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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Suggested Citation:"SUPPORTING THE CHANGES." National Research Council. 1987. Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference. Washington, DC: The National Academies Press. doi: 10.17226/18770.
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Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

THE PROFESSIONAL DEVELOPMENT OF OUTSTANDING MATHEMATICS TEACHERS June Morita Yamashita Kailua (Hawaii) High School My study of the professional development of outstanding mathe- matics teachers sought to identify the activities that these teachers value as contributing to their professional development and in which continuation at the present stages of their careers is important. The outstanding teachers are 34 winners of the 1983 Presidential Award for Excellence in Teaching Mathematics. The participation of 57 randomly selected members of the National Council of Teachers of Mathematics (NCTM) was included in order to test whether the award- ees' views are qualitatively different from the views of other persevering teachers. To supplement quantitative data, questions were asked about incentives (Lortie 1975), moonlighting, professional colleagues, career turning points, thoughts of leaving, and special work accommodations. The decision to use NCTM members (instead of a random selection of secondary mathematics teachers) as the comparison group followed Maslow's (1971) research philosophy and the theoretical framework of his study of self-actualized persons: To investigate professional development, one must begin where there is evidence of professional orientation. NCTM membership was selected as a baseline, voluntary activity that manifests a mathematics teacher's desire to grow pro- fessionally. Ratings on 19 formal and informal professional development activ- ities and 2 on classroom teaching (remedial mathematics and advanced placement or gifted mathematics) were sought. Participants were asked two questions: How important is it to you to continue this activity? How much do you think this activity has contributed to your professional growth? Responses corresponded to the following: 1 - not at all; 2 - very little; 3 - to a slight extent; 4 - to a moderate extent; 5 - to a great extent. Awardees' mean ratings (on the 5-point scale) are higher, standard deviations smaller, and participation in each activity greater. Awardees participate in more of the 21 activities (17.8) than the comparison group (11.9). Mean ratings above 4.0 were obtained from the awardees for 15 activities that contributed to professional growth and 16 on importance of continuation, and from the comparison group for 8 activities that contributed to professional growth and 3 on importance of contin- uation. The fewer comparison teachers who participate in honorific activities (such as writing for publication and consulting) rated them higher than the awardees, who gave the highest ratings to activities that are open to participation by any teacher. -65-

-66- Activlties that the awardees consider important to professional growth correlate well with three career stages defined by Lee and Pruitt (1983) which are similar to the career levels proposed by the Holmes Group (1986). These relationships are shown in Table 1. Table 2 summarizes the mean ratings, standard deviations, and percent of participation by the awardees and the comparison group in responses to the questionnaire. Implications of Findings These data constitute a beginning step toward identifying valu- able professional development activities for secondary mathematics teachers. School systems already provide in-service activities that are valued by some teachers during their skill-building stage. To meet the developmental needs of teachers who are beyond that stage, formal recognition must be given to activities that teachers in this study value as having contributed most to their professional growth: attending and participating in NCTM and affiliate group conferences, membership in those organizations, attending institutes, and advising student mathematics activities. Districts should seek ways in which they can encourage and provide opportunities to more teachers to teach in-service classes, engage in curriculum development (at a level beyond planning for courses they currently teach), write for publication, or do consulting work. It may well be that the most distinguishing difference between the awardees and the comparison teachers in this study is the number of activities in which they engage and the higher energy level mani- fested therein. If participation alone in more professional devel- opment activities affects professional development positively, then school districts should consider incentives that encourage teachers to experience more such activities.

--67- Table 1 Career Stages and Related Professional Development Activities for Mathematics Teachers Lee and Pruitt (1983) Career Stage Stage I Survival skills, instructional methods, and management skills Stage II Increase professional competence, explore new concepts and teaching techniques Holmes Group (1986) Career Level Instructors Professional Teachers Stage III Self-confident, demonstrated effectiveness, continue to grow through competence and status among peers Career Professionals Teacher Activities Take additional courses in mathematics *Read journals, esp. Math. Teacher *Join NCTM *Join NCTM affiliate group *Attend conferences *Work on NCTM/affiliate committees *Attend institutes *Advise student math. activities (Math. clubs, teams) Assume chairmanship of the mathematics department *Engage in curriculum development *Teach university classes (given the opportunity) *Read other journals (e.g., Phi Delta Kappan) *Make presentations at conferences *Teach in-service classes *Write for publication *Do consulting work *Begin at this stage and continue throughout career (rated high in both contribution to professional growth and importance of continuation).

-68- * I! I 3 oa 0) & <M <W g 8|-o r <4-l £ I i I a m a <? w ncMoovovotninin HrHHrHHHHrHOrHrHOrHrHrHHHc-rHr-H ro co o n co § OHOOOHOOHOOOOHHHHHt-<OH i-tHOOOHHHOOHHOrHHHHOi-lf-lf-l §(n t- OOOOOOOOOOOrHOHHrHHHOHrH !J|J i^J « 5 fljj« a^ J0» 2 43 J3 fi m <M O m «H -H «3 ro -P - •3sS 8ia?ir <w a tin C CX -P (fl T* R 15 »S 8 g • tj> ffl 0,0 H «4-i 3 > C L *d ^ H ' DH'Q-HCJd <w cL D ^ ff'S a • _7-H lit-

-69- References Holmes Group. Tomorrow's Teachers. East Lansing, MI: Holmes Group, Inc., 1986. Lee, Jackson F., and Pruitt, K. Wayne. "Staff Development: An Individualized Developmental Model." Kappa Delta Pi Record, 19(2):1983, pp. 51-54. Lortie, Dan. Schoolteacher: A Sociological Study. Chicago: University of Chicago Press, 1975. Maslow, Abraham H. The Farther Reaches of Human Nature. New York: Viking Press, 1971. (Additional statistical information was submitted in support of the findings in this paper. Copies of it can be obtained from the Mathematical Sciences Education Board upon request.)

ENCOURAGING THE IDEAL TEACHER AT THE DISTRICT LEVEL Jack Price Palos Verdes Peninsula Unified School District To become ideal teachers, mathematics teachers must go through three steps: "I teach mathematics;" "I teach children mathematics;" and "I help children learn mathematics." It is a difficult task for many and, for teachers to reach their full potential, they must have both financial and psychological support. There is nothing new about this idea. What is new are the ways in which local school districts can provide this support. At one time, local school districts were far more concerned about the financial support for teachers. The districts wanted to provide materials and equipment, and they still do. However, helping teach- ers learn how to use new equipment or materials was not usually a component of the "new" curriculum. Earlier, National Science Founda- tion institutes had attempted to deal with this problem, but it was too massive for a national effort. Prior to that time, in-service training was seldom seen as a necessary adjunct to the introduction of a new curriculum and/or materials and equipment. It became apparent, though, perhaps as an outgrowth of the institutes or of curriculum writing, that staff development was a necessary ingredient of change. Then, staff development was viewed generally from the financial aspect. In order to persuade teachers to take in-service training, three inducements were used: (1) released time from classroom duties; (2) credit for advancement on the salary schedule; or (3) extra pay for the extra time spent. Little appeal was made to the inherent professionalism of the teacher. But an interesting thing happened to some of the local school districts. They became old and poor. The three inducements no longer had the significance or the currency that they once had. Strangely enough, what turned out to be a better inducement was the -71-

-72- perceived value of the treatment. A case in point is the Miller Mathematics Improvement Program in California in the early 1970's. During the first year, teachers were paid to attend the program and credit was provided (self-pay). Later, no stipends were provided, but credit was available. Finally, after state funding ran out, teachers flocked to the continuation of the program--and they paid for it! Today's teachers are no different. The ideal teacher today is still most interested in something of value, something that will help him or her to work better with the children. Now, we are much more aware of the psychological needs of teachers. In the Miller Mathe- matics Improvement Program, perhaps by chance or perhaps because of research needs, teams of teachers from the same school were required, so that the teachers would have someone with whom to discuss ideas or to share momentary failures. We had begun to meet the psychological needs of the teacher. In-class support is extremely important. In California, as a part of the reform movement, a mentor-teacher pro- gram has furnished the opportunity to some extent to provide this support from colleagues. The necessity of having someone who cares cannot be underesti- mated. Many large school districts under constant bombardment about "administrative overhead" have reduced or eliminated their curriculum development/instructional improvement staff. In effect, they have eliminated research and development, professional development, qual- ity control, and the opportunity to move their districts ahead pro- grammatically. By including teachers in planning, by letting them share their talents, by praising them for their good work, and by helping them to grow professionally, their development into ideal teachers will be encouraged. For this to occur, district boards and administrators must make a commitment to provide assistance and recognition to teachers; make plans that involve ideal teachers helping others to become ideal teachers; and work out a sharing of the costs with the individual schools and a sharing of the successes with all who contri- bute to them. With these commitments (which cost very little money), local school districts will keep the ideal teachers they have and will encourage their other teachers to strive for the same high level of accomplishment.

ENCOURAGING THE IDEAL TEACHER AT THE STATE LEVEL Ted Sanders Illinois State Board of Education From a close friend who is a minister, I know that, in preparing a sermon, one never tries to make more than three points. I have 17 or 18 that I want to make, so this paper may become lengthy. I found it difficult to think about the challenge that has been presented to me and keep my focus limited to the issues surrounding the support of teachers who are in service and, particularly, to addressing the very important topic of continued professional growth and development. I also have great difficulty thinking about the ideal. I prefer Dr. Lamport's notion of talking about reality, about what is possi- ble. I would like to share with you--in reality--some of the vision that we have in Illinois and what we are trying to do, at least from the state's perspective, to realize that vision. It is not suffi- cient to talk only about teachers who are in service; undergraduate and/or graduate teacher education programs must be strengthened as well. That is not necessarily in the realm of activities for a state superintendent other than that certification and program approval requirements tend to be reflected very directly in what happens at institutions. Today, as never before, we need to think more flexibly so that, from the state's perspective and from the credentialing standpoint, we foster new approaches to training teachers. These should not be ways that would move the state merely to endorse the Holmes and Carnegie notions of moving teacher training to the grad- uate level, but ways of thinking creatively about policies that would foster that and other approaches. This would encourage institutions to proceed in those directions, something at which we have not been particularly adept. What we are trying to do now is to suggest that both the length and the content of teacher training in Illinois should be driven by definitions of what teachers ought to know and be able to do when they enter the classroom. This is a major philosoph- ical shift from our standpoint. A second thing that we are trying to do in Illinois is to create a new institution that sits between the public school districts of our state and the institutions of higher education. We are calling them clinical schools because they appear by that name most often in the literature and are analogous to teaching hospitals. In these schools, teachers going through their clinical experiences learn in settings where the very best practice takes place. We have passed the legislation to move in this direction and a statewide meeting between my office and all of the deans from both public and private institutions in the state was conducted in October, 1987. We are excited about this new entity on our landscape. -73-

-74- Ue also have made the decision to lengthen the time required for clinical experience in Illinois. It will be a few years before this is actually in place, but we are moving toward a full semester of clinical experience so that the teacher-trainee will get a sense of the full rhythm of the school. We also are committed to creating new support mechanisms during the initial years of teaching. We have been a little more cautious in this area than have other states such as Florida and California. In our 1985 legislative session, we were able to persuade the General Assembly to allow us to invest $175,000 in examining those initial years of teaching. Our goals were to ascertain what we might do in this area and to find new ways of putting support structures in place so that we continue to take advantage of the reality of the learning curve in those first years. In that quest, we worked collaboratively with Eastern Illinois University and the University of Illinois at Chicago to produce what I think is a fairly significant monograph--a set of commissioned papers that addresses some of the issues sur- rounding those initial years of teaching. From what we have learned, we will put new support mechanisms in place in our state. Continued professional development is at the heart of what we must do. It is not easy to sell professional development to state-level policymakers or the governor and the state legislators. I spent several years working with the legislature in New Mexico, then six years as Nevada State Superintendent. During the years in Nevada especially, I went to almost every session of the legislature to ask for financial support for the continued professional growth of teachers. I came away from every session empty-handed. In 1985, as Illinois' State Superintendent, the State Board of Education and I took to the legislature an educational reform package that contained a section on continued professional growth; much to my surprise, we were able to sell it. Keeping it sold is proving to be a different task, however, but the Illinois vision is based on a combination of several things which reflects what the state is trying to do to foster quality professional growth. First of all, we have announced that, as a matter of state policy, continued professional development is important. Rather than prescribe a state policy state- ment about the specifics of such growth, we have told every one of the 985 school districts in the state that they must collaborate with their teachers in designing a district policy on staff development. Some financial resources are being provided to implement this. The entire cost has not been underwritten, but some seed money has been furnished. As of the third year, $3 million per year has been invested in the support of such activities. We also are endeavoring to encourage professional growth across two different dimensions, one of which focuses specifically upon the individual teacher, either in subject matter or in teaching skills.

-75- But there is another very important dimension of staff development. This dimension appears in the work of Bob Bush, who was at the Stan- ford Research Institute for many years. In some of his research, he has described three classifications for schools, the highest of which he calls an "energized" school. These are good schools, and they are getting better. "Maintenance" schools are holding their own, neither improving nor deteriorating. Then there are "depressed" schools, which are on the decline. The characteristic that stands out in the energized schools is a principal who is engaged in collegia! fashion with his or her faculty to identify problems and find solutions to them through the vehicle of staff development. In our professional growth programs, we try to foster policies and activities that focus on both the individual and the school because both are important. We require that two other principles be observed. As a matter of state policy, we are requiring that teach- ers play an active and equal role in determining local staff develop- ment policies. That has not been an easy row to hoe. In many dis- tricts , things have gone very well; there has been open and equal collaboration. In other cases, there has been anything but a collabo- rative effort involving the faculty. The other principle we have tried to recognize is that staff development activities must be con- sistent with what we know from the limited research of how adults learn. We need to draw upon that body of knowledge. To support statewide policies that go beyond individual districts and with financial support from the state, we have created 18 educa- tional service centers. They are not really like the educational service centers or intermediate agencies that exist in other states. Our educational service centers have only one mission, and it is in direct support of teacher development. It is intended that the cen- ters benefit from economies of scale and that they also blend the variety of resources available both within and outside our state into their mission of professional growth for teachers. Illinois is put- ting $18.5 million per year into these centers. Each one is governed by a body made up of practicing classroom teachers, district adminis- trators, university faculty, and, in some instances, local school board members. We also have been rethinking our certification renewal require- ments. In Illinois, once teachers arrive at a "professional" level of certification, they have not been required to demonstrate any con- tinued growth to renew their certification. We are in the process of reconsidering this in two different ways: (1) by possibly making it mandatory for teachers to show evidence of further professional growth as a condition of their continued certificate renewal, and (2) perhaps more importantly, by looking at teachers who are returning to the work force after having been out of it for a significant period of time. Interestingly enough, slightly more than half of the newly hired teachers in Illinois each year are individuals who were trained as teachers at an earlier time. Either they have been out of the

-76- work force or they have been in it in another role and are returning to teaching. We are now requiring that, if a teacher has been absent from the classroom for a period of five consecutive years, he or she must participate in experiences that focus on subject matter compe- tence; pedagogical skills will have to be renewed in one of the new clinical schools; and, during the first year back in the classroom, each returning teacher will have to work under a mentor-teacher. We have tried to evaluate the role that school administrators play in staff development. As in many states, we have created and funded an Administrators Academy which brings a variety of training programs to practicing administrators. One of the training modules demonstrates how a principal can assess the professional growth needs of his or her faculty and develop a school-based staff development program. We are thinking very seriously about, and are engaged in testing, new initiatives that would restructure the teacher's work- place. At present, no one really knows exactly what is meant by restructuring that workplace. There are ideas about what it ought to include, but, in that restructuring, there is clear intent to empower the teacher in new ways. We are trying to engage some of our schools with the Ted Sizer Coalition of Essential Schools and other similar individuals or groups that are thinking about restructuring. We are proposing legislation that would allow us to set aside state require- ments, if necessary, to encourage and foster that change. It is a very important companion piece, particularly with the Holmes and Carnegie vision of the new teacher. Any number of such teachers can be produced, but if we are unable to restructure the school as a desirable workplace for those teachers, they will have neither a successful nor a satisfying experience. In Illinois, we are developing and attempting to validate indices that would measure conditions in schools for effective teaching and learning. Those indices would be used in our state recognition processes. Almost every state has procedures for sanctioning or approving schools. Generally, such procedures center on whether certain policies are in place, the condition of the physical plant, and so forth. We are reviewing the entire process with an eye toward including in it mechanisms for examining conditions for effective teaching and learning. We are trying to build new initiatives that recognize and reward good teaching. It would be remiss to talk about what must be done to encourage the development of ideal teachers and not talk about salaries and the value we place upon these people. Addressing the compensation question has not been easy, particularly at the state level, because one quickly runs headlong into conflicts with the district government structure, with organized teacher groups, and so forth. We may not be able to do much more at the state level than ensure a substantial increase in resources and/or foster different ways of viewing and using the teaching force. We can do some things that demonstrate, or encourage the community as a whole to think about, the value we place upon teachers. I used to

-77- think there was little value in slogans, themes, and heroes, but I have come to believe that my earlier thinking was wrong. We have tried to do some things through a program that we call "Those Who Excel," to search out, identify, recognize, and reward teachers who excel. We have a commitment from the University of Illinois whose president has agreed to waive the tuition for either a master's degree or a doctorate for the teachers we recognize. He also has communicated with his colleagues in public institutions, telling them what a good program this is and suggesting that they make the same offer in the event that these teachers would like to enroll in their institutions instead. These institutions have responded positively. As a companion piece to this activity, I have raised the money to purchase the equivalent of a sabbatical leave for these teachers so that their salary can be paid while they study. In addition, they are given a $10,000 per year stipend. I have been criticized for removing good teachers from the classroom, taking them away from the students, but I think that this program will pay significant dividends in the long term. We also are purchasing these teachers' time in a unique way for one full semester so that they can serve as our ambassadors for teaching in Illinois. They are at the state's disposal and they are in great demand across Illinois by education and community groups that want them to talk about teaching. In Illinois, if we are going to foster these goals for teachers, we also have to address the conditions of rural education in the state, particularly the conditions that exist in rural high schools. Our thinking about the rural high school as a place to work is very different in many respects than our thinking about general restruc- turing. Contrary to what you may believe, Illinois is a very rural state. In fact, 55 percent of the high schools in the state enroll fewer than 500 students. More than one third of them enroll fewer than 200 students. Our best teachers do not go to the inner cities or to the small rural high schools. We tried to address this issue several years ago, but lost it politically. However, it still is a very big issue. To get an idea of the problem, we can draw from a science classroom in a typical small rural high school--not a math classroom, but a science classroom. The following example is fairly typical, not an anomaly: a high school chemistry class being taught by a mathematics teacher who has roughly a minor in mathematics, with three hours of undergraduate coursework in chemistry--strictly lec- ture, no laboratory. Obviously, we must think about the rural high schools and schools in the inner city in different ways as we go about our restructuring. Although it was not requested, I am unable to refrain from men- tioning some of the things that I believe the federal government should be doing. There are at least four of them. The first is something that Illinois is doing already--either making grants to, or waiving tuition and fees for, those who want to prepare themselves

-78- for teaching. We need substantial increases in direct student aid for persons who will staff our classrooms, particularly our mathe- matics and sciences classrooms. I also believe that we must reinvest in the National Science Foundation (NSF) types of institutes to provide once again the kinds of concentrated and intensive growth opportunities that they afforded for the existing teaching force. The current crop of classroom teachers in this country has been in the classroom for just over 14 years on average. I can think of no better way to provide opportunities for them from which they will benefit more directly--and here I speak from personal experience. No other experience was more meaningful to me in terms of my personal and professional growth, as well as my growth in mathematics knowledge, than the experiences I had at Washington State while working toward a master of arts in teaching degree supported by the NSF-funded summer institutes program. It is unfortunate that opportunities such as those provided by the NSF institutes are not available to the new generations of teachers. There are two other new initiatives worth considering. One is to provide financial support for teachers to review their teaching techniques. From some of the laboratory work that has been done, we know that teachers can engage effectively in research and inquiry about their teaching methods; we ought to ensure that opportunities and financial support are provided for some of our teachers to inquire systematically into their teaching practices. We also ought to build financial incentives that support institutional collabo- ration, not just individual collaboration. The collaboration that occurred between Yale University and the schools in New Haven in the Yale-New Haven project is an excellent example. In some cases, Nobel laureates were paired with high school faculty to examine the pro- blems that high school teachers face in their work. We need to build, support, and encourage that kind of collaboration. It must be formal, institutional collaboration, not merely informal cooperation where one college faculty member decides it would be a good idea to teach one period a day to fifth-graders and becomes involved with the school faculty in its work. The latter is very good but, when that individual goes, so does the collaboration. The teaching profession is experiencing exciting times. In fact, these may be the best of times to be engaged in our profession. I am reminded of the friendship that developed between Thomas Jefferson and John and Abigail Adams. Although that friendship was fractured terribly during the Adams administration, it was repaired during their twilight years. Some beautiful letters were exchanged between John Adams and Thomas Jefferson, and between Abigail and Jefferson. In one of those letters, Abigail penned some words that are very appropriate today: "These are the times that a genius would dare to live. Great necessities call forth great leaders." That is pre- cisely true of our condition today. You are the leaders who are called forth. May good fortune attend you in giving that leadership to mathematics education.

SUSTAINING THE CHANGES

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