As recently as 1994, the federal law known as Goals 2000 defined the expectation that Americans would be “No. 1 in mathematics and science by the year 2000.” But the recent Third International Mathematics and Science Study, conducted under the most carefully planned and executed assessment of international achievement, painted a very different picture for the 13-year-olds tested. Forty-one countries participated in the study. American students did better than average on probability and statistics; average in fractions, number sense, and algebra; and below average in geometry, proportions, and measurement. Only 5 percent scored in the top 10 percent in mathematics; 40 percent of the Singapore students were in the top 10 percent. (“U.S. Students About Average in Global Study,” Nov. 27, 1996.)
The results would seem to disprove the contentions of some educators that the educational crisis is “manufactured.” The international math and science study’s administrators were most careful to compare students of comparable ability. The tests employed both multiple-choice items and open-ended, free-response essays. Moreover, the content of mathematics enjoys greater consensus across national boundaries than other comparable disciplines. There is consequently little reason to dispute the tests’ findings.
The results are particularly ironic in view of the fact that at no time in the nation’s history has there been more consistent concern about the level of academic achievement in mathematics. A Nation at Risk pointed the way by the clarity and sobriety of its message as far back as 1983. The critically acclaimed national standards in mathematics, sponsored by the National Council of Teachers of Mathematics in 1989, had a plethora of constructive suggestions: Mathematics should encompass both computation and analysis; where possible, more integrated instruction should be adopted, such as the spiral approach (which teaches algebra, arithmetic, and geometry simultaneously rather than sequentially) frequently used in Europe; skills such as problem-solving, estimating, higher-order thinking were all delineated as essential to enable Americans to compete in an era informed by world-class standards.
Are there approaches to mathematics instruction which do point the way to implementing the NCTM standards? Two come to mind--one relatively well-known, the other less so. The College Board’s Equity 2000 program has certainly enjoyed much favorable press and ample financial support. By focusing on a finite number of urban centers, Equity 2000 has yielded tangible successes in securing for inner-city students access to algebra in the 8th grade, securing significant support from the community, and implementing systematic professional development for teachers. From that starting point, and following the traditional sequence, they are then able to take calculus in the 12th grade, thus obviating the need to take calculus during the freshman year in college. More important, it has provided a gateway to college education for those who, without Equity 2000, would never have made it.
The other approach, exemplified by Project SEED--founded three decades ago, and currently conducting instruction and staff development in many school districts, including those of Dallas, Detroit, the greater Philadelphia area, Indianapolis, and the San Francisco Bay area--is even more radical. While sharing with Equity 2000 a conviction about the importance of increasing expectations for urban minority students, Project SEED demonstrates that the various skills identified in the NCTM standards can be developed even further down the grade sequence of the traditional elementary school. By employing Socratic-style teaching techniques and instructors who know and love mathematics, Project SEED teaches high school algebra, pre-calculus, and even college-level topics to elementary school students, actively involving every student in exciting explorations of mathematics. The discovery approach, high expectations for students, and deep investigation of concepts are what the Third International Mathematics and Science Study found to be the common factors of successful math instruction. And Project SEED’s students do indeed exemplify the capacity to think mathematically at an extraordinarily young age. Not only do they outscore students in traditional classes on standardized tests, they also take more advanced math classes years later when they reach high school.
| If achievement levels in mathematics are to be raised, K-16 should be thought of as one seamless fabric, not four unrelated way stations. | 
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This is not to suggest that either program, let alone both, has been implemented easily. On the contrary, many factors contribute to the difficulty of their successful execution. Principals who support the program come and go with the kind of alacrity which makes it difficult, if not impossible, to embed the program in the culture of a school. Communities are rarely understanding of the imperative of raising standards to meet the complexities of the 21st century workplace, requiring brain rather than brawn on the part of the responsible and successful employee. Especially with the all-pervasive practice of the misassignment of teachers, it is extraordinarily difficult to train teachers to have sufficient command of the content of mathematics and the skill to facilitate learning in the context of the multiple intelligences students bring to the classroom. Where such teachers exist, they are frequently transferred to other schools where the climate is not always accommodating of such radical departures from the status quo.
What, then, can be done to enable our students to score above average on internationally administered examinations? The first solution lies outside the confines of the school: Parents can be enormously influential in determining mathematical achievement. As Albert Beaton, the Boston College professor who directed the international study, put it, “Home factors were strongly related to mathematics and science achievement in every TIMSS country.” In a society in which the degree of family coherence is at an all-time low, it is abundantly clear that schools are the maleficiary of many social circumstances reflected in the fabric of our culture. To counter this, it is imperative for school systems to develop family-literacy programs and promote other activities which link schools to social welfare agencies and youth centers.
As has been suggested earlier, both Equity 2000 and Project SEED emphasize higher expectations as essential prerequisites to undermining the status quo. But the norm is very different. To quote San Jose Mercury News columnist Joanne Jacobs, “The average 8th grade curriculum in the United States resembles the 7th grade curriculum in top-scoring countries.” It is abundantly clear that we must ask a great deal more of all our students, especially those in elementary schools. The same holds true of their teachers.
Indeed, improved teaching techniques are essential to improvement in mathematics achievement at every grade level. Far from the rote teaching frequently misattributed to Asian classrooms, just the opposite was found in analyzing the classroom videotapes used in the TIMSS test. American teachers tell students the procedures to solve routine problems; the Japanese mathematics teachers help students understand concepts. Clearly, teachers can no longer just be “talking heads.” Cooperative learning, peer coaching, Socratic seminars, and written essays are all germane to a deeper appreciation of the complexity of both theoretical and applied mathematics. As we know from a publication sponsored in the 1980s by the Council for Basic Education, “A Conspiracy of Good Intentions: America’s Textbook Fiasco,” the quality of American textbooks is often lamented. But as Bruce Alberts, the president of the National Academy of Sciences, put it in the context of the recent international math and science study, “By trying to cover everything, we fail to teach basic concepts in depth, and our children gain no real understanding.” Nothing short of a revolution in textbook-adoption procedures can remedy this all-pervasive malaise.
For all of the rhetoric to the contrary about improvement, it seems that education is an arena that commands less respect and less political attention in America than in many other countries. Acceptable teaching conditions at the precollegiate level, especially in urban schools, are conspicuous by their absence. The best teachers are frequently rewarded by more lucrative administrative positions for which they may be temperamentally unsuited. Our schools have been asked to assume too many of the burdens associated with an increasingly incoherent society.
If achievement levels in mathematics are to be raised, K-16 should be thought of as one seamless fabric, not four unrelated way stations. Tracking should be eliminated as inimical to a sequential curriculum of basic education for all students. Teacher education will have to be revolutionized to allow four years to be spent solely on content for all prospective mathematics teachers. Education schools will have to be replaced by professional-development entities committed to integrating subject-matter content with the latest approaches to methodology infused with the case-study approach and informed by technology, in the context of higher academic standards. Only then can programs such as Equity 2000 and Project SEED become mainstream in their ability to assist the many rather than the relatively few.
The teacher of the future must be inducted under the auspices of a mentor teacher before he or she is formally admitted to the ranks of the teaching profession on the basis of an authentic-assessment-driven examination. In-service as we currently know it has to be abolished. In its place, teachers should be required to engage in regular professional-development activities of the kind aligned with national and local expectations of what students should know and be able to do at the end of a predetermined grade level.
For this country to attain anything like the expectations of Goals 2000, especially those which relate to mathematics, a revolution will have to occur. This can only take place when the general public is convinced of the necessity for so doing. And this will have to occur not just in the structure and processes of traditional education. The whole system has to be transformed to enable all Americans, rich and poor alike, to enjoy an education system that is more focused, more flexible, and more accountable to the unprecedented demands of the next century.
