Spiral Curriculum

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“Spiral Curriculum”

American schools follow a “spiral curriculum” in mathematics; that is, they spend such a substantial proportion of time on review each year that only limited progress can be made with new material… American students who perform poorly in arithmetic are subject to a special form of the spiral curriculum, which might be termed the “circular curriculum”: they repeat arithmetic over and over until they stop studying math” (Gamoran, 2001, p. 138)

Gamoran, A. (2001). Beyond curriculum wars: Content and understanding in mathematics. In T. Loveless, Ed., The Great Curriculum Debate, pp. 134-162. Washington, D.C.: Brookings Institution Press.

The Process of Education 1

http://www.infed.org/thinkers/bruner.htm

The process of education

The Process of Education (1960) was a landmark text. It had a direct impact on policy formation in the United States and influenced the thinking and orientation of a wide group of teachers and scholars, Its view of children as active problem-solvers who are ready to explore 'difficult' subjects while being out of step with the dominant view in education at that time, struck a chord with many. 'It was a surprise', Jerome Bruner was later to write (in the preface to the 1977 edition), that a book expressing so structuralist a view of knowledge and so intuitionist an approach to the process of knowing should attract so much attention in America, where empiricism had long been the dominant voice and 'learning theory' its amplifier' (ibid.: vii).

Four key themes emerge out of the work around The Process of Education (1960: 11-16):

The role of structure in learning and how it may be made central in teaching. The approach taken should be a practical one. 'The teaching and learning of structure, rather than simply the mastery of facts and techniques, is at the center of the classic problem of transfer... If earlier learning is to render later learning easier, it must do so by providing a general picture in terms of which the relations between things encountered earlier and later are made as clear as possible' (ibid.: 12).

Readiness for learning. Here the argument is that schools have wasted a great deal of people's time by postponing the teaching of important areas because they are deemed 'too difficult'.

We begin with the hypothesis that any subject can be taught effectively in some intellectually honest form to any child at any stage of development. (ibid.: 33)

This notion underpins the idea of the spiral curriculum - 'A curriculum as it develops should revisit this basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them' (ibid.: 13).

Intuitive and analytical thinking. Intuition ('the intellectual technique of arriving and plausible but tentative formulations without going through the analytical steps by which such formulations would be found to be valid or invalid conclusions' ibid.: 13) is a much neglected but essential feature of productive thinking. Here Bruner notes how experts in different fields appear 'to leap intuitively into a decision or to a solution to a problem' (ibid.: 62) - a phenomenon that Donald Schön was to explore some years later - and looked to how teachers and schools might create the conditions for intuition to flourish.

Motives for learning. 'Ideally', Jerome Bruner writes, interest in the material to be learned is the best stimulus to learning, rather than such external goals as grades or later competitive advantage' (ibid.: 14). In an age of increasing spectatorship, 'motives for learning must be kept from going passive... they must be based as much as possible upon the arousal of interest in what there is be learned, and they must be kept broad and diverse in expression' (ibid.: 80).

http://www.infed.org/thinkers/et-schon.htm

http://www.infed.org/thinkers/et-schon.htm

http://www.infed.org/thinkers/bruner.htm

The Process of Education 2

Bruner was to write two 'postscripts' to The Process of Education: Towards a theory of instruction (1966) and The Relevance of Education (1971). In these books Bruner 'put forth his evolving ideas about the ways in which instruction actually affects the mental models of the world that students construct, elaborate on and transform' (Gardner 2001: 93). In the first book the various essays deal with matters such as patterns of growth, the will to learn, and on making and judging (including some helpful material around evaluation). Two essays are of particular interest - his reflections on MACOS (see above), and his 'notes on a theory of instruction'. The latter essay makes the case for taking into account questions of predisposition, structure, sequence, and reinforcement in preparing curricula and programmes. He makes the case for education as a knowledge-getting process:

To instruct someone... is not a matter of getting him to commit results to mind. Rather, it is to teach him to participate in the process that makes possible the establishment of knowledge. We teach a subject not to produce little living libraries on that subject, but rather to get a student to think mathematically for himself, to consider matters as an historian does, to take part in the process of knowledge-getting. Knowing is a process not a product. (1966: 72)

The essays in The Relevance of Education (1971) apply his theories to infant development.

Bruner 1

http://starfsfolk.khi.is/solrunb/jbruner.htm_3.htm

Jerome Bruner (1915-).

Jerome Bruner was born in U.S.A and his influence on teaching has been important. He was possibly the leading proponent of discovery approach in mathematical education although he was not the inventor of the concept (Romiszowski.,A.J.,1997).

Bruner describes the general learning process in the following manner. First the child finds in his manipulation of the materials regularities that correspond with intuitive regularities it has already come to understand. According to Bruner the child finds some sort of match between what it is doing in the outside world and some models or templates that it has already grasped intellectually. For Bruner it is seldom something outside the learner that is discovered. Instead, the discovery involves an internal reorganisation of previously known ideas in order to establish a better fit between those ideas and regularities of an encounter to which the learner has had to accommodate.

His approach was characterised by three stages which he calls enactive, iconic and symbolic and are solidly based on the developmental psychology of Jean Piaget. The first, the enactive level, is where the child manipulate materials directly. Then he proceed to the iconic level, where he deals with mental images of objects but does not manipulate them directly. At last he moves to the symbolic level, where he is strictly manipulating symbols and no longer mental images or objects. The optimum learning process should according to Bruner go through these stages.

1. Enactive mode. When dealing with the enactive mode, one is using some known aspects of reality without using words or imagination. Therefore, it involves representing the past events through making motor responses. It involves manly in knowing how to do something; it involves series of actions that are right for achieving some result e.g. Driving a car, skiing, tying a knot.

2. Iconic Mode. This mode deals with the internal imagery, were the knowledge is characterised by a set of images that stand for the concept. The iconic representation depends on visual or other sensory association and is principally defined by perceptual organisation and techniques for economically transforming perceptions into meaning for the individual.

3. Symbolic mode. Through life one is always adding to the resources to the symbolic mode of representation of thought. This representation is based upon an abstract, discretionary and flexible thought. It allows one to deal with what might be and what might not, and is a major tool in reflective thinking. This mode is illustrative of a person’s competence to consider propositions rather than objects, to give ideas a hierarchical structure and to consider alternative possibilities in a combinatorial fashion, (Spencer.K.,1991, p.185-187).

The association of these ideas of manipulations of actual materials as a part of developmental model and the Socraterian notion of learning as internal reorganisation into a learning by discovery approach is the unique contribution of Bruner (Romiszowski.,A.J.1997, p.23).

http://starfsfolk.khi.is/solrunb/jbruner.htm_3.htm

Bruner 2

In 1960, Bruner (then a professor of Harvard University) proposed a “spiral curriculum” concept to facilitate structuring a curriculum ´around the great issues, principles, and values that a society deems worthy of the continual concern of its members´ (Bruner, 1960). The next decades many school system educators attempted to implement this concept into their curriculum. Bruner (1975) described the principles behind the spiral curriculum in the following way:

”…I was struck by the fact that successful efforts to teach highly structured bodies of knowledge like mathematics, physical sciences, and even the field of history often took the form of metaphoric spiral in which at some simple level a set of ideas or operations were introduced in a rather intuitive way and, once mastered in that spirit, were then revisited and reconstrued in a more formal or operational way, then being connected with other knowledge, the mastery at this stage then being carried one step higher to a new level of formal or operational rigour and to a broader level of abstraction and comprehensiveness. The end stage of this process was eventual mastery of the connexity and structure of a large body of knowledge”…(p.3-4).

It was in the 1980s, that a body of literature had accumulated in support of individual components of a spiral curriculum model. Reigeluth and Stein (1983) published the seminal work on “ The Elaboration Theory of Instruction”. It proposes that when structuring a course, it should be organised in a simple-to-complex, general-to-detailed, abstract-to-concrete manner. Another principle is that one should follow learning prerequisite sequence, it is applied to individual lessons within a course. In order for a student to develop from simple to more complex lessons, certain prerequisite knowledge and skills must first be mastered. This prerequisite sequencing provides linkages between each lesson as student spirals upwards in a course of a study. As new knowledge and skills are introduced in a subsequent lessons, they reinforce what is already learnt and become related to previously learned information. What the student gradually achieves is a rich breadth and depth of information that is not normally developed in curricula where each topic is discrete and disconnected from each other (Dowding, T.J. 1993).

Bruner suggested that cognitive process precede perception rather than the other way around, that a person may not perceive an object until he or she has recognised it. These cognitive theories of perception emphasise the role of knowledge in how we interpret the world.

Howard Gardner (1987,p.6) defined cognitive science as “a contemporary, empirically based effort to answer long-standing epistemological questions- particularly those concerned with the nature of knowledge, its components, its sources, its development, and its deployment. ”The theories of the constructivist are originated from this school of thought.The beginning of the 1950s and maintaining through the 1990s, educators drew on rising insight of communications specialists, learning theories, and systems engineers. The 1990s have been marked by the challenge of constructivism.

Two Types of Curriculum 1

http://www.gse.uci.edu/doehome/Deptinfo/Faculty/Becker/ED150WEB/%20Curriculum.html

Two Types of Curriculum

There are two types of curriculum widely used today. Spiral curriculum is where a wide number of topics are taught in the early grades. The topics are cycled throughout the years, developing deeper understanding through the later grades. The United States uses spiral curriculum. Mastery curriculum covers a smaller set of topics and focuses on students' deep understanding of each topic. Students who are in a mastery curriculum program score higher than those who are in a spiral curriculum (school reform). Our country might need to lean toward mastery curriculum if they want to keep up with other countries. This shift might also cause a decline in student boredom. It seems possible that a solution to boredom could be an alteration to mastery curriculum. Mastery curriculum could help the problem of teacher burn out, which could be a cause of student boredom.

A movement to mastery curriculum might help with teacher burn out as well as boredom. If the curriculum focused on a more centered set of topics, there would be less repetition on the part of the teacher and the students. The students would learn what was needed, and move on. There would be no going back in later years to dig deeper. That would have been done initially. The students would not be wasting their time relearning, and the teachers would focus on a smaller set of topics. Mastery curriculum seems like a good way to eliminate teacher burn out, which causes student boredom.

Changing something as drastic as the curriculum from spiral to mastery may also force changes in other problem areas, such as teacher burn out and dropout levels. If students are given a smaller range of things to study, looking at them in greater depth, they would probably be more inclined to stay in school, simply by eliminating boredom. Changing a curriculum to a more specialized one would also focus the teachers' attentions, allowing them to implement more exciting and engaging projects. The mastery curriculum could be taught with project-based learning and still work effectively. These changes needed to make high schools a better place might not be effective, but reducing boredom is certainly a step in the right direction.

http://www.gse.uci.edu/doehome/Deptinfo/Faculty/Becker/ED150WEB/%20Curriculum.html

Things don’t add up… 1

http://www.nychold.com/art-hook-050304.html

Things don't add up in B.C. math classes

By Bill Hook and Karin LitzckeVancouver SunEditorial Section, Issues & Ideas Page

Friday March 04, 2005

Reading and math are the two crucial elementary school subjects required for high school and life beyond, but British Columbia's elementary math curriculum is crippling learning, especially among disadvantaged students.

B.C. has used what is called a "spiral" curriculum since 1987, following a tradition of emulating U.S. educational practice.

A spiral curriculum runs a smorgasbord of math topics by students each year, the idea being that they pick up a little more of each with every pass. In reality, the spin leaves many students and teachers in the dust.

Ideally, the curriculum should cover fewer topics per year in more depth.

Presently, teachers face having Grade 4 classes who still cannot add 567 + 942 nor multiply 7 x 8 because the Grade 1, 2, and 3 teachers were forced to spend so much time on graphing, polygons and circles, estimating quantity and size, geometrical transformations, 2D and 3D geometry and other material not required to make the next step, which is 732 x 34.

And because elementary math fails to provide a solid foundation, many basically capable students simply give up when faced with the shock of high school algebra, which would be the doorway to advanced technical training at all levels. High school math teachers cannot make up Grades 1 to 7 while teaching Grade 8.

Alarm bells about the math curriculum have been ringing in B.C. since the United States, which used spiralling almost exclusively, registered a dismal performance on the Third International Mathematics and Science Study (TIMSS), a test that comparatively evaluated more than 500,000 students from 15,000 schools in 40 countries, first in 1995 and again in 1999 with the same results.

The B.C. ministry of education, to its credit, realized right away in 1995 that the U.S. performance on TIMSS suggested weaknesses in B.C.'s curriculum.

http://www.nychold.com/art-hook-050304.html


Also aware of some then-emerging data indicating that students in Quebec -- which had retained a sequential curriculum when B.C. went to the spiral -- were outperforming other Canadian students in math, Victoria commissioned researcher Helen Raptis, now a University of Victoria professor, to compare B.C. and Quebec test results and curricula.

In her report, submitted to the ministry in late 2000, Raptis showed that the average B.C. student was more than two years behind the average Quebec student in math by Grade 10, and explored the extent to which curriculum might be responsible.

Her report did not flatter B.C.'s curriculum, reading in part:

"The range of skills and operations within a specific topic area is deeper in Quebec, moving constantly between the abstract and concrete properties of mathematics concepts and maintaining a place for mental as well as rote processes.

"The B.C. curriculum is inconsistent in its treatment of abstract and concrete concepts.

"Objectives and notes throughout Quebec's curricula highlight the view that mathematics learning is interrelated and cumulative.

"These conscious links are not evident in B.C.'s mathematics curricula. Instead, learning objectives from prior years are repeated outright."

In 2002, the U.S. National Research Center for TIMSS published similar conclusions, finding that the curricula of virtually all the U.S. states had too many topics that were introduced too early, repeated too often, and covered too superficially.

The U.S. TIMSS report noted, too, that the spiral curriculum "favoured the children of well-off or sophisticated parents who could provide supplementary tutoring, and was terribly unfair to the disadvantaged. The learning of the luckier students snowballs while that of the less fortunate ones -- those dependent on the incoherent U.S. curriculum -- never begins to gather momentum."

To date neither the Raptis nor the TIMSS reports have generated any action in B.C., but California, also alarmed by the 1995 U.S. performance on TIMSS, implemented a redesigned curriculum with far fewer topics per year in 1998.

California's curriculum change was accidentally a perfect experiment. Los Angeles and San Diego refused to participate in the new curriculum and retained the spiral approach, creating an ideal "control" group.

Another group of districts and schools adopted the new curriculum with particular speed, buying matching textbooks right away in 1998. Most of these had a large percentage of economically disadvantaged and ESL students.


As the number of topics per year in the curriculum went down, student performance went up, up, and up. Fast-adopting schools with many disadvantaged students moved from about the 25th to the 60th percentile over the next five years.

Student results at schools with more affluent students jumped from about the 75th percentile to the 90th, showing that the improvement for lower-end students is not at the expense of traditionally high-performing students. The overall California average improved by 19 percentile points during this period, despite the poor performance of the refusenik districts and other districts slow to convert.

The size of the California experiment -- annually testing 2.9 million Grade 2 to 6 students over a five-year period, including more than 97 per cent of enrolled students in about 7,500 schools -- makes it another overwhelming piece of evidence.

With the data in from TIMSS and California, supported by the analysis from Raptis and by the recent PISA test that shows B.C. continuing to badly trail Quebec, the case for a major elementary school curriculum change in B.C. has been irrefutably made.

Let's hope Victoria can do the math.

Bill Hook is a research scientist at the University of Victoria; Karin Litzcke is a freelance education analyst.

Refocusing US Math and Science Ed 1

http://www.issues.org/14.2/schmid.htm

Gilbert A. Valverde

William H. Schmidt

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.

http://www.issues.org/14.2/schmid.htm


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 challenge is to create sound renovated educational systems that flood the light of reform into every corner of our nation.

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.


We should not simply move upper grade courses to lower grades; the entire process of defining content grade by grade must be involved.

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.

Dispersed control

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.

We must seek policies that foster innovation (and facilitate diffusion of successful innovations) while ensuring high standards for all.

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.

Recommended reading

L. Peak, N. Caldwell, E. Owen, H. Stevenson, L. Suter, M. Frase, W. Schmidt, J. Stigler, and T. Williams, Pursuing Excellence: A Study of U.S. Eighth-Grade Mathematics and Science Teaching, Learning, Curriculum, and Achievement in International Context. Washington, D.C.: U.S. Department of Education, National Center for Education Statistics, 1996.

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.


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