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ACTION ...moving into the 21st century Over the next two decades, the nation's schools, colleges, and universities will undergo major transitions in their math- ematics programs transitions that will involve fundamen- tal changes in curricular content, in modes of instruction, in teacher education, in professional development, in methods of assessment, and in public attitudes. Not only will calcula- tors and computers displace some of the computational drill that currently dominates the curriculum, but also their pres- ence will stimulate new approaches to understanding mathe- matics and to solving problems. The dramatic advances that have been made in the mathematical sciences over the past forty years will start to be felt in the schools, in the form of new and exciting ways to help young minds perceive and order the universe around them. If such transitions are to become reality, all major components of mathematics education" curricula, teaching, teacher education, testing, textbooks, and software must change significantly in some reasonably coordinated man- ner. National leadership is needed to coordinate efforts by the primary agents for change and to garner support for them by government, business, industry, and the public. T .................................... In the next decade, the United States has a historic opportunity to revitalize mathematics education. Although many parts of education need improvement, there are at this time both a particular urgency and a spe- cial opportunity for reform of mathematics education. Since mathematics is the foundation of science and technology, reform is needed to prepare the more highly skilled work force that the nation now needs. Because of emerging general agreement within the mathematics, mathematics education, and related professional communities on goals for mathe- matics education and means for achieving them, there is at this time a special opportunity for the nation to push ahead boldly in this area of education. 87

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Action 88 National Goals Our national goal must be to make U.S. mathematics edu cation the best in the world. Nothing less will be adequate to fulfill American aspirations. To achieve this goal will require significant actions that respond to a three-tiered challenge to: Make mathematics education effective for all Americans; Improve significantly students' mathematical achieve- ment; Develop new curricula appropriate to the mathematical needs of the twenty-first century. O . . .. - ur national goal must be to make U.S. mathematics education the best in the world. American education is a loosely coupled system grounded in state and local autonomy, although important factors (textbooks, standardized testing, teacher education, and uni- versity admissions requirements) have nationwide influence. To change mathematics education in the United States, one must influence not only teachers, but also a host of other special interest groups that control parts of the educational system: state and local agencies, teachers and administra- tors, local and state school boards, colleges and universities, textbook publishers, software developers, professional soci- eties, test-makers, state legislators, employers, parents, and the general public. Actions designed to begin these transitions must be based on a broad understanding of the total American system of mathematics education. Unless change is based on a sys- tematic overview of all pertinent issues and an assessment of current programs, it will have very little chance of achiev- ing national impact.

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...moving into the 21st century Reaching Consensus High-quality mathematics education requires national consensus on objectives and standards, leaving wide lati- tude for local variation in means of implementation. With- out common standards, different communities will move in different directions, inevitably widening the gap in mathe- matical power available to children raised and educated in different circumstances. National consensus on common ob- jectives should make possible policies that will ensure that all students benefit equally from the opportunities provided by mathematics. " .-- --.--.- ----.---.----- Duilding national consensus is the first step in renewal of school mathematics. Although pressure for change is high, little consensus exists on what mathematics students ought to learn now, much less on what they will need for the future. Lack of national focus has created such disparities among standards that it is difficult to discuss curricula in meaningful and productive contexts. Teachers have received such mixed signals that even the best of them often do not know which choices to make in those few classes where they have some discretion over what to teach. The new Curriculum and Evaluation Standards for School Mathematics, being published in early ~ 989 by the National Council of Teachers of Mathematics (NCTM), focuses na- tional attention on specific objectives for school mathemat- ics. That report, the draft of which has been reviewed ex- tensively by teachers and the public, has received widespread support in the mathematical and educational communities. It represents the first effort ever to establish national expec- tations for school mathematics. In keeping with American school traditions, the Sfanciards report is not the result of government edict, but the product 89

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Action Why Not Just Imitate Japan? International studies of math- ematics and science education show that, when compared with students in other countries, U.S. students do very poorly while Japanese students do very well. One natural response, therefore, is to think that we could improve our educational system by imitat- ing Japan. These same studies, however, document that the social con- text of education has a greater influence on student performance than does actual classroom prac- tice. Parental attitudes, student expectations, and teacher self- respect are among the most sig- nificant factors in quality educa- tion and they depend uniquely on culture. Imitating others is no solution. The United States must find a strategy that builds on the tradi- tions of this country, one whose strength lies in this nation's unique tradition of local initia- tive and decentralized authority. 90 of the nation's mathematics teachers themselves. It leaves much leeway for local initiative in implementation and for teacher ownership of specific curricula. Through the Stan- dards, parents and teachers will be able to understand in concrete terms what a school mathematics program might look like if it is to serve our national objectives adequately. The ensuing public discussion on feasibility, appropriate- ness, costs, and benefits will provide an unprecedented op- portunity to forge national consensus on goals and objectives for school mathematics. National Strategy New strategies for renewal of mathematics education must be based on what we have learned about making changes in the extremely decentralized U.S. system where local and state agencies control education. Two special strengths of American mathematics education should underpin any movement for renewal: The creative efforts of many teachers, schools, and projects around the country. The strength of coordinated national leadership which has evolved within the communities of mathematicians and mathematics educators. Together, these resources provide an "augmented grass- roots" mode! of curricular development, harnessing the power of a centralized system with the flexibility and ini- tiative of the decentralized U.S. tradition. The objective of our national strategy must be to make significant improvements in mathematics education on a na- tional scale. To do this, we must first reach consensus on the transitions required to revitalize mathematics education and then help local educational leaders move mathematics edu- cation through these transitions. Inevitably, this process will lead the American public into uncharted territory, paving a new road for mathematics education that balances national goals with local jurisdiction.

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...moving into the 21st century R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eform of mathematics education requires voluntary local implementation of common national standards. The key to success is voluntary acceptance of a common framework to guide local choices: National Standards. School mathematics programs across the nation should share a common philosophy and frame- work, a universal set of interrelated concepts and methods, held together by a simple workable philosophy, yet flexi- ble enough to allow for local and regional variations. In a highly mobile society, the basic framework should be transportable and adaptable. Local mp;lementation. Changes in mathematics curricula must be proposed and undertaken freely by those who bear direct responsibility for curricula in the schools. A deep sense of identification with those changes must be devel- oped within the entire community. In particular, teach- ers and parents need to be involved in adaptation and decision-making in a thorough and comprehensive way. Implementation will require more than good will and community dialogue; it will need professional leadership of teachers operating in a transformed school environment. No one should underestimate the complexity of the challenge; elective reform will be truly difficult to accomplish. Few teachers in today's schools have the authority or resources necessary to carry out this agenda. But as schools evolve from a mode} with teachers as hired hands to one in which teachers function as professional educators, schools should welcome the challenge to implement national standards for mathematics education. Support Structures In order for this strategy to work, the United States must develop new national support structures to help states and 91

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Action 92 localities promote excellence in mathematics education for all students. These structures must assure appropriate con- sistency among the nation's many different school districts, yet encourage a sense of local ownership by allowing adap- tation to local preferences. important parts of this national structure are in place al- ready, while other parts will emerge in coming months and years. Professional organizations (the National Council of Teachers of Mathematics, the American Mathematical So- ciety, the Mathematical Association of America, the Soci- ety of Industrial and Applied Mathematics, the American Statistical Association, the Conference Board of the Mathe- matical Sciences) are actively engaged in projects that seek to improve the teaching of mathematics. Related actions of other groups such as the National Congress of Parents and Teachers, the National Governors' Association, the National School Boards Association, and the American Association for the Advancement of Science will ensure a vigorous na- tional dialogue, which is a necessary prerequisite to national consensus. As schools are not the sole source of America's problems in mathematics education, neither can they be the sole vehicle for renewal. Informal, nonschool-based undertakings that support school-based mathematics education can be found in clubs, churches, and scouting. Community organizations electively complement schools, reaching youth- especially minorities who find school uninspiring. Being outside the formal public structures, community organizations offer a testing ground to validate the power of innovative or uncon- ventional ideas. Building national consensus requires effective national leadership. To stimulate informed debate about curricular change, the Mathematical Sciences Education Board is preparing two re- ports on concepts and principles of mathematics suitable

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...moving into the 21st century for the education of students who will work in the twenty- first century. One, a statement of philosophy and curricu- lar frameworks, provides a general structure that can guide curriculum development for the future. The other, on ma- jor strands of mathematical thought, is intended to stim- ulate creative development of new curricula that embody a broader interpretation of mathematics. These strands- chance, change, shape, quantity, dimension are examples of deep ideas of mathematics that could become organizing principles for some future mathematics curriculum. These actions of many different groups representing mathematicians, scientists, educators, and administrators- will form the basis of a national consensus for new directions in mathematics education. Leadership Real change requires action by everyone involved in math- ematics education. Current efforts to forge national consen- sus will not in themselves transform what happens in schools or colleges. Change in the institutions of education must come about as the result of intensive debate within each in- stitution. There is plenty of work for everyone: STUDENTS: Study mathematics every school year. Discover the mathematics that is all around us. Use mathematics in other classes and in daily life. Study a broad variety of mathematical subjects. 1 EACHERS: Talk with each other about mathematics. Examine current practice and debate new proposals. Engage students actively in the process of learning. PARENTS: Demand that schools meet the new NCTM Standards. Encourage children to continue studying mathematics. Support teachers who seek curricular improvements. Expect homework to be more than routine computation. 93

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Action 94 PRINCIPALS: Provide opportunities for teachers to work together. Become educated on issues in mathematics education. Support innovation. Encourage paired teaching in elementary school. SUPERINTENDENTS: Stimulate public discussion of mathematics education. Provide resources for curricular innovation. Support a climate of change. SCHOOL BOARDS: Establish appropriate standards for mathematics. Align assessment with curricular goals. Support innovation and professional development. CoMMuN~TY ORGAN~zAT~oNs: Enrich mathematical opportunities for all students. Support local efforts to improve mathematics education. Explain to the public the need for change. STATE SCHOOL OFFICERS: Promote adoption of NCTM's Standards. Encourage use of elementary mathematics specialists. Speak out publicly about mathematics education. Stress assessment of higher-order thinking. Co~EGE AND UN~vERs~TY FAcu~TY: Make introductory courses attractive and effective. Restore integrity to the undergraduate program. Lecture less; try other teaching methods. Link scholarship to teaching. Co~EGE AND UN~vERs~TY ADM~N~sTRAToRs: Reward curricular innovation and good teaching. Recognize that mathematics classes need computer labs. Diminish reliance on underprepared, part-time faculty. Emphasize and improve teacher education. Business AND INDUSTRY: Encourage students to study mathematics and science. Do not steal good teachers by hiring them away. Support local efforts to secure funds for education. Support strong continuing education, not remediation. Provide internship opportunities for teachers.

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...moring into the 21st century STATE LEGISLATORS: Work with school leaders to support effective programs. Recognize that mathematics education is an investment. Resist pressures for simplistic cures. GOVERNORS: Provide resources to encourage change. Demand new standards for mathematics education. Lead the public to make wise choices among priorities. Create enrichment programs for able students. CONGRESS: Stress education as an essential investment. Support mathematics education at all levels. Reward effective programs. THE PRESIDENT: Meet with state governors to affirm the national agenda. Focus public attention on mathematics education. Stress education as crucial to national security. Taking Action Once vigorous dialogue and grass-roots actions begin forg- ing national consensus on goals for school mathematics, sev- eral important national objectives must be addressed: Establish new standards for school mathematics. Upgrade the teaching profession. Make assessment responsive to future needs. Strengthen collegiate mathematics. The first of these will emerge, with sufficient effort, follow- ing public dialogue about the NCTM Standards. The second is currently being advocated through the work of the Na- tional Board for Professional Teaching Standards. The third, assessment, may require a new, cooperative, national mecha- nism to unlock the stranglehold that state and national test- ing programs largely secret have on today's classrooms. Finally, strengthening college and university mathematics- including specific attention to those who become teachers, how they teach, and what they teach is the primary task of the National Research Council's Committee on the Mathe- matical Sciences in the Year 2000 (MS 2000~. 95

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Action "Children are the future. Everythi1'g we dFo is for them and everything that will be done will be done by them." Clay Morgan 96 l Efforts to change must proceed steadily for many years, on many levels simultaneously, with broad involvement of all constituencies at each stage. First comes serious discus- sion; then, compromise and consensus; finally, action and change. Even as different groups work to improve curricu- lar standards, the teaching profession, assessment practices, and collegiate mathematics, other groups must help focus the diverse efforts of business, industry, government, volun- teer organizations, and educational organizations on com- mon objectives. As there is no royal road to geometry, so there are no quick fixes for mathematics education. Both for reasons of international competitiveness and sci- entific leadership, the United States must move quickly to improve the state of mathematics education. It takes a gen- eration to complete the mathematical education of a single individual. The first high school graduates of the next cen- tury entered elementary school in 1988. No longer can we afford to sit idly by while our children move through school without receiving mathematical preparation appropriate for the twenty-first century. The challenges are clear. The choices are before us. It is time to act.