THE CHALLENGE
The national spotlight is turning on mathematics as we appreciate its central role in the economic growth of this country.
—Calculus for a New Century, 1988
History has taught us that the most important future applications are likely to come from some unexpected corner of mathematics.
—Renewing U.S. Mathematics, 1990
Prosperity in today's global economy depends on scientific and technological strength, which in turn is built on the foundation of mathematics education. It is no wonder, therefore, that mathematics is in the spotlight. As the foundation of science and engineering, mathematics offers a key to our nation's future.
At the college and university level—the focus of this report—mathematics forms the core of the quantitative skills needed by our nation's scientific, technical, and managerial work force, including the nation's future mathematics teachers. Yet even this system—the linchpin of mathematics education in the nation—is beset by weaknesses that threaten the health of U.S. science and technology:

Interest in majoring in mathematics is at an alltime low among entering freshmen.

Too few students study advanced mathematics.

Major segments of our population are significantly underrepresented in mathematicallybased fields.

Fewer than 10 percent of students who complete calculus are Blacks, Hispanics, or disabled.

Retirements from college and university mathematical sciences faculties will soon exceed current U.S. doctoral degree production.

Women receive only one in five doctorates in mathematics.
In a technologically driven economy, mathematically literate employees more readily achieve positions of influence, whereas those who remain innumerate are often denied the economic and social benefits of productive jobs and stable employment. Far from achieving its ideal as an agent for social equalization, undergraduate mathematics education as currently practiced bestows uneven benefits on different groups within our society—white males learn much more, women and many minorities much less. The result has been a growing polarization of society along the dimension of mathematical power that will, if left unchecked, exacerbate social and economic tensions by widening disparities in opportunities and earning capacities.
Most faculty who teach mathematics in colleges and universities are dedicated teachers. Many have written textbooks and helped lead curriculum development. Nevertheless, deficiencies in mathematics education are pervasive throughout the U.S. system of education. The size of undergraduate mathematics by itself creates tremendous inertia which impedes reform.
Some of the most entrenched problems are being successfully attacked through local action—one project and one campus at a time:

Pilot projects to reform the way calculus and other introductory courses are taught and learned.

Professional development initiatives that launch underprepared students on successful college careers in science and mathematics.

Talented youth programs that excite students for careers in mathematics and science.

Programs for mathematics majors that address student needs and build personal selfconfidence.

Calculator methods and computer labs that transform traditional courses to meet the needs of a technological age.

Networks, collaboratives, and workshops that enhance the professional competence of school teachers.
Initiatives such as these provide both grounds for optimism and models for more widespread improvement. Their successes help dispel common myths that impede reform. They demonstrate that we know how to do better. For those who have worked hard on educational issues, it is time for redoubled effort; for those who have not, it is time to begin.
Just as U.S. mathematics has achieved worldwide preeminence, so now we are called on to achieve the same stature in mathematics education. The nation's reward will be sustained health in science, industry, and the economy.
Profiles of Institutions of Higher Education
Community Colleges
People in America have a deepseated belief that education is the path to a better life. Yet it seems that in our society that belief is not inculcated in the young, because a very large number drop out before high school graduation or stop out at graduation to work because of economic need. However, of those who drop out, stop out, or find themselves in life situations that are unsatisfactory, many will look later for opportunities for more education. A common statistic cited by community colleges is that the mean age of their student body is ''thirtysomething." The typical community college offers educational opportunity to adults, as well as educating those newly out of high school.
Any community college will contain students from all age levels and with many educational goals. An examination of the institution reveals a multipurpose mission covering a broad spectrum of community needs. Although junior colleges were established to provide the first half of a bachelor's degree for the locationbound or economically less able student, very quickly they became the community college with a greatly expanded mission, including preparation for university transfer, postsecondary liberal arts education, technical courses and practical training for specific jobs, vocational degree programs, developmental instruction for those with weak academic skills, retraining programs for local businesses, multicultural education, English as a second language, continuing education activities, enrichment courses for senior citizens, literacy tutor training, and noncredit programs on community issues such as health, nutrition, insurance, finance, and law.
There are nearly 1400 twoyear colleges in the United States with a total enrollment of nearly 5 million students, 25 percent of whom are enrolled in mathematics or statistics courses offered by approximately 1150 departments. Of these departments, 90 percent had mathematics or statistics programs and 70 percent offered some type of degree. The number of fulltime faculty members in mathematics and statistics departments is 6600, with another 11,600 individuals teaching on a parttime basis. Almost 90 percent of the instruction by this faculty was below the calculus level, and 90 percent of the instruction is devoted to nonmajors. Collectively, twoyear colleges enroll nearly 40 percent of all undergraduate students and account for nearly 40 percent of all undergraduate mathematics course enrollments. Nearly 10 percent of U.S. students who receive a doctorate in the mathematical sciences began their undergraduate studies in a twoyear college.
Liberal Arts Colleges
Approximately half of the bachelor's degreegranting institutions in the United States are small fouryear colleges whose mission is to provide a broad, liberal education. Primarily residential, most of these colleges tend to serve regional constituencies, although a few wellknown institutions have a more national character. Most liberal arts colleges have 1200–2000 students, virtually all of whom are between 18 and 22 years old. Largely because of their success in promoting a community of learners, these colleges are unusually productive as a source of Ph.D. scientists and mathematicians. Most of these institutions also prepare teachers through programs that involve their departments of mathematics and science in essential leadership roles.
In the majority of liberal arts colleges, 3–5 percent of the graduates major in mathematics—several times the national average. Faculty in these departments devote most of their energy to teaching and advising: they generally teach three or four courses each term, supervise several independent study projects, and advise students—especially firstyear students—about their entire college program. In matters of appointment, reappointment, tenure, and promotions, liberal arts colleges emphasize teaching as a top priority together with scholarship in a broad context, including research, curriculum development, expository writing, and professional leadership.
Of the approximately 1000 fouryear liberal arts colleges, more than 80 percent are private. The total enrollment is approximately 560,000 students, more than half of whom are enrolled in mathematics or statistics courses. There were 3450 fulltime and 1550 parttime faculty members in mathematical sciences departments at fouryear colleges, with 33 percent of the faculty teaching at least one course at the remedial level and 68 percent teaching courses at the precalculus level. Virtually all liberal arts colleges offer mathematical sciences programs, and more than 90 percent offer undergraduate majors in mathematics or statistics. Liberal arts colleges enroll approximately 10 percent of the nation's undergraduate students; their graduates account for one in six U.S. students who receive a Ph.D. in the mathematical sciences.
Comprehensive Universities
The comprehensive university, in structure and mission, is situated between the liberal arts college and the major research university. This segment of higher education is growing in size and now accounts for nearly 40 percent of the total enrollment in baccalaureate institutions.
Generally, comprehensive universities are relatively large, statefunded universities that offer degrees in all the traditional liberal arts and sciences and in most professional areas. Responsibility for professional programs is an important ingredient in the definition of a comprehensive university. Since in many cases comprehensive universities grew out of normal schools or the state colleges of education, undergraduate instruction is still their basic mission. Today, however, they offer numerous master's degrees, but few programs leading to the doctorate. Their faculties consist primarily of individuals holding Ph.D. degrees from major research universities. The student body is typically older, parttime, and diverse. Average test scores and other performance measures for students entering the comprehensive universities are usually lower than those of students entering landgrant, Ph.D.granting institutions in the state.
Because of their historical ties to education and a primary mission of undergraduate teaching, the comprehensive university more commonly has small class sections in the introductory mathematics courses than does the research university. Since doctoral programs seldom exist, there are fewer graduate students available; hence introductory courses are taught by faculty. Although both faculty and administration seek to encourage scholarship and research, the resources for such activities are often not part of the institution's budgets and federal and private funding agencies are less likely to support mathematics or scientific research in institutions without Ph.D. programs. Nevertheless, despite heavy teaching responsibility and lack of funds, a portion of the faculty do successfully conduct quality basic research. The balance of commitment to scholarship and to teaching that resides in these highly trained faculties provides fertile soil for the seeds of change in undergraduate mathematics education.
Comprehensive universities enroll approximately 2.7 million undergraduates; total enrollment in mathematical sciences courses exceeds 650,000. Approximately 85 percent of the students in these institutions take at least one mathematics course during their studies. The approximately 400 comprehensive universities employ 6250 fulltime and 3050 parttime faculty members in the mathematical sciences. About 4 percent of the mathematical sciences departments in these universities offer a doctorate, 38 percent offer a master's, and 56 percent a bachelor's as the highest degree. Graduates of comprehensive universities account for one in six U.S. students who receive a Ph.D. in the mathematical sciences.
Research Universities
A research university is a large, complex institution with a multiplicity of purposes. A large staff of researchers, postdoctoral fellows, and other professionals as well as faculty and students, both graduate and undergraduate are involved in research, education, and service. The nation, the states, and local communities rely on research universities for most of the basic research that is done in the United States as well as for a large part of the applied research. Research universities educate a large proportion of the scholars, researchers, and teachers not only for schools, colleges, and universities but also for business and industry. With few exceptions, all doctoral degrees awarded in the United States are from research universities.
This multiplicity of purposes and constituencies is reflected in the budget of a research university, which is typically several hundred million dollars and is drawn from many sources, including federal agencies, state and local governments, foundations, industry, and tuition. This broad base of support applies whether the institution is public or private.
Research and graduate education are often seen as the primary mission of a research university, especially in engineering and the sciences. This emphasis often influences other priorities, although concern for undergraduate teaching is a growing concern. States and the nation look increasingly to research universities for economic development and to maintain or regain economic competitiveness. Finally, society also looks to research universities for leadership in health care and social programs.
Faced with this overwhelming set of institutional responsibilities, a department of mathematical sciences at a research university is pulled in many directions. It is called on to teach mathematics (often including statistics) at all levels to an increasing number of students; to maintain research excellence and help support such excellence in engineering and the sciences; to help support the renewal and invigoration of school mathematics; and to help recruit and attract American students to mathematics and areas depending on mathematics.
Research universities enroll over 2.5 million undergraduates. Approximately 190 of the 260 research universities in the United States offer a doctoral program in mathematics or statistics. There are 735,000 students enrolled in mathematical sciences courses at these institutions and 6800 fulltime faculty members. About two out of three students take at least one mathematics or statistics course; twothirds of the total enrollment is generated by students not majoring in the mathematical sciences. Over 75 percent of instruction is at the calculus level or lower; only 4 percent is at the graduate level. Research universities collectively award 40 percent of the bachelor's degrees, 75 percent of the master's degrees, and nearly 100 percent of the doctoral degrees in mathematics. Baccalaureate graduates of research universities account for two out of every three U.S. students who receive a Ph.D. in the mathematical sciences.