore and Japan.
Other members of the president's National Mathematics Advisory Panel have also praised the NCTM's new approach--opening the possibility that the national experts might be on the same page as the teachers' group when the panel issues its draft report in February.
If only. Alas, the leadership of the NCTM has already begun to backpedal. Focal Points, says NCTM president Francis "Skip" Fennell, "is not a new version of the Standards." It is not a back-to-basics document, Virginia Warfield, a consultant on Focal Points, told a think tank in Washington. NCTM executives wrote letters of protest to newspapers whose coverage portrayed the document as a new departure.
The mixed signals coming from the NCTM may reflect the fact that many of the council's members are teachers with degrees in education, not math; many of them have been committed to Reform Math for decades, and oppose change. Fennell says that among the group's 100,000 members, it's possible "there are some people who would be concerned about us moving in this direction." Maybe he needs to sound ambivalent to appease them.
But this equivocation robs the NCTM's recommendations of much-needed momentum. Already responsible for the ground lost over the last 15 years, the council may now contribute to national paralysis.
To learn what paralysis looks like, consider New York City. In 2002, facing heavy pressure from parents, the city launched a review of its Reform Math programs (such as TERC's Investigations), under which 43 percent of the city's students were performing below grade level. But with NCTM and an army of education experts still solidly behind Reform Math, the back-to-basics parents, armed only with their children's experience and a few studies, were outgunned. The city did step back from the brink, but only just.
New York selected a new program called Everyday Mathematics. This is "the least objectionable among the reform programs," explains Harvard's Schmid. "They do have a discussion of algorithms, but not one that is designed to get children proficient" speedily and without distractions. That's because the program describes several alternative ways to solve a problem, such as ancient Egyptian multiplication, rather than teaching one method. It downplays mastery of long division, and puts calculators in the hands of kindergartners. Everyday Mathematics is used by over two million children across the country--including many in Fairfax County, Virginia, near Washington, D.C., where a parents' movement failed to secure the adoption of the back-to-basics textbook Saxon Math a few years ago.
It's easy to see why grassroots movements founder. Parents don't always want to stick their necks out while their kids are in school, for fear of stigmatizing their children. And the forces aligned against change--administrators, education consultants--are powerful, entrenched, and wealthy.
Yet without real change, children will continue to be caught in the middle, striving all day to master material their parents consider unsuitable, then getting extra help with the basics at home at night. In the state of Washington, the private tutoring business has grown steadily since the implementation of Reform Math in 1993. In Brookline, Massachusetts, which has used Reform Math programs Innovations and MathScape, 26 percent of students aged five to ten get outside tutoring, according to a school-system report.
Teachers can be caught in the middle as well. Elizabeth Carson, executive director of NYC HOLD, the city's main back-to-basics group, says she's heard plenty of accounts of teachers closing the door and teaching the basics--instead of the Reform Math that is part of the official curriculum--out of earshot of their administrators. And the Brookline report shows that most elementary school teachers saddled with Reform Math programs think the programs focus too little on computation and traditional algorithms.
The trouble is, "all this talking is going on while our children right now are losing their educations. We don't have ten years, we don't have two years," says Carson, who places blame for the lost years squarely on the NCTM. She's disappointed with the group's retreat from its back-to-basics document: "Either they understand what's wrong with the course they've led us on, or they don't."
The picture isn't all grim. Parents are reaching for their own solutions, teaching drill-and-basics-heavy Sing apore Math, Saxon Math, and Sadlier-Oxford Progress in Mathematics after hours and trading the books on eBay. Some schools and school systems in Massachusetts, Georgia, and Maryland have returned to the basics, adopting Singapore Math and Saxon Math and achieving positive results on their state tests. Perhaps most important, mighty California pioneered a return to the basics with a revision of its math standards starting in 1997, and has tightened its list of approved textbooks in recent years, a victory for parents' groups there.
To be sure, the California standards contain opt-out provisions; yet the state is moving forward. So are Indiana and, to a lesser degree, Massachusetts. If Washington now joins these three, and Utah, North Carolina, and Florida--all soon to revise their standards--follow, the back-to-basics approach could be sufficiently prevalent to influence the publishers of math textbooks. States typically revise their standards once a decade. Market-driven, the publishers are guided by the standards of the most populous states.
Which is why national momentum is so important. If the NCTM promotes its changes aggressively--and if the National Mathematics Advisory Panel proposes changes along similar lines, and these influence states through the No Child Left Behind reauthorization in 2007, as well as through National Science Foundation and National Research Council funding of math-education projects--then the math curricula in the public schools may well improve.
Of course, misguided standards are only one piece of the poor-performance puzzle. Another, possibly larger, problem in math education is the fact that most teachers have a weak educational background in math, as Sandra Stotsky, another member of the national math panel, stressed. A new study from the Education Schools Project shows that only 28 percent of applicants to the education program of a typical public university pass the math portion of their application test the first time they take it. Moreover, only 41 percent of principals surveyed nationally say education graduates are "very well" or "moderately well" prepared to implement state curriculum standards. But fixing teacher education--for instance, requiring teachers to have a degree in their substantive field first, and a specialization in education second--takes a generation. It's also expensive.
Meanwhile, the consequences of the public schools' failure to teach math to a high standard are far-reaching. In 2000, 16 percent of university freshmen took remedial classes in mathematics. For community-college freshmen, the figure was 35 percent. Universities are filling the math gap with better-schooled foreigners: Over half the Ph.D.s in math and engineering, and almost half of master's degrees in computer science, awarded by American institutions are being earned by foreigners, and the foreign population in undergraduate math, engineering, and computer science departments is growing as well. In the broader economy, business groups complain that their employees' math skills are weak. High-tech companies in particular decry the shortage of qualified American job-seekers.
A new direction is essential. Francis Fennell of the NCTM says his group has shipped out 300,000 copies of Focal Points since its release early this fall. That's a start. What's needed now is a clear renunciation of Reform Math, along with all the faddish clutter that still distracts students and teachers in the classroom, and a firm endorsement of the basics--memorization of the multiplication tables and mastery of long division, fractions, and algebra. Fortified by an unambiguous message from the NCTM, the National Mathematics Advisory Panel and the 50 states could conceivably reshape the teaching of math--so as to add to the skills and life chances of American schoolchildren instead of subtracting from them.
Melana Zyla Vickers is a columnist for TCSDaily.com.