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Introduction
For the American school curriculum, the twentieth century ended like it began, with an intense debate over what schools should teach and how they should teach it. In 1902 John Dewey, who would eventually become the twentieth century's most famous advocate of school reform, wrote about two "sects" fighting over the curriculum. One group sought to "subdivide each topic into studies; each study into lessons; each lesson into specific facts and formulae. Let the child proceed step by step to master each one of these separate parts, and at last he will have covered the entire ground." The other camp, observed Dewey, believed "the child is the starting point, the center, and the end." Because this view focused so intently on the child, Dewey concluded, "It is he and not the subject-matter which determines both the quality and quantity of learning." A student-centered approach required a particular type of pedagogy, Dewey noted with approval, a teaching style recognizing that "learning is active."
Dewey's observations could have been written in 1999. Nearly a century had passed, but neither side had surrendered. Cease-fires had been fleeting. Decade after decade the conflict that Dewey had observed-and later became an important participant in himself-kept recurring. The terms education progressive and education traditionalist arose as labels for its partisans, who usually kept their squabbles within the walls of the nation's schools of education. Occasionally, however, the disagreement burst into the headlines, captured the nation's attention, and reminded everyone of the bitterness and rancor in which the politics of education is steeped.
At the end of the century, the debate focused on reading and math. This book is about the public conflict that swirled around these two subjects in the 1990s. The "education sects" that Dewey described so long ago still existed-in reading, in the proponents of "whole language" and "phonics," and in math, in the advocates and opponents of "NCTM math reform," referring to the reform agenda of the National Council of Teachers of Mathematics. The book includes contributions from influential scholars on both sides of the disputes, as well as chapters by distinguished nonpartisans. It examines what fueled the controversies, clarifies adversarial positions, analyzes the politics of the disputes, and investigates how curricular conflicts may have affected policy and practice.
In October 1999 the Program on Education Policy and Governance (PEPG) at Harvard University invited leading scholars to a two-day conference on the math and reading controversies. The meeting was held at the Charles Hotel in Cambridge, Massachusetts, and was jointly sponsored by the John M. Olin Foundation and the Kennedy School of Government's A. Alfred Taubman Center for State and Local Government. A crowd of nearly 100 participants and observers attended.
The papers presented at the conference make up the chapters of this book. They are organized by subject-first math, then reading-and prefaced with an essay by E. D. Hirsch Jr. At the conference, a welcoming dinner was held, with Hirsch as guest speaker. Although Hirsch clearly takes sides in these debates, his remarks offer a philosophical starting place for appreciating all the views expressed in the book. Whether you agree or disagree with Hirsch-or any of the other authors presented here-I think you will see that they agree on one point. The school curriculum is important. What we decide to be the proper content of schooling has significant consequences, not only for today's students and schools, but for tomorrow's society as well.
In the opening chapter, Hirsch argues that the reading and math wars are rooted in an age-old conflict between romantic (progressive) and classical (traditional) orientations toward education. The classical orientation believes in explicit, agreed-upon academic goals for children; a strong focus on discipline and order in the classroom; the primacy of teacher-led instruction; and regular testing to assess student performance. Traditionalists are skeptical that children naturally discover knowledge or will come to know much at all if left to their own devices. Traditionalists are confident that evidence, analysis, and rational thought are greater assets in the quest for knowledge and virtue than human intuition and emotions.
The romantic tradition reveres nature and natural learning. Instead of establishing explicit academic goals for children, educational progressives value a multitude of learning outcomes. They are more likely to insist on particular instructional approaches for teachers and particular characteristics of the learning environment than on the exact learning to occur, largely because of faith that, in the right setting, the proper learning for each child will unfold. These beliefs are religious, that is, they are based on faith rather than empirical tests of what is true. As Hirsch puts it, "We know in advance, in our bones, that what is natural must be better than what is artificial" and "our natural impulses work providentially for good in ways beyond our comprehending." Standards, rules, hierarchies of skill, rote practice and memorization, and the curriculum are all artificial constructions of culture and society.
Gail Burrill begins the book's math chapters with a call for overhauling an outmoded curriculum. The curriculum reflects its historical time. Burrill argues that progressive reform is essential in mathematics because of the rapid changes in today's society and the future demands that students will face from technological innovations. She points out that the math curriculum is largely an invention of the early twentieth century, when most students completed only eighth grade and advanced courses such as algebra, geometry, and calculus were reserved for the few students who went to college. The NCTM's landmark 1989 document, Curriculum and Evaluation Standards for School Mathematics , offers an agenda for reform that Burrill enthusiastically supports. Three critical aspects of math instruction are altered: a shift in content from learning skills and procedures to using math for problem solving, a shift in teaching from disseminating information to stimulating student thinking and inquiry, and a shift in assessment from serving as end-of-the-unit tests to assisting teachers in diagnosing and addressing students' strengths and weaknesses.
Much of the NCTM blueprint is grounded on a progressive theory of teaching and learning known as constructivism. Michael T. Battista argues that scientific research supports constructivist approaches over traditional ways of teaching math. A narrow focus on computation may produce students who are able to come up with the right answers but are unable to explain why the answers are correct or to discern the appropriate calculations to arrive at them. Stressing memorization and imitation over understanding, thinking, and reasoning renders students' knowledge of mathematics impersonal and shallow. Battista quotes students defending incorrect answers. They possess a blind confidence in the results of procedure, even if the procedures are incorrect and the answers inconsistent with intuition, logic, or concrete reality.
Battista draws a distinction between a simplistic view of constructivism as "discovery" learning, teaching with manipulatives or other nonrigorous forms of teaching that allow students to do whatever they want, and the sophisticated theory and empirical evidence supporting what he calls "scientific constructivism." Math learning occurs as students cycle through phases of action, reflection, and abstraction that allow them to build ever more sophisticated mental models of mathematics. These models are tied to real-world quantities and rooted in interactions with, and the need to explain, one's environment. Battista cites several studies, including one of his own, in which students in constructivist-oriented classrooms improved on achievement tests measuring conceptual understanding or problem-solving skills without a loss in computational ability. Failed math reform programs, Battista concludes, are due to flawed mechanisms for converting theory into practice-teacher training, textbook creation, and teaching-not flaws in the theory of constructivism or the body of research supporting it.
David C. Geary argues that constructivism is theoretically suspect in light of the evolutionary history of the brain. Are human beings hardwired to learn math? Children almost certainly have an inherent sense of numbers, counting, and simple addition and subtraction, competencies that are found in preindustrial cultures and even in limited form among chimpanzees and other primates. Like language, these competencies seem to develop from an innate capacity that is elaborated through a child's natural activities, especially social play. This evolved capacity lays the foundation for children grasping simple arithmetic.
But innate mechanisms are not sufficient to lead children to most of the mathematics taught through formal schooling. Learning how the base-10 system operates, for example, is more difficult than learning rudimentary number-counting skills, just as learning how to read and write is more difficult than learning the language of one's parents. Children are not inherently motivated to study math, Geary argues, which makes the value that the larger society and culture place on academic pursuits, along with a teacher's ability to organize and guide instruction, all the more crucial. Instructional practices that are predicated on children's natural instincts, such as constructivism, are doomed to fail a large proportion of children, Geary concludes.
Do we know anything about how these theories play out in classrooms? Roger Shouse examines data from the National Education Longitudinal Study (NELS:88) and explores whether practices similar to math reformers' recommendations succeed in raising student achievement. He reports several surprising findings. The first is that, in 1990, 62 percent of tenth graders said that their math teachers asked them to "really understand the material, rather than just give an answer" and 77 percent said they were "really challenged" in the subject. Both figures are higher than those from any other academic subject, contradicting the notion that in 1990, about the time of the release of the NCTM standards, rote learning and "drill and kill" methods dominated math instruction.
Does math reform work? In eighth grade the effect of practices usually endorsed by math reformers is a mixed bag. Many practices have a different effect on achievement in schools serving advantaged and disadvantaged populations. Reformers frequently recommend grouping students heterogeneously by ability, for example. But students in detracked, mixedability classes evidence lower math achievement, and the negative effect is especially pronounced for students in disadvantaged schools. The effect of calculator use is significantly negative in disadvantaged schools but slightly positive elsewhere. An emphasis on algebra and problem solving boosts achievement in all types of schools.
Shouse also looks at the tenth grade, where some traditional practices are shown to be effective. Achievement gains are associated with learning facts, rules, and problem-solving skills but not from the use of hands-on activities. Textbooks and daily review are helpful, but student discussions are not. Achievement falls when teachers stress "the importance of math in everyday life." Other findings favor reform. Calculators seem to raise achievement, even though computers do not. Negative effects were detected for an emphasis on "speedy computations," a finding any reformer would applaud, and an emphasis on "students' questions about math" and "math concepts" produced positive results.
Adam Gamoran argues that the conflict over the math curriculum poses a false dichotomy between rigorous content and in-depth understanding. Taking the position that they are both desirable, he reviews several studies to show that they are both present in successful math classes. He first details studies by James Stigler of UCLA comparing Japanese and American teachers' instructional styles. The studies suggest that Japanese students' superior math achievement may be due to instructional practice. Japanese math teachers typically present a problem, discuss alternative solutions generated by students, present a general formula, and then provide time for students to apply the formula while working on problems on their own. American teachers, on the other hand, typically demonstrate how a formula works, then assign practice problems for students to complete. Gamoran argues that the Japanese approach demands content mastery from students while encouraging deeper exploration of the material and allowing students the time to think.
Gamoran describes an American program, Modeling in Mathematics and Science Collaborative, which exhibits many of the Japanese education traits and shows promising results on achievement tests. He reviews the favorable findings of a study by Fred Newmann and colleagues of authentic pedagogy-instructional techniques that combine constructivist principles with the mastery of disciplinary content. He also describes a study of transition courses, where math classes featuring a hands-on, problem-solving curriculum are offered as an alternative to general math classes for students not yet ready for advanced mathematics. These studies suggest that progressive instructional strategies can be effective if directed toward the learning of serious content.
Richard Askey declares his stand in his chapter title: good intentions are not enough. Askey agrees that NCTM reformers are seeking to improve mathematics in schools, but he identifies several flaws in their approach. The NCTM standards do not address the problem that Askey considers the most critical in math reform: the lack of classroom teachers' firm content knowledge. The NCTM also did not examine the math curriculum of other countries or include mathematicians in the writing of the standards.
Askey points out that teaching mathematics well using indirect strategies, methods favored by the NCTM, means that teachers must possess a deeper understanding of the subject than has been expected in the past.
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Excerpted from The Great Curriculum Debate Copyright © 2001 by Brookings Institution Press Excerpted by permission. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
