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Suggested Citation:"Front Matter." 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:"Front Matter." 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:"Front Matter." 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:"Front Matter." 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:"Front Matter." 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:"Front Matter." 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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The Teacher of Mathematics: « Issues for Today and Tomorrow Proceedings of a Conference Sponsored by MATHEMATICAL SCIENCES EDUCATION BOARD National Research Council Washington, D.C. and CENTER FOR ACADEMIC INTERINSTITUTIONAL PROGRAMS University of California Los Angeles, California Orfl« from National Technical October 1987 information Springfield, Va. 22161 Order NQL .

Gli - ?<- NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This report has been reviewed by a group other than the authors according to procedures approved by a Report Review committee con- sisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and advising the federal government. The Council functions in accordance with general policies determined by the Academy under the authority given to it in 1863 by its congressional charter, which established the Academy as a private, nonprofit, self-governing membership corporation. The Council is the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. It is administered jointly by both Academies and the Institute of Medicine. Dr. Frank Press and Dr. Robert M. White are chairman and vice chairman, respectively, of the National Research Council. The Mathematical Sciences Education Board was established in 1985 to provide a continuing national overview and assessment capability for mathematics education and is concerned with excellence in mathematical sciences education for all students at all levels. The Board reports directly to the Governing Board of the National Research Council. A limited number of free copies of these proceedings can be obtained from: Mathematical Sciences Education Board National Research Council 2101 Constitution Avenue, N.W. Washington, D.C. 20418

PREFACE These proceedings contain papers and speeches presented at the third in a series of national conferences sponsored jointly by the Mathematical Sciences Education Board (MSEB) and the Center for Academic Interinstitu- tional Programs (CAIP) on critical issues in mathematics education. This meeting was held at the University of California in Los Angeles (UCLA) on October 16 and 17, 1987, and was attended by 150 participants from across the country. The first two conferences dealt with testing and curriculum in mathematics. The focus of the third conference was on teacher educa- tion. It was organized by HSEB's Committee on Teacher Education, chaired by John Dossey. The Mathematical Sciences Education Board was established by the National Research Council in 1985 to provide national leadership, coordina- tion, services, recommendations, and information for improving the quality of mathematical sciences education in the United States for all students at all levels. The Board has 34 members and constitutes a unique coali- tion of mathematics teachers and supervisors, college and university mathematicians, educational administrators, and representatives of business and industry. The Center for Academic Interinstitutional Programs is located at the Graduate School of Education at the University of California at Los Angeles. The center is concerned with the continuity of curriculum and instruction between UCLA and its feeder institutions, schools, and commu- nity colleges. CAIP offers professional development institutes in the summer and throughout the academic year for teachers, instructors, and counselors, both onsite and at UCLA. The center also works with state and national bodies to establish and implement educational policies. -iii-

The Mathematical Sciences Education Board and the Center for Academic Interinstitutional Programs gratefully acknowledge support for this conference from the: National Science Foundation (Under Continuation of Contract No. TE-I-8550917) and the Carnegie Corporation of New York Any opinions, findings, conclusions, or recommendations expressed herein are those of the authors or speakers and do not necessar- ily reflect the views of either the National Science Foundation or the Carnegie Corporation of New York. -iv-

CONTENTS PREFACE ill OVERVIEW OF THE CONFERENCE 1 John Dossey NEW PERSPECTIVES ON THE EDUCATION OF TEACHERS 5 Shirley A. Hill THE VISIONS AND THE CHALLENGES THE ISSUE OF REFORM: WHAT HAVE WE LEARNED FROM YESTERYEAR? 17 Thomas J. Cooney MATHEMATICS TEACHING IN SCHOOLS: IMAGINING AN IDEAL THAT IS POSSIBLE 37 Magdalene Lampert TOWARD A NEW VISION OF LEARNING AND TEACHING 43 Albert Shanker PROFESSIONAL ASSESSMENT FOR PROFESSIONAL TEACHERS 59 Rick Marks SUPPORTING THE CHANGES THE PROFESSIONAL DEVELOPMENT OF OUTSTANDING MATHEMATICS TEACHERS 65 June Morita Yamashita ENCOURAGING THE IDEAL TEACHER AT THE DISTRICT LEVEL 71 Jack Price ENCOURAGING THE IDEAL TEACHER AT THE STATE LEVEL 73 Ted Sanders SUSTAINING THE CHANGES A DISCUSSION OF THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS' GUIDELINES FOR THE POST-BACCALAUREATE EDUCATION OF TEACHERS OF MATHEMATICS 81 Donald J. Dessart A DISCUSSION OF THE MATHEMATICAL ASSOCIATION OF AMERICA'S GUIDELINES FOR THE POST-BACCALAUREATE EDUCATION OF TEACHERS OF MATHEMATICS 87 Calvin T. Long -v-

-vi- APPENDIX Conference Program 97 Participants 103 Members of the Program Committee 115 Members of the Mathematical Sciences Education Board 117

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