A Splintered Vision:
William H. Schmidt, Curtis C. McKnight, Senta A. Raizen
"There is no one at the helm of mathematics and science education in the U.S.; in truth, there is no identifiable helm. No single coherent vision of how to educate today's children dominates U.S. educational practice in either subject, nor is there a single, commonly accepted place to turn to for such visions. Our visions to the extent that they exist at all are multiple. ...The study summarized below represents an effort to describe the nature of the diffuse vision of mathematics and science education in the U.S. and to raise questions relevant to policy making."
U.S. National Research Center for the Third International Mathematics and Science Study
posted to site:
An Investigation of
U.S. Science and Mathematics Education
William H. Schmidt
Curtis C. McKnight
Senta A. Raizen
With the collaboration of
Pamela M. Jakwerth
Gilbert A. Valverde
Richard G. Wolfe
Edward D. Britton
Leonard J. Bianchi
Richard T. Houang
U.S. National Research Center for the Third International Mathematics and Science Study,
Michigan State University
Third International Mathematics and Science Study
THE SPLINTERED VISION: AN OVERVIEW
There is no one at the helm of mathematics and science education in the U.S.; in truth, there is no
identifiable helm. No single coherent vision of how to educate today's children dominates U.S.
educational practice in either subject, nor is there a single, commonly accepted place to turn to
for such visions. Our visions to the extent that they exist at all are multiple.
These splintered visions produce unfocused curricula and textbooks that fail to define clearly
what is intended to be taught. They influence teachers to implement diffuse learning goals intheir classrooms. They emphasize familiarity with many topics rather than concentrated attention
to a few. And they likely lower the academic performance of students who spend years in such a
learning environment. Our curricula, textbooks, and teaching all are "a mile wide and an inch
This preoccupation with breadth rather than depth, with quantity rather than quality, probably
affects how well U.S. students perform in relation to their counterparts in other countries. It thus
determines who are our international "peers" and raises the question of whether these are the
peers that we want to have. In today's technologically oriented global society, where knowledge
of mathematics and science is important for workers, citizens, and individuals alike, an important
question is: What can be done to bring about a more coherent vision and thereby improve
mathematics and science education?
Reforms have already been proposed by political, business, educational and other leaders.
Extensive efforts are underway to implement these standards, but the implementation process
itself is shaped by the prevailing culture of inclusion. Like the developers of curricula and the
publishers of textbooks, teachers add reform ideas to their pedagogical quivers without asking
what should be taken away.
The study summarized below represents an effort to describe the nature of the diffuse vision of
mathematics and science education in the U.S. and to raise questions relevant to policy making.
Purpose of A Splintered Vision
A Splintered Vision (written by William Schmidt, Curtis McKnight and Senta Raizen of the U.S.
National Research Center for the Third International Mathematics and Science Study and
published by Kluwer Academic Publishers) discusses data from the analysis of 491 curriculum
guides and 628 textbooks from around the world as part of the recently completed Third
International Mathematics and Science Study (TIMSS). It also presents detailed accompanying
data on teacher practices in the U.S. and two other countries: Germany and Japan.
The TIMSS is a large-scale, cross-national comparative study of the national educational systems
and their outputs in about 50 countries. Researchers examined mathematics and the sciences
curricula, instructional practices, and school and social factors, as well as conducting
achievement testing of students. They collected data from representative documents that laid out
official curricular intentions and plans, analyzed entire mathematics and science textbooks, and
searched entire K-12 textbook series for selected "in-depth" topics (subareas within the subject
matter.) In six countries TIMSS conducted classroom observations, teacher interviewing, and
The TIMSS curriculum and teacher data are extensive and cannot be explored in a single report.
The results of analyses of these data are being reported in a series of volumes, three of which are
The present report intends to document and characterize the state of U.S. mathematics and
science curricula, textbooks, and teaching practices and place them in a cross-national context.
Unfortunately, this study could only provide a snapshot of the "moving target" that is educational
practice in the U.S. These data were collected in 1992-93, when the mathematics standards hadonly existed for three years and the science standards were not finalized.
The intervening years
have been a time of change for state curriculum standards and textbooks. The TIMSS data on
teacher practices discussed here were collected in 1995.
This report is meant to be descriptive and, to a lesser extent, interpretive. It is not a plea for
specific reforms. We seek to provide data germane to the ongoing public debate about science
and mathematics education policies in the U.S.
Curricula in both mathematics and science in U.S. schools are unfocused in comparison with
those in other countries studied. The lack of curricular focus is more true in mathematics than in
science, though physical science guides closely resemble mathematics in their fragmentation.
U.S. curricula are unfocused in several respects:
- Topics Covered
Mathematics curricula in the U.S. consistently cover far more topics than is typical in
other countries. The number of mathematics topics in the U.S. composite
is higher than
the 75th percentile internationally in all grades until ninth, when schools typically teach
specific courses such as algebra, geometry, etc. In science, the tendency toward inclusion
is similar, though less pronounced. The number of science topics in the U.S. composite
exceeds the 50th percentile internationally in all but one grade until the tenth, when
schools tend to abandon general science approaches for specific courses, such as
chemistry and physics.
In both mathematics and science, topics remained in our composite U.S. curricula for
more grades than all but a few other TIMSS countries. The U.S. approach can be
characterized as "come early and stay late." In mathematics, the U.S. practice is to add far
more topics than other countries do in grades one and two and then repeat these topics
until grade seven. In grades nine and 11 the U.S. composite curriculum drops many more
topics than other countries. On average, mathematical topics remain in the U. S.
composite curriculum for two years longer than the international median. Only five
countries have higher average durations. In science, U.S. practice is to introduce new
science topics at intervals, especially grades one and five, with little change in the
intervening grades. In grades 10 to 12 the U.S. composite curriculum drops many more
topics than other countries. Average intended duration is close to the international median
in earth sciences and life sciences, but the U.S. average duration in the physical sciences
is two years longer than the median and higher than all but seven countries. In
mathematics, the tendency to retain topics over many grades may reflect the traditional
approach of distributed mastery the idea that mastering pieces of a subject would lead to
mastery of a bigger whole. U.S. curricula lack a strategic concept of focusing on a few
key goals, linking content together, and setting higher demands on students. This
propensity for inclusion extends even to reform proposals. Many reform recommendations simply add to the existing topics (or are implemented by adding to
existing content), thereby exacerbating the existing lack of curricular focus.
U.S. curricula in mathematics and science seek to do something of everything and less of
any one thing. Given roughly comparable amounts of instructional time, this topic
diversity limits the average amount of time allocated to any one topic. In mathematics,
this accumulation may be a product of our model of distributed mastery over the grades.
The reasons for the better results in science are less clear but seem related to general
science approaches that move from topic to topic.
- Variations Among States
While the core of mathematics topics was broad, it varied little among the states. The
number of core science topics was much smaller, and the overlap among state curricula
was also small. While students in U.S. states might have studied a number of science
topics roughly equal to the international median, the differing curricular intentions of
various states are such that students in different states likely studied only a few common
- Defining the "Basics"
Student achievement in mathematics and science in any country is largely shaped by
what educational policy makers in that nation regard as "basic" in these subjects and how
well they communicate and support those basics. The U.S. mathematics instructional
practices defined de facto eighth grade basics of arithmetic, fractions and a relatively
small amount of algebra. In Germany, Japan, and internationally, the basics were defined
as algebra and geometry. For science, the picture is more complex since U.S. curricula
include single area courses, such as physical sciences, life sciences, or earth sciences.
These courses defined a more restricted, focused set of basics, but they applied only to
the subset of students receiving those particular courses.
Textbooks play an important role in making the leap from intentions and plans to classroom
activities. They make content available, organize it and set out learning tasks in a form designed
to be appealing to students. Without restricting what teachers may choose to do, textbooks
drastically affect what U.S. teachers are likely to do under the pressure of daily instruction. The
question thus arises: Do U.S. mathematics and science textbooks add guidance and focus to help
teachers cope with unfocused curricula? Unfortunately, the answer is "no." The splintered
character of mathematics and science curricula in the U.S. is mirrored in the textbooks used by
teachers and students. American textbooks are unfocused in several ways:
How Teachers Deal with the Splintered Vision
- Topics Included
The U.S. mathematics and science textbooks include far more topics than was typical internationally at all three grade levels analyzed. In mathematics, U.S. textbooks are far
above the 75th percentile of the TIMSS countries in the number of topics covered. For
example, U.S. mathematics textbooks designed for fourth and eighth graders cover an
average of 30 to 35 topics, while those in Germany and Japan average 20 and 10
respectively for these populations. As a result, typical mathematics textbooks in the U.S.
look quite different than those of a nation such as Japan. The typical eighth grade U.S.
textbook (non-algebra) is larger and more comprehensive than the average Japanese text,
but it contains fewer sequences of extended attention to a particularly important topic.
The U.S. textbooks' sequences are also shorter and have more breaks. The lesson by
lesson organization of the U.S. book is much less focused than the Japanese book, and
there is far more skipping among topics in successive segments. In science, the
differences are even greater. At all three population levels, U.S. science textbooks
included far more topics than even the 75th percentile internationally. The average U.S.
science textbook at the fourth, eighth, and 12th grade has between 50 and 65 topics; by
contrast Japan has five to 15 and Germany has just seven topics in its eighth grade
The propensity of U.S. curricula to do something of everything but little of any one thing
is mirrored in textbooks. The few most emphasized topics account for less content than is
the case internationally. Among the fourth grade mathematics textbooks investigated, the
five topics receiving the most textbook space accounted on average for about 60 percent
of space in the U.S. textbooks but over 85 percent of textbook space internationally. At
the eighth grade level, the five most emphasized topics in non-algebra U.S. textbooks
accounted for less than 50 percent of textbook space compared to an international
average of about 75 percent. An exception are U.S. eighth grade algebra books which
were highly focused, the five most emphasized topics accounting for 100 percent of the
books. Among the U.S. fourth grade science textbooks investigated, the five topics
receiving the most attention accounted for an average of just over 25 percent of total
space in U.S. textbooks compared to an average of 70 to 75 percent internationally.
Among the U.S. eighth grade science textbooks investigated, the five most emphasized
topics in more general science texts accounted for about 50 percent of textbook space
compared to an international average of about 60 percent. In contrast, U.S. eighth grade
science books oriented to a single area were highly focused, with the five most
emphasized topics accounting for more of the textbooks than was true in the international
U.S. eighth grade science textbooks emphasized understanding and using routine
procedures, which represent the less complex, more easily taught expectations for student
performance. This emphasis was typical of what was done internationally. It is not,
however, typical of the diverse and more demanding performances called for in current
U.S. science education reform documents. Most U.S. schools and teachers make selective
use of textbook contents and rarely, if ever, cover all of a textbook's content. Publishers
can reasonably expect that those who adopt and buy a particular textbook will feel free to use only the contents that suit their purposes. Unfortunately, the result is large textbooks
covering many topics but comparatively shallowly. Even in the largest textbooks, space is
still limited. It is impossible for textbooks so inclusive to help compensate for unfocused
official curricula. Thus, our analysis shows that U.S. textbooks support and extend the
lack of focus seen in those official curricula.
Teachers in the U.S. are sent into their classrooms with a mandate to implement inclusive,
fragmented curricula and armed with textbooks that embody the same "breadth rather than
depth" approach. How do they handle such a situation? Not surprisingly, the instructional
decisions made by U.S. teachers mirror the inclusive approach of the tools they are given. U.S.
teachers handle the splintered vision they get in several ways:
Is This The Best Our Teachers Can Do?
- Topics Covered
U.S. mathematics and science teachers typically report teaching more topics than their
counterparts in other countries, including Germany and Japan. This is true for science
teachers even when using a single area textbook such as physical science, life science, or
Since instructional time for science or math within a school year is limited, the data show
that teaching more topics means that teachers spend little time on most topics. U.S. eighth
grade mathematics teachers indicated that they taught at least a few class periods on all
but one topic area included in the teacher survey's questionnaire. They devoted 20 or
more periods of in-depth instruction to only one topic area, fractions and decimals.
However, in Germany and Japan many other topic areas received this more extensive
coverage. According to the survey, the five topic areas covered most extensively by U.S.
eighth grade mathematics teachers accounted for less than half of their year's instructional
periods. In contrast, the five most extensively covered Japanese eighth grade topic areas
accounted for almost 75 percent of the year's instructional periods. U.S. eighth grade
science teachers also indicated that they would devote at least some class time to every
topic area surveyed. None was omitted completely and no topic was marked to receive
more than 13 class periods of attention by eighth grade physical and general science
teachers. Additional topic areas received more extensive coverage in Germany and Japan.
On average U.S. eighth grade general science teachers' most extensively covered topics
accounted for only about 40 percent of their instructional periods, but this percentage was
also lower for science in Germany and Japan (about 50 to 60 percent).
- Number of Activities
U.S. teachers engage in more teaching activities per lesson than their counterparts in
other countries. More than 60 percent of U.S. eighth grade mathematics and science
teachers reported using six or more activities in a typical class. In Germany only 25
percent reported using six or more activities, and even fewer reported doing so in Japan.
U.S. mathematics and science teachers work hard and often face demanding workplaces. Our
data show that they are scheduled to work about 30 periods each week, which is more than
teachers in Germany (just over 20 periods) and Japan (fewer than 20). These teachers rarely have
the luxury of being idealists. Unfocused curricula and inclusive textbooks set few boundaries for
instructional decisions and appear to require a little bit of everything. It is easier for real teachers
making real decisions in the real workplaces of U.S. schools to settle for the first alternative that
seems good enough rather than search for the best possible instruction. They try to cover as
much as they can rather than teach just a little. In a word, they "satisfice" The data shows that
U.S. mathematics and science teachers are aware of and believe in more effective, complex
teaching styles than they practice. They often have information that would help them do their
work more effectively. Their beliefs suggest that they might choose to organize instruction
differently under circumstances less consumed by the need for coverage. Effective teachers
should not be unusual, nor should effectiveness require extraordinary efforts and dedication by
teachers. The reality, however, is that U.S. teachers are placed in situations in which they cannot
do their best. We have yet to unleash the effectiveness of U.S. teachers. It seems likely that
fundamental changes are needed in teacher knowledge, working conditions, curricula quality,
student expectations, and textbook content.
What Can We Expect from U.S. Students?
In mathematics, we have a highly fragmented curriculum, textbooks that are a "mile wide and an
inch deep," and teachers who cover many topics but none extensively. We make low demands on
students and have a more limited conception of "the basics" than the international norm. It seems
highly likely that U.S. student achievement in mathematics will be below international averages.
Our science curriculum is less fragmented. Science achievement seems likely to be closer to
international averages, but still not what we desire and certainly below some, if not most, of our
economic peers. U.S. students' achievements the yield of our aggregate national education
"system" in mathematics and the sciences are likely to be disappointing and many of the reasons
are not under students' control. We must make substantial changes if we are to compete and to
produce a quantitatively and scientifically literate workforce and citizenry.
How Has Our Vision Become So Splintered?
Culture affects education, even in supposedly fixed disciplines such as mathematics and science.
Countries differ in the priorities they give to these disciplines, in the way they organize
instruction and the value they ascribe to academic success. The qualitative differences found in
mathematics and science instruction across France, Japan, Spain, Switzerland, Norway and the
U.S. suggest that strong cultural components, even national ideologies, are at work in the
teaching of these subjects. The current state of our nation's composite visions guiding
mathematics and science education are clearly shaped by cultural forces particular to the U.S.,
starting with the nation's decentralized approach to education.
The Impact of Reform
- A System With Many Actors
Education in the U.S. always has been guided by agencies and organizations local, state, and national, official and unofficial that take their share of responsibility for education.
There are many actors, including states, schools, commercial publishers, national
associations, test publishers, teachers, and the federal government. While the
independence of these groups is essential to education in the U.S., the result is a
composite of sometimes corresponding, sometimes conflicting separate visions. The
conversations that cumulatively shape the national visions of mathematics and science
education in the U.S. appear to be held in the tower of Babel. Our earlier statement that
there was "no one helm" for mathematics and science education should not be taken as
implying that there should be either a single helm or a single helmsman. At its best, our
system of distributed educational responsibility allows local preferences and community
needs to help determine what occurs in local schools. It also provides laboratories to test,
implement, and replicate new approaches. At its worst, our system requires that we seek
consensus on needed changes site by site. Given the cultural context in which
mathematics and science education is carried out in the U.S., a decentralized system with
many actors s inevitable. We hope the splintering is not.
- A Diverse Market for Curricula and Textbooks
U.S. textbook publishers face varied, often conflicting, demands for what should be in
mathematics and science textbooks. Official mathematics and science curricula vary
widely among states and districts. Over 35 states have textbook adoption policies, but in
many states districts are free to choose any textbook. Textbook publishers are
understandably eager to produce products that will appeal to as many markets as possible.
The results are large textbooks that embrace virtually all suggestions offered by the
various actors. They include something for everyone. If a clear, coherent vision of what is
important existed and was shared by virtually all textbook publishers, it is likely that the
resulting materials could soon lead to wide official adoption reflecting that coherent
- Standardized Tests
The cacophony of conflicting demands seen in curricula and textbooks is exacerbated by
pressures to provide for successful student performance on common standardized tests.
These include state assessments and the National Assessment of Educational Progress
(NAEP) tests as well as commercially produced and locally mandated standardized tests.
Despite a seeming sameness about most standardized tests, there are differences in
content emphases and student performance demands. These differences are sufficient to
constitute yet another set of demands to try to reconcile.
- Mass Production and Mass Education
U.S. education has been influenced profoundly by a deeply seated American ideology
springing from our national experience with the power of industrial and assembly line
production. This ideology revolves around the idea of producing uniform,
interchangeable parts that can be assembled into desired wholes. Translated into
education, such thinking views school mathematics and science as partitioned into many
topics that form the building blocks of curricula. As a result, our students may grasp the
pieces but not the whole. We have applied the term incremental assembly to this ideology and believe that it may well keep the U.S. from finding other, more coherent and
powerful ways to think about and organize curricula. This is unfortunate. Henry Ford,
presumably, did not try to make all models simultaneously on the same assembly line.
The lack of focus in U.S. mathematics and science education also has roots in behavioral
psychology, which has pushed education in the direction of behavioral objectives and
programmed instruction. This notion may help explain our curricula of many small
topics, frequent low demands, and interchangeable pieces of learning to be assembled
In the U.S. today we live in a climate of reform and talk of reform. Professional organizations
concerned with mathematics and science education issue platform documents setting out
agendas, benchmarks and "standards." These powerful, demanding, and insightful calls for
reform offer coherent visions of what might be done to make major improvements in their
targeted educational practices. What has been their impact on mathematics and science
Who Are Our Curricular Peers?
- Awareness of Reforms
As late as two years ago, state mathematics and science curriculum guides, plans, and
statements of intentions still called for coverage of far more topics than most other
countries did and, far more than would be indicated by current reform agendas in
mathematics and science education. The same can be said of textbooks. U.S. mathematics
and science teachers are generally aware of these reforms. More than 75 percent of U.S.
mathematics teachers indicated familiarity with the NCTM Standards. Fewer U.S.
science teachers indicated similar familiarity with the corresponding science frameworks,
but those were released five years after the mathematics report. These data suggest that
more time alone will not be enough. Failure to create widespread change in teaching
practice does not appear to be due to lack of information.
- An Unfocused Reform
U.S. mathematics and science educators approach reform in the same inclusive style as
they deal with traditional content they add its recommendations but do not take away.
This is clearly contrary to the recommendations of the NCTM Standards. Textbooks have
been affected to some extent by mathematics education reform recommendations, but in a
similar inclusive manner. As a result, students cannot focus on or be successful in either
the old or new curricula. This development is troubling because the reform agendas
typically are coupled with more demanding, time-consuming and complex performance
expectations that require paying careful attention to a smaller number of strategic topics.
Adding more topics will not help. The impact of science reform recommendations
remains untested as yet. Reform documents themselves often emerge from compromise
among professionals, and this compromise may prevent them from stating a single vision.
Even when a reasonably coherent voice emerges for reform for example, the NCTM
Standards in math education and the National Research Council's National Science Education Standards our organizational context causes it to be heard as simply one more
voice in a "babel" of competing voices. This "babel" becomes so overwhelming that it is
hard for official actors to separate "signal" from "noise" or to prioritize the voices to
which they will listen. In such a systemic context, splintered visions are likely to remain
- The Need for Time
The lack of success reform measures have had to date does not imply that they have been
futile. Rather, they imply that reform may take considerable time. Slow progress is
certainly no reflection on the quality or power of mathematics and science reform efforts
that have yet to be as effectual as their supporters wish in this climate. Certainly it would
be drastically wrong to conclude, based on these "early returns," that these reforms have
failed. Rather, it seems more appropriate to be amazed at their current successes.
If we take seriously that the proportions of curricula, as set forth in state guidelines and
textbooks, set bounds on what is broadly achieved by those taught, we should identify those
countries that set similar bounds to their students' achievement. In grade eight mathematics, the
U.S. composite curriculum as represented by textbooks is most like those of Australia, New
Zealand, Canada, Italy, Belgium (French language system), Thailand, Norway, Hong Kong,
Ireland, and Iceland. In grade eight science our curriculum is most like that of New Zealand,
Iceland, Greece, Bulgaria and the Peoples' Republic of China.
Are These the Peers We Want?
While the curriculum of any country is interesting and has some important features, we must ask
if these are the countries with whom we are and will be trying to compete. As a nation we desire
to empower and inform our citizenry comparably as well as to effectively compete economically
with other developed countries. We want attainments similar to the European Union, to the
APAC countries (especially Japan and the "young tigers" of Korea, Singapore, etc.), and, most
definitely, with the other G-7 countries. When we find ourselves most similar to countries other
than those with whom we seek to be peers, we have reason for deep concern. In matters of what
is basic in teaching children mathematics and science, we are not peers with the composite of
other TIMSS countries. We as a nation must be concerned.
What is Necessary for Reform to Succeed?
The U.S. vision of mathematics and science is splintered. We are not where we want to be. We
must change. But the required change is fundamental and deeply structural. There are no single
answers or instant solutions. Most nations do not share similarly splintered visions in
mathematics and science education. Theirs are more coherent. While central guiding visions do
not alone guarantee student achievement, they contribute to optimal attainments. These shared
visions are insufficient to ensure desired achievements, but they seem necessary starting points.
The U.S. has a decentralized educational system in which the component organizations do not
always work towards common goals, nor do they always aim at producing important combined
results. Formal mechanisms of coordination either by regulation or rewards for selected
behaviors have proven politically sensitive and are in limited use. Given such a culture of education, how can a focused vision be achieved? Several principles would seem to be at work:
- Effective Reform Will Necessarily Be Systemic
Information- and motivation-based reforms and improvement policies alone will not
bring fundamental improvements. Any serious attempt at change in U.S. science and
mathematics education must be deeply structural. The fundamental problem is not a
conglomeration of individual problems. Any effective reform in this context will
necessarily be systemic affecting several parts at once. Not every systemic reform
automatically will address the core of our problems. Appropriate structural reform must
pursue focused and meaningful goals. We may not be able to do everything and do any of
it well. Instead, it appears we must make choices regarding which goals are more
important and how many goals we can effectively pursue.
- Effective Reform Must Respect Cultural Context
Whatever actions are taken must be appropriate to our educational federalism and our
context of shared educational responsibility. When discussion suggests the need for more
powerful and coherent guiding visions, they must be sought in processes that will achieve
wide consensus necessary for change in our context. A corollary is that we may learn
from other countries but we cannot emulate their centrally administered changes. Any
reform in the U.S. must seek visions that can achieve broad consensus.
The U.S. needs powerful mathematics and science education because they:
Perhaps we do not need a central focus for our curricula and teaching. Perhaps the value of
diversity outweighs the value of focus. Perhaps our de facto emphasis on breadth will prove
more effective overall than other countries' strategies of focusing on strategic topics. That is a
matter for further empirical evidence and public discussion.
- Provide a strong basis for our democracy by helping create a literate and informed
- Help each individual to grow, develop, reach his or her individual potential, and become
more autonomous and empowered; and
- Provide a sound basis for continuing national prosperity in a competitive, information-driven,
technological, and changing international arena.
Both conventional wisdom and a considerable body of research, however, suggest that focus and
selection are needed in situations in which too much is included to be covered well. The impact
of these unfocused curricula and textbooks in mathematics and science likely includes lower
"yields" from mathematics and science education in the U.S. Focus would seem to be a necessary
but not a sufficient condition for high student attainments.
What kinds of mathematics and science education do we, as a nation, want for our children?
While this is a central question for public debate, it seems likely that we want educations that:
Questions to Ask
- Are more focused, especially on powerful, central ideas and capacities;
- Provide more depth in at least some areas, so that the content has a better chance to be
meaningful, organized, linked firmly to children's other ideas, and to produce insight and
intuition rather than rote performance; and
- Provide rigorous, powerful, and meaningful content that is likely to produce learning that
lasts and not just learning that suffices for the demands of schooling.
The authors of this report do not represent any official or policy-making group. Our job has been
to design relevant research, analyze its results carefully, and report them objectively. Because of
who we are, we do not feel it appropriate to make specific recommendations. We can, however,
at least ask questions questions that our results lead us to believe important for those who do set
Most of these questions are not original with us, although their form here has been influenced by
the data we investigated. In fact, some efforts are currently underway to address these questions,
including the National Science Foundation's State Systemic Initiatives and the recently convened
executive committee of the National Governors' Association in conjunction with business
leaders. Those efforts may include answers to several pressing questions raised by these findings:
Certainly these are not the only questions that must be asked and answered on the way to the
revolution or, if one prefers, to a fruitful evolution in mathematics and science education. We
have not touched on whole domains of issues for example, concerns for equity in educational
opportunity because we did not want a report on the "splintered vision" of our children's
education to be itself unfocused. Others must join in seeking answers to the questions raised here
and the others we did not raise. Our data can help.
- How can we focus our mathematics and science curricula and textbooks around an
intellectually coherent vision?
- How can we raise expectations and demands on our students?
- How can we help our teachers to do the best they can in teaching mathematics and
science to our students?
- How can we find a better model for curriculum and instruction?
- How can we develop a new vision of what is basic and important?
Presently, however, our story is simple. The U.S. vision of mathematics and science education is
splintered. We are not where we want to be. We must change.
1 The first, Characterizing Pedagogical Flow, discusses curriculum data in mathematics and science along with
classroom observations and teacher interviews in six TIMSS countries. The second and third, Many Visions, Many
Aims: A Cross-National Investigation of Curricular Intentions in School Mathematics and Many Visions, Many
Aims: A Cross-National Investigation of Curricular Intentions in Science Education, are reports that present data on
the full set of almost 50 TIMSS countries.
2 At that time the National Council of Teacher of Mathematics (NCTM) Standards (for mathematics education) had
only existed for about three years. The American Association for the Advancement of Science's (AAAS)
Benchmarks (for science and mathematics literacy) had been released only in preliminary form. The National
Academy of Science's National Research Council's Science Education Standards had yet to be fully formulated or
released. Therefore this report cannot offer any conclusions about these reforms.
3 Because the U.S. does not have a national curriculum we aggregated states to find a representative average.