Refocusing U.S. Math and Science Education
International comparisons of schooling hold important lessons for improving student achievement.
The Third International Mathematics and Science Study (TIMSS) is the most ambitious cross-national educational research study ever conducted, comparing over half a million students' scores in mathematics and science across 5 continents and 41 countries. TIMSS is far more than the "academic Olympics" that so many international comparative assessments have been in the past. It included a multiyear research and development project that built on previous experience to develop measures of the processes of education. Classroom observations, teacher interviews, and many qualitative and quantitative information-gathering strategies played a part in this development effort. The result was a set of innovative surveys and analyses that attempted to account for the varying roles of different components of educational systems and to measure how children are given opportunities to learn mathematics and science.
The situation regarding what children learn in the United States is disheartening. We are not at all positioned to reach the high expectations set for our nation by the president and our state governors. We are not likely to be "first in the world" by the end of this century in either science or mathematics.
In the fourth grade, our schoolchildren performed quite well on the paper-and-pencil test in science; they were outperformed by only one country and were above the international average in mathematics. Yet the eighth-grade U.S. students fell substantially behind their international peers. These students performed below the international average in mathematics and just above the average in the written science achievement tests.
The better performance of U.S. fourth-graders than eighth-graders is not cause for celebration. It suggests that our children do not start out behind those of other nations in mathematics and science achievement, but somewhere in the middle grades they fall behind. These results point out that U.S. education in the middle grades is particularly troubled-the promise of our fourth-grade children (particularly in science) is dashed against the undemanding curriculum of the nation's middle schools.
TIMSS points to aspects of our school systems that bear close reexamination. In the past, many critics have attempted to place the blame for U.S. schoolchildren's poor performance on cross-national achievement tests on a variety of factors external to schooling. However, early analyses of TIMSS data suggest that schooling itself is largely responsible.
What you teach is what you get
How has this come to pass? What features of the processes of schooling appear to be related to the overall mediocre performance of U.S. schoolchildren, and how are these processes related to the deterioration of achievement levels in the years between grades 4 and 8?
Findings from this study are still being released, and TIMSS researchers the world over continue to work on reporting and analysis. Thus, much of what has currently been published merely scratches the surface of the vast interrelated information sources available in TIMSS. Yet preliminary results have been remarkably consistent in the message they send about the role of U.S. curriculum and instruction in fostering mediocre achievement.
"Curriculum" is a word with many commonly accepted meanings. In this article, we understand curriculum to be made up of at least three interrelated levels. The "intended curriculum" is what our schools, school districts, states, and national organizations have set as goals for instruction in each of our school systems. This aspect of the curriculum is examined in TIMSS through its study of textbooks, curriculum guides and programs of study, and surveys of educational authorities. The "implemented curriculum" is the pursuit of goals in the classroom-the array of activities through which students and teachers engage in the process of learning. In TIMSS, this aspect of the curriculum is studied through videotapes and surveys of teachers' instructional practices, beliefs about education and the subjects they teach, and other features of the opportunities they give students to learn mathematics and science. Finally, the "attained curriculum" is the knowledge, skills, and attitudes that individual students acquire and are able to use. This final aspect of the curriculum is measured in TIMSS through paper-and-pencil and practical achievement tests as well as surveys.
What do all our measures of the curriculum tell us about U.S. schooling as compared to schooling in other countries, especially those whose students significantly outperformed our schoolchildren on the TIMSS achievement tests? The findings point to elements common to most high-achieving countries that are not shared by the United States. These findings make up what appear to be a set of conditions for the realization of higher standards of mathematics and science achievement for larger numbers of schoolchildren. The fact that these conditions are shared by most high-achieving TIMSS countries suggests that they are necessary conditions. The fact that they are sometimes shared by countries that did not outperform the United States warns us that they are not sufficient in themselves to guarantee higher achievement. These findings suggest a number of important lessons that challenge common practice in the United States. However, we cannot merely emulate the practices of other countries. We must reconsider our own practices in the light of this new knowledge and then apply it to generate new alternatives for our own context.
An unfocused curriculum
One striking feature of U.S. textbook and curriculum guides as compared to those of other countries is the magnitude of the differences. Our textbooks are much larger and heavier than those of all other TIMSS countries. Fourth-grade schoolchildren in the United States use mathematics and science textbooks that contain an average of 530 and 397 pages, respectively. Compare this to the international average length of mathematics and science textbooks intended for children of this age of 170 and 125 pages, respectively.
Also striking is how our textbooks differ from most others in the number of topics they cover. Figure 1 shows that U.S. textbooks cover far more topics in grades 4 and 8 than do those of 75 percent of the nations participating in TIMSS. The number of topics is much smaller in Japanese and German textbooks, for example. Japanese schoolchildren significantly outperformed U.S. schoolchildren in TIMSS; German schoolchildren did not.
Does it matter that our textbooks are so comprehensive? Preliminary analyses suggest that it does. This is true because breadth of topics is presented in these textbooks at the expense of depth of coverage. Consequently, our textbooks are limited to perfunctory treatment of subject matter. The amount of instructional time that teachers are likely to devote to the coverage of each element in this broad list of topics and skills is also severely constrained.
This issue of teachers' use of textbooks is, of course, vital. Information collected from the national random sample of teachers in TIMSS indicates that the majority appear to be attempting the Herculean task of covering all the material in the textbook. Rarely can this dubious goal be accomplished, but the result is that U.S. teachers cover more topics per grade than is common in most TIMSS countries. The implications this has for what is done with topics in terms of their exploration, close examination, and hence learning, are clear. A curriculum that emphasizes the coverage of long lists of topics instead of the teaching and learning of a more focused set of basic contents, to be explored in depth and mastered, is a curriculum that is apt to result in the squandering of the resources that teachers and children bring to bear on the teaching and learning of these contents. The unfocused curriculum is not a curriculum of high achievement.
The unfocused curriculum of the United States is also a curriculum of very little coherence. Attempting to cover a large number of topics results in textbooks and teaching that are episodic. U.S. textbooks and teachers present items one after the other from a laundry list of topics prescribed by state and local district guides, in a frenzied attempt to cover them all before the school year runs out. This is done with little or no regard for establishing the relationship between various topics or themes on the list. The loss of these relationships between ideas encourages children to regard these disciplines as no more than disjointed notions that they are unable to conceive of as belonging to a disciplinary whole.
The TIMSS videotape study of grade 8 mathematics lessons in the United States, Japan, and Germany further illustrates the episodic nature of the implemented curriculum in this country. Mathematicians from U.S. universities were asked to examine transcripts of mathematics lessons from Germany, Japan, and the United States (all indications of the country in which the lessons were taking place were removed from the transcripts). These mathematicians rated each lesson according to the overall quality of the mathematical content presented in them. Coherence of the content-that is, the establishment of clear, disciplinarily valid linkages among the topics and skills in the lesson-was an important part of the rating. Figure 2 shows the ratings and the substantial differences between the three countries studied. It is apparent that U.S. instructional practices mirror the incoherent presentation of mathematics that characterizes our intended curriculum.
A static conception of basics
Public discussion about education in our country rages about the importance of what are known as "basics." How we define the fundamental content and skills that children need to acquire to be regarded as educated matters more and more as the United States struggles with the formulation of educational policies that are intended to be in place as we enter the new millennium. Participants from all points of the political spectrum and educators representing a broad range of divergent educational approaches and philosophies are engaged in this debate. Information from TIMSS has clear implications for these discussions.
In the United States, it appears that a common implicit definition of basics in education is content and skills that "are so important that they bear repeating-and repeating and repeating." Arithmetic, for example, is a set of contents and skills that are revisited in U.S. classrooms year after year. Even in grade 8, when most high-achieving TIMSS countries concentrate their curriculum on algebra and geometry, arithmetic is a major part of schooling in this country.
Other nations act as if far more mathematics and science topics are basic. In these countries, basics are so important that when they are introduced the curriculum focuses on them. They are given concentrated attention so that they can be mastered, and children can be prepared to learn a new set of different basics in following grades. Such focused curricula are the motor of a dynamic definition of basics. Among the highest-achieving countries, each new grade sees new basics receiving concentrated attention to prepare students for the mastery of more complicated topics that are yet to come.
TIMSS' studies of curricula, textbooks, and teacher's instructional practices show that the common view of educational basics is different in the United States. At grade 4, the definition of basic content in the United States does not differ substantially from that in high-achieving countries. However, in our country, the same elementary topics that form the core content in grade 4 appear repeatedly in higher grades. What new content does enter the curriculum rarely does so with the in-depth examination and large amount of instructional time that characterize other countries. In fact, on average we introduce only one topic with this type of focused instructional attention between fourth and eighth grade in either mathematics or science. Most TIMSS countries introduce 15 topics with intense curricular focus during this period. The highest-achieving TIMSS countries introduce an average of 20 topics in this way.
In the U.S. curriculum guides and textbooks, about 25 percent of the topics covered in the eighth grade are new since the fourth grade. For most TIMSS countries, about 75 percent of the topics are new. This persistence of old topics and lack of instructional focus on topics that are newly introduced at each grade may help explain the drop in U.S. student achievement levels between grades 4 and 8. The persistence of elementary content in middle school suggests that the lauded "spiral curriculum" in the United States is in fact a vicious circle.
As suggested above, the consequence of lack of focus and coherence and the static approach to defining what is basic is that U.S. curricula are undemanding when compared to those of other countries, especially during the middle grades. Materials intended for our mathematics and science students mention a staggering array of topics, most of which are introduced in the elementary grades. This mention does not include much more than the learning of algorithms and simple facts. Demanding standards would require more sophisticated content, taught in depth as students progress through the grades.
Recently, TIMSS's discovery that grade 8 curricula in most high-achieving nations largely concentrate on algebra, geometry, and advanced number topics in mathematics and on physics and chemistry in science has led to some proposals that grade 9 algebra courses be given in grade 7 or 8. This is a recent example of a common pitfall of interpretation of findings from comparative studies such as TIMSS-the rush to emulate "successful" countries. However, this approach ignores the findings regarding other aspects of curriculum.
The point is not merely that these contents are taught in the eighth grade. It is also that the curriculum in these countries carefully builds up to the study of these topics. This is accomplished through a process of focused and coherent transitions from simple to increasingly more complex content and skills. Thus, we should not simply move upper-grade courses to lower grades; the entire process of defining content grade by grade must be involved. In addition, the inclusion of more complex content in the middle grades is not the only factor to be considered. High academic standards require students to reason, analyze, and develop the ability to solve problems and understand the processes of science and mathematics. Thus, more ambitious performance expectations for students are necessary as well.
Many of the lessons above invite important additional questions: How do high standards become embodied in educational policy? What type of authority is attached to curriculum guides, programs of study, textbooks, tests, etc.? The study of TIMSS nations and their contrast with U.S. educational policy is again suggestive of important challenges confronting our educational system
There are many bodies guiding education in the United States. There are close to 16,000 local school districts in public education alone, a variety of intermediate districts, and many other private and public bodies concerned with education. Respect for local control has resulted in state and national standards (mostly proposed by national professional or scientific organizations such as the National Council of Teachers of Mathematics or the National Research Council) that can provide little guidance for implementation, because these standards compete with many others for the attention of school administrators and teachers. Add to this mix a wide array of commercially produced textbooks and standardized tests, each embodying yet another definition of what is basic, and the situation can be depicted as a veritable Tower of Babel.
Standards that transcend local boundaries are common in most TIMSS countries and are present in all countries outperforming the United States. Yet not all countries have national standards in the sense of one set of standards mandated for all students from a central government authority. In Belgium, separate standards apply for Flemish- and French-speaking school systems. In Switzerland each canton, and in Germany each of the länder, defines standards for its school systems. Despite this, most countries have consensus on the question of basics grade by grade. The result is that the disparate voices of various bodies harmonize in a consensual view of the basics, producing a coherent vision to guide their systems.
Many TIMSS nations are as concerned with educational equity as the United States is, viewing the education of the elite as no more important than the education of children from households of low social and economic status. These countries mostly have policies that attempt to ensure equity by ensuring a common educational standard, instead of policies that leave standards entirely up to localities. "High standards for all," instead of high standards for some and lower standards for others, is the policy these countries follow. They favor a consensus on what it means to succeed in school. This stands in marked contrast to the U.S. approach of essentially allowing each locality to define its own standard of success, as if the economic system did not ultimately hold all children to a common standard.
In the United States, state governors and the federal legislative and executive branches have defined national objectives for U.S. education that transcend local boundaries. They have stated that the national goal is to be "first in the world in mathematics and science education" by the end of this century. Accomplishing this national goal in the context of locally defined curricula presents a singular challenge. How can we attempt to increase national average achievement in the current chaotic curricular environment? The answer would appear to be that we cannot.
Many in the educational community fear this lesson of TIMSS the most. Some believe that standards that transcend localities will make local innovations difficult or impossible. Others fear that an approach favoring high standards for all will unfairly hold our nation's underprivileged schoolchildren up to standards that they cannot hope to reach. Still others worry that our brightest children will be held back by such an approach.
However, standards need not preclude innovation. This is demonstrated in a recent study of innovations conducted in Asia, Europe, and America by the Organization for Economic Cooperation and Development (OECD). Noteworthy innovations were found in countries with national standards and other types of overall standards. In addition, when well defined, a "high standards for all students" approach can help guide policymakers in ensuring access to the resources necessary to help underprivileged schoolchildren meet these standards. In fact, this is a common justification for the "high standards for all" approach in many TIMSS countries.
To rise to the challenges that beset our educational systems, we must seek policies that foster innovation (and facilitate diffusion of successful innovations) while ensuring high standards for all. That this is difficult is certain, but refusing to contend with this issue is likely to ensure mediocre average performance into the 21st century, with inferior achievement being retained as the special patrimony of many of our country's poorest and most disadvantaged students. A national commitment to high achievement is clearly incompatible with restricted standards. Courage in formulating ambitious educational goals should not be coupled with timidity in addressing the question of ensuring access to the high standards that would make accomplishing these goals possible for the majority of our students.
A "high standards for all" curriculum is not only demanding for students; it places great demands on all the resources of the system. If the United States were to take up the challenge of formulating such standards, many elements of the system would require alteration. Textbooks, standardized tests, and other instructional resources, including time for instruction and its preparation, would need to be reexamined to ensure that they support teachers and students in their new roles as implementers of this curriculum. Our existing systems of education are experienced in the type of instruction an episodic curriculum requires. But new tools will be needed if new types of curriculum are devised.
One of the most important resources of our system is teachers. New focused and demanding goals will require new approaches in the preparation of new teachers and in the support of teachers already in service. A focused and demanding curriculum for teachers will also be required.
Splintered versus integrated reform
It is clear that there are no simple fixes to the challenges facing U.S. education. Reforming our policies and practices is a challenge to the very structure of teaching and learning in our country, involving standards, tests, textbooks, teaching methods, teachers, and other factors.
Changing only a few of these factors is unlikely to affect mean achievement in this country. Isolated attempts at reform are also not likely to be effective in changing national patterns. Because educational systems are involved, integrated systemic strategies, instead of widely dispersed foci of reform, are required. Localized reforms have their place-they engage the creativity and knowledge of our teachers, administrators, and communities. The challenge before us as a nation, however, is not merely to permit the random generation of innovations locality by locality like so many fireflies swarming in the night. The challenge is to create sound renovated educational systems that flood the light of reform into every corner of our nation. Translating innovations into institution-building requires the commitment of educational systems. Until this happens, most of our schoolchildren will be unable to benefit from even the most brilliant local reform efforts.
Perhaps the most significant contribution of TIMSS is in understanding systemic and institutional alternatives. Lessons from TIMSS have challenged and no doubt will continue to challenge our most basic assumptions about schooling and how our educational systems provide access to learning. TIMSS allows us to learn from high-achieving countries as well as other countries and to translate these lessons into new approaches to old problems that take into account our own history, culture, and institutions.
TIMSS is very much a work in progress. Its many interrelated sets of information are still being used to answer a number of questions concerning education in mathematics and science. Already, however, it has taught us important lessons with profound implications for the conduct of schooling in our country. At the U.S. national research center for TIMSS, we are continuing the work that we hope will contribute to understanding these lessons better and to learning new ones. However, we have shown that there is much that the United States can learn from schooling in other countries. We have uncovered a number of challenges for education and educational policies that have clear implications for the achievement of our students in mathematics and science as we reach the 21st century.
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W. H. Schmidt, D. Jorde, E. Barrier, I. Gonzalo, U. Moser, K. Shimizu, T. Sawada, G. A. Valverde, C. McKnight, R. S. Prawat, D. E. Wiley, S. A. Raizen, E. D. Britton, and R. G. Wolfe, Characterizing Pedagogical Flow: An Investigation of Mathematics and Science Teaching in Six Countries. Dordrecht, The Netherlands: Kluwer Academic, 1996.
W. H. Schmidt, C. C. McKnight, S. A. Raizen, P. M. Jakwerth, G. A. Valverde, R. G. Wolfe, E. D. Britton, L. J. Bianchi, and R. T. Houang, A Splintered Vision: An Investigation of U.S. Science and Mathematics Education. Dordrecht, The Netherlands: Kluwer Academic, 1997.
W. H. Schmidt, C. C. McKnight, G. A. Valverde, R. T. Houang, and D. E. Wiley, Many Visions, Many Aims: A Cross-National Investigation of Curricular Intentions in School Mathematics, Vol. 1. Dordrecht, The Netherlands: Kluwer Academic, 1997.
W. H. Schmidt, S. A. Raizen, E. D. Britton, L. J. Bianchi, and R. G. Wolfe, Many Visions, Many Aims: A Cross-National Investigation of Curricular Intentions in School Science, . Vol. 2. Dordrecht, The Netherlands: Kluwer Academic, 1997.
U.S. Department of Education, National Center for Education Statistics, . Pursuing Excellence: A Study of U.S. Fourth Grade Mathematics and Science Achievement in International Context. Washington, D.C.: U.S. Government Printing Office, 1997.
Gilbert A. Valverde is associate director and William H. Schmidt is executive director of U.S. National Research Center for the Third International Mathematics and Science Study at Michigan State University in East Lansing, Michigan.