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Teacher of Mathematics: Issues for Today and Tomorrow : Proceedings of a Conference (1987)

Chapter: NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS

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Suggested Citation:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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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Page 7
Suggested Citation:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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.
×
Page 8
Suggested Citation:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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.
×
Page 9
Suggested Citation:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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.
×
Page 10
Suggested Citation:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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.
×
Page 11
Suggested Citation:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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.
×
Page 12
Suggested Citation:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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.
×
Page 13
Suggested Citation:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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.
×
Page 14
Suggested Citation:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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.
×
Page 15
Suggested Citation:"NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS." 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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Page 16

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NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS Shirley A. Hill Chairman, Mathematical Sciences Education Board and Professor of Mathematics and Education University of Missouri-Kansas City The focus of this conference is on teaching mathematics in the general sense. My remarks are more specific, in particular, about perspectives on the education and preparation of teachers. However, we cannot talk about teacher education and teacher preparation except in the contexts of teaching and of the profession in general. I shall attempt to set the stage for the proceedings in order to try to bring out some of the issues that are crucial in teacher education today. These are interesting times in teacher education. Many things are happening and there are a number of initiatives that hold great promise for the future. But none of them is without the attendant risks that profound changes entail. The implications of today's proposals and movements and their goals and objectives are profound. In fact, they are often revolutionary in their goals--revolutionary because they ask for and, indeed, demand deep structural changes in schooling, in institutions, in the governance of schools, in attitudes about schooling, learning, and teaching, and in deeply entrenched traditions. They are also revolutionary in terms of a concept that is new to education and that may be the most important premise underlying the very serious movement today in education generally and in teacher education specifically. It is the premise that we cannot achieve change by any one or two of the means proposed--not by them alone. We cannot achieve change by intervening at only one or two or several points in the system, not by just changing textbooks, tests, even school law and governance, not by changing the practice of legisla- tive mandates or the teaching profession itself--not alone. Altera- tions in all of these are probably necessary for the overall changes needed, but no one is sufficient by itself. In part, our failures in the past to make sustained changes were failures to understand this point and this concept. Our professional organization reports, pronouncements, recommendations, and guidelines have not had the deeper effects we had hoped they would have. They have been responsible, but often naive. They have been intellectually sound, but in some ways simplistic. Our task today is to change a very complex system by moving at once on all points, in an interrelated, interactive, coordinated, and planned way. -5-

-6- Can this be done? Will it be done? We cannot afford not to try. What are the risks? There are always negative aspects to any revolution. In other words, if we have to bring down traditional structures to make room for new and untested ideas, if we strike down what has been built up over long periods of time, what will be left if we fail and if the new ideas do not keep their shining promises? To undertake what is being proposed, and what many of you are doing already, requires either extraordinary hubris or else one must be convinced of its dire need. We are at that point--dire need. Others would say this is arguable, and there is evidence on both sides of that issue. After all, we are not without operational standards today. There are the standards of professional groups, whether called standards or guidelines. There are the standards of accreditation agencies which have been in place a long time and are revised frequently. There are the standards represented by state requirements and state testing. Certainly, the present system has its defenders. Each component of the system will find proponents-- defenders who will not welcome change. When we talk about change, we must consider those serious vested interests. But, at some point, we have to assume the good faith of all of the players in the game. My own positions on teacher preparation rest on these assumptions: • First, the system of education of teachers, both initial and continuous, needs a drastic overhaul now. • Second, the forces in motion at this time will result in substantial change, but the choice of whether this change is structural and sustained is still ours to make. • Third, old distinctions--for example, between pre-service and in-service, between undergraduate and graduate, between teacher and supervisor, between coursework and apprentice- ship, between theory and practice--should be discarded and abandoned. They no longer serve a purpose. • Fourth, we must accept what I call the "discrepancy" model of teacher education: this is that an individual completing the formal teacher education program, whether undergraduate or graduate, is not a complete teacher yet. Teacher education should be a continuum, a seamless whole, a continuing process; as in life itself, we continue to learn and to change. We have all read a great deal about the recommendations made in the report entitled A Nation Prepared: Teachers for the 21st Century, issued by the Task Force on Teaching as a Profession of

-7- the Carnegie Forum on Education and the Economy. When teacher assessment for purposes of certification is discussed, two questions are often asked. They are questions that we need to consider at length. First, "What should a teacher know?" (in our case, "What should a teacher of mathematics know?") and, second, "What should a teacher (of mathematics) be able to do?" I accept these questions as starting points, but I submit that they are too limited. They are intended to encompass more. First, "What should a teacher know, understand, and believe?" And, second, "What should a teacher be able to do, and what criteria should this teacher have in making judgments about what to do and when to do it?" These questions have to be applied in both licensing and certifying teachers. It is important to make a clear distinction between those two words. When I say "licensing," I mean the state's legal responsibility to provide teachers with licenses to teach. When I use the words "certificate" and "certifying," I mean a professional standard. To what and when, in the continuum of teacher education, do we apply these particular questions in their specific detail? To start our discussion, let me suggest that we begin completely at the beginning by asking ourselves the question, "What is a teacher?" And, for our opening discussion, I propose three parts for the answer: • First, a teacher is an educated person, in the current jargon, perhaps, a culturally literate person, but I would go well beyond that; a teacher is a liberally educated person whose education is a foundation for thought, choice, and the application of values in all realms of life, including the teaching profession. • Second, a teacher is a specialist; a teacher is an authority, an expert in teaching, in subject matter, and in content. This includes the understanding of content- specific pedagogy and all that this entails. It also means an understanding of the context of application of the content in which the teacher is an authority. • Third, the teacher is a skilled craftsman and artist. This is the vocational education part of preparing to be a teacher--the teacher's ability to deal with all aspects of the job, the teacher as a manager. Now, what is a professional? Traditionally, the term "professional" has included at least the last two components of my three-part answer--a specialist and a skilled craftsman. In fact, professions other than teaching typically have included an emphasis on these two. A colleague of mine, a philosopher, has been critical for many years of the training in a number of the professions because he says that it produces "skilled barbarians." Perhaps that is an apt term. In teaching, especially when we finally have the kind of

-8- profession that everyone respects as a profession in every sense, it will not be enough to be only a specialist and a skilled craftsman. Teachers should be known by all of society as educated people of that society. Professionalism also demands demonstrated standards determined by the profession itself. It demands self-governance, ethics, commitment, and a positive self-image — a good and positive self-image of the profession. I would like to turn now to the salient points of two reports that recommend changes in teaching and teacher education--movements that have a good deal of momentum today and which may have consid- erable influence. One of these reports is by the Holmes Group and is called Tomorrow's Teachers. The second is the Carnegie report I mentioned earlier, entitled A Nation Prepared. Tomorrow's Teachers states: We have become convinced that university officials and professors must join with schools, and with the teacher organizations and state and local school governments that shape the schools, to change the teaching profession. Schools, no less than universi- ties, are places in which teachers learn. Here is the idea of teacher education occurring in schools as well as in colleges and universities. Teacher education is a continuum. Teachers are not completed professionals upon graduation. There are two major points in the Holmes Group report that are radical. One is the proposal of a differentiated teaching profes- sion. Let me quote further: It seems indisputable that teachers' assignments must be changed. The best education will be no antidote to demeaning jobs that make little room for what has been learned, that offer few incentives for learning more, and that are swamped with clerical and other responsibilities....Above all else, teaching must make room for top practitioners who can lead their field to improvement. This means jobs in which fine teachers can use their pedagogical expertise to improve other teachers' work, as well as to help children. It means jobs in which teachers can become experts in a specialized area. And here is what they propose: [J]obs in which real leaders can exercise the responsibilities and reap the rewards of serious professionalism. They call these leaders "career professionals" and they would play a role in teacher education not unlike that of a clinical professor of medicine. However, the majority of the teaching force would be "professional teachers," people who have proved their competence at

-9- work through rigorous qualification examinations. These jobs would differ from those of today's teachers in their more serious educa- tional requirements. They would be j obs in which teachers would continue to learn and improve, among other ways, through their work with one another and with the career professionals. Finally, many teachers would be novices. They are called "instructors." They would be beginning teachers. Work as instructors would offer many talented people an opportunity for service and learning and give them a chance to explore a job about which they might be uncertain. Instructors would be qualified to teach, but their work would be supported and supervised by career professionals. This array of teaching assignments would make room only for well-educated teachers. The second of the radical changes is the one we have been hearing a great deal about. It proposes an extended initial preparation for teachers and includes a degree in a discipline: [T]he undergraduate education major must be abolished in our universities. For elementary teachers, this degree has too often become a substitute for learning any academic subject deeply enough to teach it well. These teachers are certified to teach all things to all children. But few of them know much about anything because they are required to know a little of every- thing. .. .Professionally certified teachers should teach only subjects they both know well and can teach well. The report continues by stating that these changes should not stop with abolishing the undergraduate education major. It says: We argue...that eliminating those majors without dramatically improving the academic subjects that undergraduates learn would be a sad error. To cut down on courses in pedagogy for intending schoolteachers without improving pedagogy in the universities would make a horrible joke of educational reform. This item draws attention to the responsibilities of the universi- ties. Much needs to be done at the university and college levels to improve pedagogy and to "revise the undergraduate curriculum so that future teachers can study the subjects they will teach with instruc- tors who model fine teaching and who understand the pedagogy of their material." Another part of the Holmes report that is central to the present topic states: Finally, along with all of these changes, our schools and universities must open up new connections with schools. One connection would be to bring expert teachers into universities as more important and more responsible participants in professional education....Bringing expert teachers into universities will require forging new arrangements with schools to redefine those teachers' jobs.

-10- This suggests joint appointments and the clinical medical faculty analogy holds again. The Holmes Group recommendations certainly could not take place without some basic structural changes in the schools. I believe that those changes will have to go hand-in-hand and be made interactively, not just in parallel, with changes in teacher education. If we try to alter the preparation and education of teachers without those structural changes in the schools, the changes we make will be irrelevant at best, and counterproductive at worst, with the loss of some small gains that we have made already. I agree with the call for stronger subject matter preparation for teachers and with the need for teachers to be liberally educated people. I also agree that pedagogy should be primarily content-specific. There is a point which is often missed in the political and public discussions about the criticism of teachers as "education majors." Often, the education major is simplistically characterized in the media as someone who is prepared to be a teacher and has taken a lot of education courses, but does not know specific subject matter. Obviously, that is a misunderstanding of teacher preparation. Our secondary preparation programs and licensing requirements already demand a strong major in the subject matter field. That major often requires for high school teachers of mathematics a stronger mathematics program than for many other degrees associated with applications of mathematics. The subject matter preparation for secondary mathematics teachers may include more mathematics than is required for engineering, for example. And, yet, the public appears to be quite content with the idea that engineers, retired engineers, retired military personnel, and retired whatever else can step in as fully prepared mathematics teachers. The Holmes Group report is somewhat facile, often silent, in its delineation of what the subject matter major for an elementary teacher should be. It does acknowledge that the elementary teacher cannot be educated in depth in all subject areas, but, having diagnosed that problem, it has not come to grips with the solution. I, too, want a liberally educated person who knows the subject matter he or she teaches, instructing at every level of the elementary schools. There is far too little mathematics in the preparation of elementary teachers. For a literature major or a history major teaching mathematics at those levels, there may be less. And I would assume that teachers in the fields of literature and history would have the same concerns about mathematics majors teaching elementary school children. The concept of the self-contained classroom, with a teacher who teaches many subjects, cannot assume that he or she is a specialist in all of them. This dilemma has led to proposals in some quarters that mathematics in the elementary school, beginning with the fourth grade, be taught by teachers who are prepared as specialists in mathematics. There appears to be increasing support for this proposal.

-11- The concept of a degree in a specific discipline for all teachers has some potential side-effects that could be counterproductive. The typical requirement in mathematics for elementary teachers is one or two courses. But, since the early 1970's (earlier in some places), these courses have been courses designed for teachers. They can be solid content courses and are surely more appropriate than the precalculus or first calculus courses. There was a consensus in the mathematics community on the general concept of these specially designed courses and they represent a small but significant gain in elementary teacher preparation. Would taking proposals for subject matter majors for elementary teachers too literally result in the loss of even these modestly small steps in progress? It could. Another problem addressed occasionally in the Holmes Group report is the phenomenon of the isolation of teachers. In 1975, a study by the National Advisory Committee on Mathematical Education of the Conference Board of the Mathematical Sciences, entitled Overview and Analysis of School Mathematics, Grades K-12, pointed out that a large proportion of teachers have never seen another teacher teaching since their own student teaching experience. The more recent Second International Mathematics Study shows that teachers' meetings in this country typically cover administrative or housekeeping details; the study contrasted this with Japan, where teachers' meetings typically cover teaching or curricular matters. Perhaps at the heart of this problem is the issue of time: time to share, time to plan, and time to interact with other teachers. Our teachers have not had that time. American teachers have not had a window on the world of teaching; rather, they have had a mirror that reflects their own experience with their own schooling, and with only their own experiences as a teacher. No one in the world today works in such splendid isolation as teachers. Even in advanced research, much work is done in cooperative situations. Schools will need to provide time, not just for individual thinking in research and planning, but the time for teachers to interact, to learn from one another, and to plan together. From the Carnegie Task Force report, A Nation Prepared, I want to mention two major ideas. One concerns the initial preparation of teachers. The Carnegie report says that The undergraduate years should be wholly devoted to a broad, liberal education and a thorough grounding in the subjects to be taught. It also notes that elementary teachers need solid undergraduate preparation as much as secondary teachers and must be able to demonstrate a substantive understanding of each subject they teach. This, the report maintains, may mean that elementary teachers will have to "organize themselves differently" and teach fewer subjects. Surely, the writers would concede that teachers cannot do this without support. School districts, administrators, and teachers must

-12- restructure cooperatively. It may mean specialist teachers of mathematics teaching well down into the grades of the elementary school. The report goes on to say that Arts and sciences faculties must join their education colleagues, and, together with the leaders of professional and disciplinary societies, begin by undertaking a thorough review of the undergraduate curriculum for the education of prospective teachers....Arts and sciences faculties also need to give careful scrutiny to their undergraduate majors. These majors are typically constructed with the needs of other professions in mind. The second major point, and one on which the Carnegie Task Force has taken a major initiative already, is that teaching should be established in all respects as a profession. To accomplish this, the Carnegie report proposed the creation of a National Board for Professional Teaching Standards. The board's primary functions would be to establish standards for high professional teaching competence and to issue certificates to people who meet these standards. This means certification by a professional body, not licensing--which is the domain of the states. These two need to be kept distinct, whatever may be the terms in current usage. The National Board for Professional Teaching Standards has been incorporated. Ultimately, a majority of the membership of the board will be elected by holders of the certificates. That is the goal. Initially, the members are appointed. The board is not likely to succeed unless the standards it sets are high, it represents a broad consensus of those concerned with the goals of public education, and, above all, it represents the views of the developing profession itself. It must represent the views of the developing profession itself on the question of what standards of practice should be considered fully professional. What is envisioned is a profession organizing itself, developing its own standards, governing itself, and providing certificates for those who demonstrate by agreed-upon assessment methods that they meet the standards. The process is conceived to be voluntary. There is a bargain implicit throughout the Carnegie report that forms an important element. The bargain is this: the profession, talking to society, says: "We are willing to develop the high standards that are demanded in this profession, to hold ourselves to them, and to monitor ourselves with respect to them." Society, for its part, needs to be willing to provide the conditions necessary for a true profession. The conditions include not just adequate financial compensation, but also an environment that provides teachers autonomy as decision-makers in their realms of expertise. This bargain is a remarkable social compact and is, in my view, feasible.

-13- What about assessment? It should enable the board to judge the quality of the candidates In general education, In their mastery of the subjects they teach, In their knowledge of good teaching practices in general, and in their mastery of the techniques required to teach those subjects. To accomplish these objectives, the assessment techniques will have to go far beyond multiple-choice examinations. They will have to employ state-of-the-art techniques, and likely will be in large part performance-based. The board is especially mindful of equity issues. The problem of the underrepresentation of minorities in the teaching force is deeply rooted and especially troubling, and will not be solved by the actions of a national board, however farsighted. But a national board with clear objectives related to the representation of minority teachers can do much to help. The certification process envisioned by the task force that wrote the Carnegie report would be completely voluntary. There is no requirement that would be imposed on new teachers or teachers currently in the work force to participate. But the task force expects that many people will wish to do so because the certificate will be an unambiguous statement attesting that its holder is a highly qualified teacher. There are challenges for everyone in the continuing initiatives in education today. If society wants professional teachers, it must be willing to provide the conditions to make that possible. There is a serious challenge to our teacher education programs, even at the initial level. What we have in these suggestions is a real challenge to course design in our colleges and universities. We will have to do a lot of redesigning, not just at the program level, but in the courses themselves and in the ways in which they are taught. Schools, too, must take responsibility for continuing, systematically planned teacher education. The education of teachers will be a continuous process, a seamless fabric going through college and on into the early years of teaching. I would like to close by quoting two influential people who made the following remarks recently: • Lewis Branscomb, formerly the chief scientist at IBM and now at the Kennedy School of Government at Harvard University, said, "There is no way we will have good schools unless we are willing to trust the teachers. After years of teacher- bashing, we must entrust education to the teaching profession." • Governor Thomas Kean, of New Jersey, said, "Our task must be put in the context of overall school improvement, but teaching, great teachers, are the key to that process."

-14- We have immense support for what we are about to do. We have opportunities that we have never had. The climate is right. Yes, there are dangers; there are the risks (these always go along with real change), but we have the best opportunity that we have ever had to make significant, positive changes in teaching, in the profession of teaching, and, most important, in the schools and in education itself. I hope you have a very productive conference. We appreciate your participation and hope you will share your ideas. We all can learn together. The ideas you share will play a critical role in the work of the Mathematical Sciences Education Board. The issues we will address here are of extreme importance to the board. They are to all of you. Thank you--and enjoy the conference.

THE VISIONS AND THE CHALLENGES

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