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A CHALLENGE OF NUMBERS People in the Mathematical Sciences Prepared by Bernard L. Madison and Therese A. Hart for the Committee on the Mathematical Sciences in the Year 2000 Mathematical Sciences Education Board Board on Mathematical Sciences Commission on Physical Sciences, Mathematics, and Resources National Research Council National Academy Press Washington, D.C. 1990

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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 consisting of members of the National Academy of Sciences, the National Academy of Engineer- ing, and the Institute of Medicine. The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the fur- therance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scien- tific and technical matters. Dr. Frank Press is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sci- ences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineer- ing programs aimed at meeting national needs, encourages education and research, and recognizes the superior achieve- ments of engineers. Dr. Robert M. White is president ofthe National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the exami- nation of policy matters pertaining to the health of the pub- lic. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Samuel 0. Thier is president of 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. Functioning in accordance with general poli- cies determined by the Academy, the Council has become the principal operating agency of both the National Acad- emy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council 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 Committee on the Mathematical Sciences in the Year 200O, which was appointed at the beginning of 1988, is a three-yearproject ofthe Mathematical Sciences Education Board and the Board on Mathematical Sciences. Its purpose is to provide a national agenda for revitalizing mathemati- cal sciences education in U.S. colleges and universities. Support for this project and for the publication and dis- semination of this report was provided by grants from the National Science Foundation and the National Security Agency. Cover photograph reprinted courtesy of the University of Maryland and with permission from John Consoli, pho- tographer. Copyright (I) 1989 by John Consoli. Library of Congress Catalogue Card Number 89-64078 International Standard Book Number 0-309-04190-2 Available from: National Academy Press 2101 Constitution Avenue, N.W. Washington, D.C. 20418 First Pnniing - April 1990 Second Printing - November 1990 Third Printing - January 1992 Summaries of this report may be obtained from MS 2000, 2101 Constitution Avenue, N.W., Washington, D.C. 20418 Printed in the United States of America

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Committee on the Mathematical Sciences in the Year 2000 William E. Kirwan (Chairman), President, University of Maryland Ramesh A. Gangolli (Vice Chairman), Professor of Mathematics, University of Washington Lida K. Barrett, Dean, College of Arts & Sciences, Mississippi State University Maria A. Berriozabal, Councilwoman, City of San Antonio, Texas Ernest L. Boyer, President, Carnegie Foundation for the Advancement of Teaching William Browder, Professor of Mathematics, Princeton University Rita R. Colwell, Director of the Maryland Biotechnology Institute and Professor of Microbiology, University of Maryland John M. Deutch, Provost, Massachusetts Institute of Technology Ronald G. Douglas, Dean, Division of Physical Sciences and Mathematics, State University of New York, Stony Brook Patricia A. Dyer, Vice President for Academic Affairs, Palm Beach Community College Lloyd C. Elam, Distinguished Service Professor of Psychiatry, Meharry Medical College Sheldon L. Glashow, Higgins Professor of Physics, Harvard University Nancy ]. Kopell, Professor of Mathematics, Boston University Donald W. Marquardt, Consultant Manager, E. I. du Pont de Nemours & Co. David S. Moore, Professor of Statistics, Purdue University Jaime Oaxaca, Vice Chairman, Coronado Communications Moshe F. Rubinstein, Professor of Engineering and Applied Science, University of California, Los Angeles Ivar StakgoicI, Chairman, Department of Mathematical Sciences, University of Delaware S. Frederick Starr, President, Oberlin College Lynn Arthur Steen, Professor of Mathematics, St. Olaf College Staff 'lames A. Voyluk, Project Director Bernard L. Madison, Project Director (through August 1988) Therese A. Hart, Research Associate (through November 1989) Craig E. Hicks, Project Assistant . . .

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Mathematical Sciences Education Board Alvin W. Trivelpiece (Chairman), Director, Oak Ridge National Laboratory Shirley A. Hill (Past Chairman), Curators' Professor of Mathematics and Education, University of Missouri- Kansas City Iris M. Car! (Vice Chairman), Elementary Mathematics Instructional Supervisor, Houston Independent School Distnct, Texas Lillian C. Barna, Supenntendent of Schools, Tacoma Public Schools, Washington L`ida K. Barrett, Dean, College of Arts and Sciences, Mississippi State University C. Diane Bishop, Supenntendent of Public Instruction, State of Arizona Constance Clayton, Superintendent of Schools, School District of Philadelphia, Pennsylvania Paula B. Duckett, Elementary Mathematics Teacher, River Terrace Community School, Washington, D.C. Joan Duea, Elementary School Teacher, Price Laboratory School and Professor of Education, University of Northern Iowa Joseph W. Duncan, Corporate Vice President and Chief Economist, The Dun & Bradstreet Corporation Wade Ellis, fir., Mathematics Instructor, West Valley College, California Shirley M. Frye, Director of Curriculum and Instruction, Scottsdale School District, Arizona Ramanathan Gnanaclesikan, Head, Information Science Research Division, Bell Communications Research Donald L. Kreider, Vice Chairman, Mathematics and Computer Science Department, Dartmouth College Martin D. Kruskal, Professor of Mathematics, Rutgers University Katherine P. Layton, Mathematics Teacher, Beverly Hills High School, California Steven J. Leinwand, Mathematics Consultant, Connecticut State Department of Education Richard S. Lindzien, Sloan Professor of Meteorology, Massachusetts Institute of Technology Gail Lowe, Principal, Acacia Elementary School, Thousand Oaks, California Steven P. Meiring, Mathematics Specialist, Ohio State Department of Education Jose P. Mestre, Associate Professor of Physics, University of Massachusetts 1V

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Calvin C. Moore, Associate Vice President, Academic Affairs, University of California, Berkeley Jo Ann Mosier, Mathematics Teacher, Fairdale High School, Louisville, Kentucky Leslie Hiles Paoletti, Chairman, Department of Mathematics and Computer Science, Choate Rosemary Hall, Connecticut Lauren B. Resnick, Director, Learning Research and Development Center, University of Pittsburgh; liaison with the Commission on Behavioral and Social Sciences and Education, National Research Council Yolanda Rodriguez, Middle School Mathematics Teacher, Martin Luther King School, Cambridge, Massachusetts Thomas A. Romberg, Professor of Curriculum and Instruction, University of Wisconsin, Madison Isadore M. Singer, Institute Professor, Department of Mathematics, Massachusetts Institute of Technology Lynn Arthur Steen, Professor of Mathematics, St. Olaf College William P. Thurston, Professor of Mathematics, Princeton University Manya S. Ungar, Past President, The National Congress of Parents and Teachers Zalman Usiskin, Professor of Education, The University of Chicago John B. Walsh, Vice President/Chief Scientist, Boeing Military Airplanes Nellie C. Weil, Past President, National School Boards Association Guido L. Weiss, Elinor Anheuser Professor of Mathematics, Washington University; liaison with the Commission on Physical Sciences, Mathematics, and Resources, National Research Council Staff Kenneth M. Hoffman, Executive Director Marcia P. Sward, Executive Director (through August ~ 989) v

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Board on Mathematical Sciences Phillip A. GrifO~ths (Chairman), Provost and James B. Duke Professor of Mathematics, Duke University Lawrence D. Brown, Professor of Mathematics, Cornell University Ronald G. Douglas, Dean, College of Physical Sciences and Mathematics, State University of New York, Stony Brook David Eddy, J. Alexander McMahon Professor of Health Policy and Management, Duke University Frederick W. Gehring, Professor of Mathematics, University of Michigan James G. Glimm, Chairman, Department of Applied Mathematics and Statistics, State University of New York, Stony Brook William H. Taco, Executive Director, American Mathematical Society Joseph Kadane, Professor of Statistics, Carnegie-Mellon University Gerald J. Lieberman, Professor of Operations Research and Statistics, Stanford University Alan Newell, Head, Department of Mathematics, University of Arizona Jerome Sacks, Head, Department of Statistics, University of Illinois Guido L. Weiss, Elinor Anheuser Professor of Mathematics, Washington University Shmue! Winograd, Director, Mathematical Sciences Department, IBM Thomas J. Watson Research Center Staff Lawrence H. Cox, Director V1

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Commission on Physical Sciences, Mathematics, and Resources Norman Hackerman (Chairman), Chairman, Scientific Advisory Board, Robert A.Welch Foundation Robert C. Bearclsley, Senior Scientist and Chairman, Department of Physical Oceanography, Woods Hole Oceanographic Institution B. Clark Burchf.'el, Schlumberger Professor of Geology, Massachusetts Institute of Technolo~v George F. Carrier, Professor Emeritus, Harvard University Ralph J. Cicerone, Chair, Geosciences Department, University of California at Irvine Herbert D. Dean, The Dow Chemical Company (retired) ~, ~. ~. . ., ~_ . . . ~. . my, refer a. ~ag~eson, Immune K. ~ umer Professor of c~v~1 Engineering, Massachusetts Institute of Technology Dean E. Eastman, Vice President, IBM T. I. Watson Research Center Marye Anne Fox, Roland Pettit Centennial Professor of Chemistry, University of Texas Gerhart FriedIander, Consultant, Brookhaven National Laboratory Lawrence W. Funkhouser, Chevron Corporation (retired) Phillip A. Grimths, Provost and James B. Duke Professor of Mathematics, Duke University Neal F. Lane, Provost, Rice University Christopher F. McKee, Professor of Physics and of Astronomy, University of California at Berkeley Richard S. Nicholson, Executive Director, American Association for the Advancement of Science Jack E. Oliver, Director of INSTOC, Cornell University Jeremiah P. Ostriker, Chairman, Department of Astrophysical Sciences, Director, Princeton University Observatory, Princeton University Philip A. Palmer, Principal Consultant, E. I. du Font de Nemours & Company Frank L. Parker, Professor of Civil and Environmental Engineering, Vanderbilt University Denis J. Prager, Deputy Director, Health Program, MacArthur Foundation David M. Raup, Professor, Department of Geophysical Sciences, University of Chicago Roy F. Schwitters, Director, Superconducting Super Collider Laboratory Larry L. Smarr, Director of National Center for Supercomputing Applications, Professor of Astronomy and Physics, University of Illinois at Urbana-Champaign Karl K. Turekian, Silliman Professor of Geology and Geophysics, Yale University Staff Myron F. Uman, Acting Executive Director . . V11

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Preface During the last decade of this century, the U.S. educational system will face many challenges, but few more important than the renewal and revitalization of the mathematical sciences. Problems in mathematical sciences education exist at all levels elementary, high school, and postsecondary. These problems are caused by many factors, including a static curriculum, insufficient resources devoted to instruction, inadequate numbers of well-trained teachers, declining student interest, and more generally, the public's failure to understand fully the importance of education in science for the well-being of our society. The problems manifest themselves in the product of the educational enterprise-the scientifically trained work force that must serve the needs of our society. The demands of the next decade and the twenty-first century will require that large numbers of America's work force be equipped with higher levels of mathematical sophistication. Yet, the National Science Foundation and other organizations project that by the year 2000, unless there is a dramatic change, our nation will face a significant shortfall of people with the necessary skills in the mathematical sciences. In response to this crucial situation the National Research Council has established the Committee on the Mathematical Sciences in the Year 2000, under the direction of the Mathematical Sciences Education Board and the Board on Mathematical Sciences, to assess the present state of collegiate education in the mathematical sciences, to identify existing problems, and to recommend action that can remedy this situation. Itis hoped that this analysis by the committee will lead to a rational agenda for renewal and revitalization of the mathematical sciences and to a strategy for implementation that will stimulate all sectors of our society into action. The present descriptive report, A Challenge of Numbers, is one of three planned by the committee. It describes the circumstances and issues related to the human resources in the mathematical sciences, principally students and teachers at U.S. colleges and universities. The mathematical sciences, based largely in academia, are crucial not only for the development of new knowledge but also as a needed resource in the education of our technological work force. As with other scientific professions, the challenge of meeting the growing need for workers in the face of shrinking supplies will require a program of national action, but the situation in the mathematical sciences is particularly severe. Stetson trom the educational pipeline In mathematics has given rise to low degree production at all levels in colleges and universities, and socioeconomic forces have resulted in unprecedentedly low interest in mathematics as a major among entering freshmen. At the same time, growing enrollments in lower-level mathematics courses with small or no increases in staffing levels have created less than . . . vail

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an ideal environment for faculty in the mathematical sciences. Because of the fundamental role of mathematics in support of science and engineering, the problems in the U.S. educational system will not be corrected unless the problems in mathematics education are corrected. On the other hand, a revitalization of the mathematical sciences could lead the way in effecting change across the educational spectrum. A Challenge of Numbers contains data from a large number of existing sources. It provides in one place a comprehensive set of data describing the demographic situation in the mathematical sciences. This report does not provide answers, nor does it draw conclusions. Rather, it serves as a reference. As such, it will be an important source of data for the Committee on the Mathematical Sciences in the Year 2000 in formulating its recommendations. Also, it is hoped that the report will be used by educators and administrators in industry, government, and education to alert policymakers about the urgent need for revitalization of the mathematical sciences. This is the second report of the MS 2000 project. The first, Everybody Counts, was published jointly with the Mathematical Sciences Education Board and the Board on Mathematical Sciences and provided a general analysis of the trends and needs in mathematics education. The next review paper, to be published in late spring 1990, will assess the college and university curriculum, and the final paper, due in summer 1990, will report on resources available for instruction in the mathemati- cal sciences. Following the completion of the review papers, the Committee on the Mathematical Sciences in the Year 2000 will be in a position to issue its final recommendations in a report to the nation scheduled for late ~ 990. On behalf of the committee, ~ want to express our gratitude to Bernard L. Madison and Therese A. Hart for their work in compiling the necessary background information and for writing A Challenge of Numbers. They have provided an important service to the members of the Committee on the Mathematical Sciences in the Year 2000 and to the mathematical sciences community by making these data available in a convenient and accessible format. HE in, William E. Kirwan Chairman, Committee on the Mathematical Sciences in the Year 2000 President, University of Maryland at College Park 1X

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Contents Preface viii List of Figures List of Tables List of Boxes . ~ X11 XlV XV Introduction and Historical Perspective The MS 2000 Project and the Scope of This Report 1 Three Roller Coaster Decades 2 National Efforts Toward Renewal Contents of This Report ~ 2 The U.S. Labor Force and Higher Education Introduction More Skills and Greater Adaptabiliry 10 Growth in Science-Based Occupations 11 Higher Education in the United States 12 The Pool of Potential Students and Workers 13 Persistence in College Enrollment 14 Shifting Interests of College Students 15 Natural Sciences and Engineering 16 The Challenges and the Responsibility 1 ~ 3 College and University Mathematical Sciences Introduction 19 Strong at the Top 20 Mixed Precollege Indicators 22 Troublesome Transitions from High School to College 24 Remediation in College 28 Service Courses 30 Mathematics as an Academic Competency and Subject 32 x 1 9 19

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4 Majors in Mathematics and Statistics Introduction 35 Unclergraduate Majors 37 Degrees for Secondary School Mathematics Teachers 40 Graduate Students 42 Master's Degree Recipients 45 Doctoral Degree Recipients 48 Patterns and Prospects 52 5 Mathematical Scientists in the Workplace Introduction 53 General Characteristics and Trends 54 Employment of Recent Graduates 56 Secondary School Mathematics Faculty 58 Characteristics of College and University Faculties 61 What Faculty Members Do 62 Faculty Members by Duties and Credentials 65 The Research Faculty 67 Faculty Salaries 68 Ages of Faculty Members 68 Women ant] Minorities on the Faculty 70 Two-Year College Faculty Mobility 70 Four-Year College ant! University Doctorate Faculty 70 Four-Year College ant! University Nondoctorate Faculty 70 Summary 71 6 Issues and Implications Bibliography Appendix Tables 35 53 73 75 87 X1

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List of Figures 1.1 Total number of scientists and engineers. 1.2 Ph.D. degrees in mathematics, 1986-1987. Left: Total undergraduate enrollments in mathematical sciences departments. Right: Mathematical sciences faculty at colleges and universities. Mathematical sciences degrees awarded. 1.3 1.4 2.1 2.2 2.3 2 3 The educational requirements of the work force are increasing. Percent distribution of undergraduate enrollments by race and ethnic group. The pool of college students is changing, 18- to 24-year-old population. 4 6 10 13 13 2.4 Percent of 18- and 19-year-olds who are high school dropouts, by ethnic group. 14 2.5 Enrollment in institutions of higher education as a percent of high school graduates. 14 2.6 Shifting interest in selected majors. 17 3.1 SAT mathematics scores, 1967 to 1987. 22 3.2 ACT mathematics scores, 1973 to 1988. 22 3.3 Percent increase in enrollments in selected mathematics courses in colleges and universities, 1965 to 1985. 3.4 Undergraduate enrollments in mathematical sciences departments at U.S. colleges and universities. 4.1 4.2 4.3 30 32 Students in the mathematical sciences pipeline about half are lost each year. A representation of U.S. students in the mathematics pipeline. Number of mathematical sciences degrees awarded by U.S. institutions, 1950 to 1986. 36 36 37 4.4 Percentage of entering college freshmen expecting to major in mathematics. 38 4.5 Bachelor's degrees awarded in the mathematical sciences, 1970 to 1986. 38 4.6 Bachelor's degrees awarded in the mathematical sciences, 1970 to 1986. Number of bachelor's degrees awarded in mathematical and computer sciences, 1970 to 1986. 4.7 4.8 4.9 Expected versus actual number of bachelor's degrees in mathematical sciences. Left: Interest in mathematics and education among entering college freshmen. Right: Degrees in mathematics and education among exiting college seniors. Percent of full-time graduate students in doctorate-granting institutions who are non-U.S. citizens, 1975 and 1986. 4.10 Mathematical sciences graduate students enrolled full-time in doctorate- granting institutions, 1975 to 1986. x~ 39 41 44 44

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4.11 Percent of non-U.S. citizens as mathematical sciences graduate students by type of institution, 1977 to 1986. 4.12 Source of major support for mathematical sciences graduate students in doctorate-granting institutions, 1986. 4.13 Types of major support for graduate students in doctorate-granting institutions, 1986. 4.14 Master's degrees awarded, mathematical sciences. 4.15 Master's degrees in mathematical sciences, distribution by subfield. 4.16 Ph.D. degrees in mathematics. 4.17 Doctoral degrees in mathematical sciences, distribution by subfield and sex. 4.18 Number of doctorate recipients in broadly interpreted mathematical sciences. 5.1 Percent of recent mathematics degree holders employed in a science or engineering job, 1976 and 1986. Field of employment for recent mathematics degree recipients, 1986. Primary work activities of recent mathematics degree recipients, 1986. 5.4 Median annual salaries of recent science and engineering graduates. Supply and demand of new elementary and secondary school teachers, 5.5 5.6 5.7 5.8 5.9 1970 to 1992. Left: Number of full-time mathematical sciences faculty members at colleges and universities. Right: Number of part-time mathematical sciences faculty members at colleges and universities. Mathematical and computer sciences enrollments per FTE of faculty. Mathematical sciences faculty salaries, 1970 to 1985 (in 1985 dollars). Age distribution of full-time mathematical sciences faculty in four-year colleges and universities. 5.10 Estimated number of retirements of full-time college and university mathematical sciences faculty. 5.11 Top: Source of new hires of two-year college full-time faculty in mathematical sciences. Bottom: Destination of departing mathematical sciences two-year college full-time faculty. 5.12 Source of two-year college part-time faculty in mathematical sciences. S.13 Left: Source of new hires of doctorate faculty in mathematical sciences, 1983 to 1988. Right: Destination of departing mathematical sciences doctoral faculty, 1983 to 1988. 44 45 46 46 47 48 51 51 55 57 58 58 59 60 61 63 64 65 66 68 69 . . . X111

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List of Tables 2.1 Attainment rates of advanced degrees for selected fields, 1971 to 1985 4.1 Mathematical sciences bachelor's degrees per 1,000 mathematical sciences enrollments, 1965 to 1985 Changes in mathematical sciences majors by undergraduate grade point averages, 1981 freshman cohort 1985 bachelor's degrees awarded in mathematical sciences Summary of responses on quality and quantity of undergraduate majors 1987 SAT scores by intended college major 1986 GRE scores by undergraduate and intended graduate major Summary of responses on quality and quantity of graduate students 1985 master's degrees awarded in mathematical sciences programs 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Attainment rates of master's and doctoral degrees 4.10 Ratio of new doctorates in mathematics to new doctorates in selected other fields, 1970 to 1985 4.11 Mathematics majors going on to doctoral study in other areas of science and engineering, 1960 to 1985 4.12 Ethnic representations among new mathematical sciences doctorates, U.S. citizens, 1977 to 1986 Ethnic representation among all new research doctorates, U.S. citizens and permanent residents, 1977 to 1986 Estimates of the number of mathematical scientists by National Science Foundation (NSF), Bureau of Labor Statistics (BLS), and Conference Board for Mathematical Sciences (CBMS) Type of employer of mathematical scientists by degree level, 1986 Professional activities of four-year college and university mathematical sciences faculty 5.5 5.6 5.4 Professional activities of two-year college mathematical sciences faculty Numbers of mathematical sciences faculty members by teaching area and type of institution, 1987 Age distribution of mathematical sciences faculty members in 105 research universities, 1980 and 1986 Full-time mathematical sciences faculty by ethnic origin and sex, 1985 5.8 Estimate of average annual net flow into doctoral faculty at four-year colleges and universities, 1982 to 1987 x~v 18 37 39 40 41 42 42 45 47 48 49 49 50 50 54 56 62 64 67 68 69 71

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List of Boxes I-1 I.2 {.3 2.! Computer Science Sources of Data Statistics Degree Programs in Mathematics 2.2 Degree Programs in Statistics 3.1 Professional Organizations 3.2 AMS-MAA Survey Reports 3.3 CBMS Surveys 3.4 Minorities and Women 3.5 Intervention Programs 3.6 The Texas Prefreshman Engineering Program 3.7 Professional Development Program 3.8 The Mathematics, Engineering, Science Achievement Program Is 8 11 12 21 25 26 27 28 29 31 33 xv

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