Teachers of mathematics should take an active role in their own professional development by accepting responsibility for-

experimenting thoughtfully with alternative approaches and strategies in the classroom;

reflecting on learning and teaching individually and with colleagues;

participating in workshops, courses, and other educational opportunities specific to mathematics;

participating actively in the professional community of mathematics educators;

reading and discussing ideas presented in professional publications;

discussing with colleagues issues in mathematics and mathematics teaching and learning;

participating in proposing, designing, and evaluating programs for professional development specific to mathematics;

participating in school, community, and political efforts to effect positive change in mathematics education.

Schools and school districts must support and encourage teachers in accepting these responsibilities.

Elaboration

Teachers develop as professionals on an ongoing basis. Focusing on their classroom practice, they experiment with alternative approaches to engage students in mathematical ideas, possible strategies for assessment, and different ways of organization. They analyze and adapt strategies that they try, examining how well they help students develop mathematical competence and confidence. They incorporate such strategies into an ever-growing and more complex repertoire. Beyond the classroom walls, teachers also evolve as participants in a wider educational community. They read, talk with colleagues, take the initiative to press for changes, and raise their voices to speak out on current issues. Teachers' professional development, within and outside their classrooms, is a product of their reflectiveness and participation in educational opportunities that will enhance and extend their growth and development. As professionals, teachers take responsibility for their own growth and development.

There is a voice that is not heard often enough in schools these days: the concerned voice of the informed mathematics educator. We invite you to develop this voice. Having it, you can and should become an authority figure in your school-maybe not a power figure, in the sense that a principal has power-but an authority nonetheless. Your authority will come from knowing the things about the teaching and learning of mathematics that can be clearly known-knowing what is being tried about the country and with what success, knowing current opinions on what ought to be done, knowing your own program from stem to stern, and, above all, knowing the questions that one must keep asking. (Ohio Mathematics Education Leadership Council 1989, p. 1)

In addition, professionalism among teachers is built through a support system that links them to colleagues inside and outside the schools. Teachers should be able to turn to colleagues for information concerning any aspect of mathematics education in order to expand their views of mathematics, their resources for teaching, and their repertoire of teaching and learning skills. Such interchange provides intellectual refreshment and places teachers in the role of partners in the process of education. It also provides opportunities for heightened awareness of the responsibility for fostering their own professionalism by building collegial networks, reading professional literature, becoming involved with professional organizations, and initiating contact with teacher educators at local colleges and universities.

Teachers can take an active role in their professional development through such activities as-

• forming special-interest groups within their schools to investigate ways technology might better enhance their teaching;
• participating in summer programs to learn new topics in mathematics such as statistics or discrete mathematics;
• meeting with teachers from neighboring school districts to explore how they can jointly offer advanced mathematics courses for their students via telecommunications;
• working on curriculum renewal with other mathematics faculty to change the nature and kinds of courses that are being offered and align their program with the Curriculum and Evaluation Standards;
• joining local mathematics associations, attending meetings, making presentations, and assuming leadership roles.

Teachers who are engaged proactively in making mathematics education better demonstrate this in many ways. What is essential is that they view themselves as agents of change, responsible for improving mathematics education at many different levels: the classroom, the school, the district, the region, and the nation.

Vignettes

6.1 Dick Richey is a mathematics teacher in a large high school. Five years ago he was disenchanted with teaching. He was bored, his students were bored, and there did not seem to be any challenge in the job. He even considered leaving teaching.

Professional publications can help teachers keep in touch with the mathematics education community. In addition to providing substantive ideas about mathematics teaching, they can be sources of information about professional development opportunities.

Recognizing that significant teacher change requires ongoing support over time, the institute planners have developed a. three-year program.

He read about a three-year, federally funded summer institute on the teaching of algebra in an issue of the NCTM News Bulletin in the faculty resource room. He decided to apply but was rather apprehensive when he was selected.

During the first three-week summer session he was immediately thrust into the midst of twenty-four experienced teachers. Two university professors were determined to involve him in thinking deeply about what he was doing in his classes. Some of the mathematics content in the sessions was new to him. Other sessions focused on using technology to teach mathematics. Still others centered on teaching strategies and research on teaching and learning. Sharing and collegiality dominated their work together.

Through designing and participatingIn professional development opportunities the teacher and his colleagues contribute mutually to one another's growth.

Continued contact and collaboration over an extended period of time support the teachers in changing their practices.

Dick was terrified when he had to "go public" for the first time. He wasn't sure that what he was trying to do in his classes was anything new. Much to his surprise other teachers seemed to be very interested and gave him some other new ideas.

The continuing support and yearly visits from the professors helped Dick maintain his renewed perspective on his teaching. Throughout the program, the institute participants shared their ideas and struggles through electronic mail. In fact, this network continued and grew to include a great many high school teachers across the state.

In the years since the institute, Dick has continued togrow as a professional. Subsequently, he has been chosen to participate in additional summer programs. He and a colleague recently published a manual on teaching with graphing calculators.

6.2 Stacy Washington, a fourth- and fifth-grade teacher for three years, has grown increasingly dissatisfied with her mathematics teaching. She feels that she has successfully made the other subjects she teaches come alive for her students, encouraging them to think for themselves and engaging them in group discussions.

The teacher asks questions that challenge his students' thinking and encourage them to listen to one another and, as a group, makes sense of the athematics.

Through observing a colleague, the teacher reflects on her own teaching.

The students have not been taught the definition of slope, but they are discovering patterns that relate to the slope of the lines. Jon asks questions like, "Will this always be true? How do you know? Do you agree? Why?"

Stacy tries to imagine her students in a similar discussion. She realizes that she knows little about what her students are thinking about the mathematics they are learning.

Jon's teaching is not composed of techniques that Stacy can assimilate through a single observation. Following up with a discussion of issues and concerns provides Stacy with insights into the decision making underlying his teaching.

Professional development continues to be an ongoing process for this experienced teacher.

Through participation in professional organizations teachers can contribute to their own development.

Afterwards Stacy has the opportunity to talk to Jon. He understands her concerns about her mathematics teaching and reflects on his own experience.

As a mathematics major, he knows firsthand that learning mathematics involves more than memorizing rules and practicing them, but it took some experimenting to foster the sort of inquiry and discourse that Stacy had observed in his classroom. "in fact, I am always earning more and trying out new ideas," he explains. "Getting my master's degree in mathematics really helped me think about the relationship between advanced mathematics and what I teach in middle school."

Jon shows Stacy his copy of the NCTM Curriculum and Evaluation Standards for School Mathematics and encourages her to join NCTM to take advantage of their regular publications. As they look through it together, she is struck by the emphasis on understanding that goes beyond getting right answers. They discuss several strategies that Stacy might use in her class to start things off.

Teachers can grow professionally through ongoing participation in the community of mathematics educators on local as well as broader levels.

The collegial interaction involved in classroom observations and subsequent discussions can contribute to the professional development of both teachers.

Stacy leaves convinced that her students should explain their answers and that they should learn to listen to, and make sense of, other students' solutions. She and Jon agree to meet regularly to share their progress and struggles. They plan to invite their colleagues to join them in these discussions. Jon also offers to observe Stacy's class when she feels ready.

Throughout the rest of the year, Stacy's progress is gradual and steady. Eventually Stacy is comfortable having Jon and LaTasha visit her classroom. LaTasha also asks if she could arrange for other teachers to visit some of Stacy's math lessons.

The principal supports field placements but recognizes that his teachers need to be involved in any planning that will include students in their classrooms.

The teachers recognize that they need to participate in their professional community, in this case, helping future colleagues participate in fruitful field experiences.

Such involvement helps the teachers in their efforts to experiment with alternative strategies for assessing their students.

Before the start of the semester, Dr. Jackson raised her concerns with Dr. Pruitt, the principal of a local elementary school. Dr. Pruitt agreed that the field experience should be an integral part of the prospective teachers' program and promised to talk with his teachers.

At school, Dr. Pruitt shared Dr. Jackson's concerns with his staff. The teachers agreed that field experiences are essential to professional education. They selected a representative from each grade level to meet with Dr. Jackson to discuss the matter.

At the meeting, the teachers wanted to know what kinds of field experiences Dr. Jackson had in mind. She indicated that she had two major goals: to have her students observe the kind of mathematics class being recommended by the Curriculum and Evaluation Standards and to have students conduct one-on-one clinical interviews in order to have the experience of analyzing a child's thinking. The teachers were excited about the clinical interviews, since it would provide them with another assessment resource.

By their involvement, the teachers are participating in schools' efforts to effect positive change in the mathematics education of preservice teachers.

Teachers help Dr. Jackson refine her program, enhancing opportunities for her students to gain experience working with small groups of children.

The teachers are being asked to participate in educational opportunities that permit them to share their expertise with preservice teachers.

Together, the teachers and Dr. Jackson developed the following plan. For five weeks during the semester, probably during the seventh through the eleventh weeks, the teachers will rearrange their schedules once a week so that math time will fit Dr. Jackson's course times. They would also reserve another week for the interviews.

Before the meeting ended, one teacher indicated she was interested in having university students teach small groups of students some mathematical activities. Dr. Jackson was enthusiastic, since it was compatible with one of the course assignments-creating mathematical task files. The request was well received by the other teachers. They decided that the last three classroom visits would be used for this purpose.

After the meeting, Dr. Jackson and Dr. Pruitt discussed how they might help each other. Dr. Jackson expressed an interest in having some teachers participate as guest speakers because the prospective teachers valued the opinions of practicing teachers. Dr. Pruitt agreed to discuss this proposal with the district office, hoping to give teachers release time to visit Dr. Jackson's classes.

In addition, Dr. Jackson also indicated that she would like to explore ways that she could do some teaching, perhaps teaming with one of the teachers for a few months in planning and teaching mathematics. Dr. Pruitt was delighted and suggested that they plan another meeting to discuss this further.