Teaching is a complex interaction between the teacher, the content being taught, and the students. In order to make change in the teaching and learning of mathematics, each of these - teacher, curriculum and student - must be considered. It is the total environment in which teaching and learning takes place that must be reformed.

In the Curriculum and Evaluation Standards for School Mathematics the argument is made that what is needed is a design change strategy This means that new ways of doing things within the system - new roles for teachers and students, new goals, new structures - must be explored to find solutions to persistent problems that result in students failing to become mathematically powerful.

The Curriculum and Evaluation Standards for School Mathematics is an initial step in this process of design change. It provides guidance for the restructuring of the school mathematics curriculum and for evaluating students and programs. These standards are not a prescription for what must be done at each grade level. They present a vision of what a high-quality mathematics education for students should entail. The Professional Standards for Teaching Mathematics provides similar guidance about the kinds of teaching environments, actions, and activities that are needed in order to realize the goals for students that are envisioned in the Curriculum and Evaluation Standards for School Mathematics. Teachers, administrators, parents, other educators, and policymakers in government, business, and industry are expected to work collaboratively to reach consensus on how their school mathematics programs need to be changed and what steps are needed to make that change.

A dialogue on school reform is taking place on many fronts. In local areas, individual schools, districts, and universities are approaching change in different ways and taking steps in different sequences. What is important is that there be systematic long term commitment to change that heads in an appropriate direction. One of the strengths of the educational system in North America is its diversity. Different combinations of ideas and strategies will provide many ways to achieve the goal of reforming mathematics teaching and learning. In addition to the possible paths discussed in the Curriculum and Evaluation Standards for School Mathematics, the following suggestions focus specifically on teaching and the profession of teaching.

Professionalism. At the present time, teaching as a profession does not receive the public support and esteem that it deserves. Teachers often find themselves in positions where decisions that greatly impact their ability to teach are being made by persons who do not have the expertise that teachers have gained through their education and experience. Yet it is the teachers who are held accountable to the public for the mathematics proficiency of their students. A number of efforts are already under way to rethink the roles of teachers as professionals. This movement to raise teaching to a profession with all of the rights and responsibilities entailed is consistent with the vision contained in these Professional Standards for Teaching Mathematics. For example, as the National Board for Professional Teaching Standards moves toward the certification of teachers for differentiated roles in their schools, we expect that it will look to these teaching standards for guidance in developing policies and procedures for the evaluation of mathematics teaching. Professional mathematics teachers are accountable for teaching mathematics in an intellectually honest and effective way and for making appropriate instructional decisions. Further, they must be an integral part of the ongoing development and regulation of the profession. Mathematics teachers entering teaching should have the support of mentors who are experienced teachers of mathematics. Not only should programs for the professional development of teachers become an established part of school life, but they should be responsive to teachers' needs at all stages of development. As teachers become more experienced and effective, they should be promoted and accepted as leaders in their schools and in the profession as a whole.

Schools have a great deal to gain by supporting teachers' professional development. The teacher is the key to learning in the classroom. Through the individual acts of teachers, the reform of school mathematics will become a reality. Teachers who have the self-esteem and the intrinsic reward that comes from being encouraged to grow in their profession will provide an environment for students in which students see the excitement and usefulness of mathematics. Further, these teachers will provide role models to attract talented students to enter the teaching profession.

Structure of schools. With the growth of professionalism comes the need for a fundamental rethinking of the structure of schools. At the present time teachers are often faced with trying to teach mathematical inquiry in time periods that are entirely inappropriate. Changes, such as meeting classes less often but for a longer period of time, should be explored. Teachers need time to plan, discuss problems with their colleagues, visit another teacher as a peer coach, study, and revise and develop curriculum. Some teachers find it difficult to obtain permission and support to attend professional mathematics meetings. Yet it is through such stimulation that teachers grow and maintain their knowledge about, and enthusiasm for, teaching mathematics and making improvements in classroom instruction. Providing teachers with the support to make instructional decisions is essential. Mathematics teachers often do not have the necessary resources to do their jobs well. They need calculators, computers, software, manipulatives, and other resources to create the kinds of environments for learning that students need and deserve. Giving teachers more responsibility in the budgeting of school resources is also an effective way of improving mathematics instruction. These kinds of changes, and others perhaps not yet conceived, may provide the stimulus needed to effect real change.

We must think creatively and courageously consider changes in the basic structure of schools; try alternatives and carefully study the effects; and create different working models of school structures in which students' mathematical power and teachers' professional growth far exceeds today's models.

Entry into the profession. The current shortage of qualified mathematics teachers and the changing nature of the pool from which teachers come has spurred experimentation with different forms of initial licensure. Induction programs that offer a form of in-school apprenticeship to persons holding undergraduate subject matter degrees are being tried in various places. Other forms of initial licensure for teachers are likely to be tried. These Professional Standards for Teaching Mathematics will provide guidance for such induction and licensure programs. Whether teachers enter teaching through four-year, five-year, or induction programs, it is essential that they know the subject matter of mathematics, how students think about mathematics, strategies for teaching mathematics, how to select or create mathematical tasks, and how to create an environment for learning mathematics in which all students develop mathematical power.

Teachers of elementary, middle, and high school mathematics need broad and deep knowledge in three fundamental domains: mathematics, mathematics teaching, and students. This knowledge should be appropriate to the level that they will teach or are teaching. However, teachers need to know both where their students have been and where their students are going mathematically. This means that an elementary school teacher needs to have experience with the big ideas of school mathematics at all levels. In addition, the high school teacher needs to understand what significant mathematical ideas are taught prior to high school and how they are represented. Middle school teachers need to be able to connect what they are teaching to the elementary school experiences of students and also to anticipate the growth of mathematical ideas as the students proceed into high school. Therefore, all programs need to be examined carefully to determine whether teachers in the program are being helped to develop a broad range of vision about the mathematics curriculum, student learning, and teaching.

School mathematics as a part of mathematics. Mathematics has changed dynamically in the past twenty-five years, but school mathematics has not reflected these changes. It has become an entity that is not perceived even by teacher education students at colleges and universities as having much to do with "real" mathematics. Part of the responsibility for this schism between school mathematics and the mathematics studied at university rests on the shoulders of university and college mathematicians. Preservice teachers seldom have opportunities to see how the mathematics that they are studying relates to the mathematics of schools. In addition, students at both levels, school and college, are often being taught an outmoded curriculum that has very little to do with what is important in mathematics today. A reexamination of the relationship of school mathematics and mathematics is a necessary part of the needed reform.

Collegiate curriculum. In the Curriculum and Evaluation Standards for School Mathematics and the Professional Standards for Teaching Mathematics a vision to guide reform of school mathematics curriculum, teaching, and evaluation is articulated. However, if teachers are to change the way they teach, they need to learn significant mathematics in situations where good teaching is modeled. The collegiate community is beginning to examine aspects of the college undergraduate curriculum. We believe that this effort should be expanded to include consideration of the entire undergraduate curriculum and, perhaps even more important, to the models of instruction used in collegiate classrooms. For example, technology and its use in doing, teaching, and learning mathematics is a responsibility of the mathematics community as well as the mathematics education community. Teachers need to learn in technology-rich environments if they are to teach using technology.

Collaboration between schools and universities. As new structures for the professional development of teachers are created, the lines between universities and schools should become blurred. The interaction of university faculty and school faculty as colleagues with different areas of expertise is likely to improve the teaching and learning of mathematics at both the collegiate and school level. Mathematicians have a responsibility to find creative ways to share the excitement of new advances in mathematics both with school teachers and with their students. The pool of young people who are interested in pursuing professions in mathematics or the sciences is far too small for the needs of society. From this pool of young people who have an interest in mathematics will come the teachers of tomorrow. Raising the prestige and rewards of teaching is critical to attracting talented and caring young people into teaching.

Of particular concern is the small representation in the scientific pool - and hence in the pool of teachers - of women, ethnic minorities, handicapped, and other underrepresented students. Mathematicians and mathematics educators at all levels have a responsibility to invest time, energy, and their creative talents in finding ways to communicate the excitement and the usefulness of mathematics to young people, and to devising programs that help underrepresented students succeed in their study of mathematics. Beginning at the university level is too late. To have the desired impact we must begin at the elementary school level. Mathematics educators at all levels need to take responsibility and work together to get all students interested in mathematics in elementary school and to help maintain that interest through middle school, high school, and beyond.

As schools and universities strengthen their ongoing communication, mathematics programs can be articulated between elementary school, middle school, high school, and college. Support groups can be established for teachers at all levels who are attempting to implement the standards.

Expectations. One of the curious aspects of our society is that it is socially acceptable to take pride in not being good in mathematics. A phrase often heard by those who teach mathematics is, "Oh, I was never any good at mathematics." Other societies make the assumption that all students can learn mathematics and that learning is a matter of effort. In our society, we are more likely to think that persons are either born with a mathematical mind or they are not. Our expectations have a great deal to do with how we respond to students and consequently to what students believe that they can do. Teachers, counselors, parents, school administrators, and students themselves need to have high expectations that every student can learn mathematics. The two sets of standards challenge us to create learning environments for students and for teachers in which the building of confidence in the learning and doing of mathematics is a primary goal.

Accrediting and certificating agencies. Just as tests are influential in determining the mathematics curriculum, accrediting agencies such as the National Council for the Accreditation of Teacher Education and state or provincial certificating agencies influence collegiate teacher preparation programs. These agencies can be a constraint on needed change or a force for the improvement of teaching. Such agencies can play a positive role for reform as they work with the professional organizations and schools to be sure that their guidelines are in tune with the goals and vision of teaching that the profession espouses.

For example, accrediting agencies can set guidelines that expect schools of education and mathematics departments to be technology-rich environments in which to learn. These standards documents are the consensus of the mathematics and mathematics education communities and can provide guidance to accrediting agencies in determining their criteria for judging mathematics teacher preparation programs.

States and provinces have departments of education that are responsible for the monitoring of school programs, requirements, and offerings. They also are the principal agents for the initial certification of teachers. In both of these roles, state departments of education should review their practices in light of these standards documents. An additional role for departments of education is to assure that professional development opportunities are organized and available to help teachers and schools implement these standards for school mathematics curriculum and teaching.

Networking with other disciplines. An interesting aspect of school reform is that different disciplines are discovering common goals and common strategies for achieving them. For instance, language arts teachers are working on communication, which is a major goal for the mathematics curriculum at all levels. Networking, sharing ideas, learning from each other, and helping to support another discipline in our mathematics classrooms helps everyone succeed. Students can see the commonality of strategies for attacking problems and the help that discussion and argumentation is to the refining of ideas. They also should see this in social studies, science, language arts, and all school subjects. Cross-discipline studies give additional meaning to strategies and concepts and add interest and variety to the learning process. Given the few hours in a school day and the amount of material to be covered, it is in the best interest of teachers in all disciplines to seek common ground and to support each other.

Research. The vision set forth in the Professional Standards for Teaching Mathematics is based on a set of values and beliefs about mathematics teaching and learning that are consistent with current research. However, these standards suggest a research agenda with respect to teacher education and learning to teach. There is much that we need to know that cannot be determined from current practice. We need experimentation and careful research, new structures of schools, new interactions between universities and schools, new teacher education programs, school and university professional development programs, teaching and learning with computing technology and other forms of technology and tools, new forms of instruction in university and school mathematics classes, and other aspects of reform. Researchers are already engaged in accumulating evidence in many of these areas. It is important that these efforts continue and that universities and the mathematics education community value such research. Results of such studies are needed to guide us on the many possible paths to reform in mathematics teaching and learning.

The kind of teaching envisioned in these standards will take time. We need to understand the trade-offs of changing from "covering" a broad set of mathematical topics to more in-depth investigations of, perhaps, fewer mathematical situations. We need to understand better how to meet the mathematical needs of a diverse student population. We need to understand better how small groups and classroom discourse can be used to facilitate students learning to make mathematical judgments and to enhance their mathematical power. The instructional use of manipulatives, calculators, computers, and other tools and technologies for teaching mathematics needs to be continually studied, with a particular concern for the needs of diverse students. As reform proceeds, many other issues will arise that will need careful study. Research is yet another arena in which schools and universities have much to gain by collaborating with each other.

There are many possible next steps to improving mathematics teaching and learning. If we make a long-term commitment to the standards set forth within this document and in the Curriculum and Evaluation Standards for School Mathematics, if we approach the task with the will to persevere, if we are critical of the steps we take, and if we make mid-course corrections, we will make progress toward the goal of developing mathematical power for all students. The picture of mathematics teaching and learning that is presented in these standards is an ambitious one. We will not reach this goal overnight. Such change will take much work and dedication from teachers and many others. However, this effort is essential if we are to improve mathematics learning for our students. We must be impatient enough to take action and patient enough to sustain our efforts until we see results.

We urge you to start by reading both sets of standards. Talk to your colleagues. Discuss these ideas with parents; school and university administrators; and others in government, business, and industry. Collectively and individually set goals for change; establish a plan that will guide change over the next several years. Seek resources to support that plan. Be a part of working to make mathematical power a reality for every student.