Conference Material

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.

• 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 vision.

• 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 later.

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 education?

• 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 splintered.

• 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:

• Provide a strong basis for our democracy by helping create a literate and informed citizenry;

• 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:

• 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 policy.

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:

• 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.