In addition to the trends discussed in Chapter 4, the mathematical sciences are also being affected by pressures on the academic environment. This chapter discusses emerging changes in, and pressures on, academe that appear likely to affect academic mathematical scientists. As noted in a recent report from the National Research Council, all of the normal funding streams of research universities are under stress:
American research universities are facing critical challenges. First, their financial health is endangered as each of their major sources of revenue has been undermined or contested. Federal funding for research has flattened or declined; in the face of economic pressures and changing policy priorities, states are either unwilling or unable to continue support for their public research universities at world-class levels; endowments have deteriorated significantly in the recent recession; and tuition has risen beyond the reach of many American families. At the same time, research universities also face strong forces of change that present both challenges and opportunities: demographic shifts in the U.S. population, transformative technologies, changes in the organization and scale of research, a global intensification of research networks, and changing relationships between research universities and industry. In addition, U.S. universities face growing competition from their counterparts abroad, and the nation’s global leadership in higher education, unassailable for a generation, is now threatened.1
1 National Research Council, 2012, Research Universities and the Future of America: Ten Breakthrough Actions Vital to Our Nation’s Prosperity and Security. The National Academies Press, Washington, D.C. pp. 3-4.
The mathematical sciences are likely to experience stresses and disruptions in the coming decade and a half, affecting both research and teaching. The business model of mathematical sciences departments will undergo major changes, owing to cost pressures, online course offerings, and so on. There may be less demand for lower-division teaching, but expanded opportunities for training students from other disciplines and people already in the workforce.2 Mathematical scientists should work proactively—through funding agencies, university administrations, professional societies, and within their departments—to be ready for these changes.
Mathematical science departments, particularly those at large state universities, have a tradition of teaching service courses for nonmajors. These courses, especially the large lower-division ones, help to fund positions for mathematical scientists at all levels, but especially for junior faculty and graduate teaching assistants. The teaching of mathematical sciences, both to majors and nonmajors, justifies the positions of a substantial portion of those faculty members performing mathematical sciences research. But this business model is already changing, and it faces a number of challenges in the coming years. University education has become more expensive, straining family budgets severely and often leaving students with substantial debt when they graduate. The desire to reduce these costs is pushing students to take some of their lower-division studies at state and community colleges. It is also leading university administrations to hire a second tier of nonladder faculty with larger teaching loads, reduced expectations of research productivity, and lower salaries, or to implement a series of online courses that can be taught with less faculty involvement. New methods of teaching, particularly for introductory courses, may precipitate changes in the existing model. While these trends have been observed for a decade or more, financial concerns may be increasing pressure to shift more teaching responsibilities in these ways. The result could be a reduction in the number of faculty slots in many departments.
The pressure to economize is, if anything, increasing. In his 2012 State of the Union speech, President Obama said, “So let me put colleges and universities on notice: If you can’t stop tuition from going up, the funding you get from taxpayers will go down. Higher education can’t be a luxury—it is an economic imperative that every family in America should be able to afford.” Three days later he unveiled “a financial aid overhaul that for the first time
2 An analysis from the National Science Foundation (NSF) (Kelly Kang, 2012, “Graduate Enrollment in Science and Engineering Grew Substantially in the Past Decade but Slowed in 2010,” InfoBrief from NSF’s National Center for Science and Engineering Statistics, NSF 21-317, available at http://www.nsf.gov/statistics/infbrief/nsf12317/nsf12317.pdf) found that overall graduate enrollment in science and engineering grew 35 percent from 2000 to 2010, to more than 550,000. As documented in Chapter 3 of this report, many science and engineering fields are increasingly reliant on the mathematical sciences.
would tie colleges’ eligibility for campus-based aid programs—Perkins loans, work-study jobs and supplemental grants for low-income students—to the institutions’ success in improving affordability and value for students.”3
At the same time that these changes are taking place, there are countervailing opportunities. As discussed in Chapter 3, there is a broadening and overall expansion in the number of applications of the mathematical sciences. This increases the number of students who may be interested in courses within mathematical sciences departments, including some at the upper-division level. In addition, career paths in an expanding palette of areas come with an expectation of mid-career acquisition of new quantitative skills. Creating pathways for those already in the workplace to learn these new skill sets provides a major opportunity for mathematical sciences departments.
How mathematical sciences departments adapt to and manage these changes and opportunities will strongly affect the health of the profession and the quality of education offered by U.S. universities. The pace of change to the business model for education may well be similar in magnitude to that which currently roils the publishing industry. The mathematical sciences community needs to get out ahead of these potential changes and proactively make the most of its new opportunities.
Universities are also feeling other pressures that, directly or indirectly, could affect the state of the mathematical sciences in 2025. For example, many graduate students from overseas pay full tuition, so there is some incentive for universities to actively recruit them. In particular, self-funded master’s students from abroad, or students seeking professional master’s degrees, can be helpful to department finances, but will too many such students change the research environment?
Fiscal stresses on colleges and universities are also leading to the establishment of some for-profit educational institutions. This trend took root for continuing education, but it is now playing an increasing role in undergraduate education. It is difficult to say how widespread for-profit colleges and universities may become or how their presence might change the environment for the mathematical sciences, but it is a trend that mathematical scientists should monitor. In traditional settings, some educators are experimenting with lower-cost ways of providing education, such as Web-based courses that put much more burden on the students, thereby allowing individual professors to serve larger numbers of students. Mathematics and statistics, because they do not involve laboratory work, would appear to be promising targets for online delivery.
For example, the Math Emporium at Virginia Tech uses four untenured mathematics instructors to lead seven entry-level courses with enrollments
3 Tamar Lewin, 2012, Obama plan links college aid with affordability, New York Times, January 27.
of between 200 and 2,000, for a total of 8,000 students per year, according to a 2012 article in the Washington Post.4 According to that article, “Virginia Tech students pass introductory math courses at a higher rate now than 15 years ago, when the Emporium was built. And research has found the teaching model trims per-student expense by more than one-third, vital savings for public institutions with dwindling state support.” It goes on to quote Carol Twigg, president of the nonprofit National Center for Academic Transformation, that the Emporium model has been adopted by about 100 colleges and community colleges.
In general, there is pressure to find less costly means of delivering classroom knowledge. An extreme scenario would be greater decoupling of teaching and research, with fewer universities focused on leading research. Movement in that direction would have a large impact on the mathematical sciences because the size of most mathematical science departments is driven by the teaching load. If teaching duties are offloaded to other mechanisms (community colleges, online learning, for-profit institutions), university mathematics and statistics departments may lose some critical mass. Such a reduction in service teaching could also weaken ties between mathematical scientists and other departments.
Some online courses with mathematical content have already proven to be tremendously popular, and this early attention will only increase the interest (by students and university administrations, at least) in experimenting with this modality. A 2012 article in the New York Times5 pointed to the enormous number of people around the globe who enrolled in courses offered in the fall of 2011 by Stanford University: 160,000 students in 190 countries enrolled for a course in artificial intelligence, 104,000 for a course in machine learning, and 92,000 for an introductory database course. According to that article, other major universities, such as the Massachusetts Institute of Technology (MIT) and the Georgia Institute of Technology, are also beginning to offer “massive, open, online courses” or MOOCs. Other courses with mathematical content are offered through Coursera.org, which “is committed to making the best education in the world freely available to any person who seeks it.”6 As of October 11, 2012, the listings included the following:
• Model Thinking, from the University of Michigan;
• Introduction to Mathematical Thinking, from Stanford University;
4 Daniel de Vise, 2012, At Virginia Tech, computers help solve a math class problem. Washington Post, April 22.
5 Tamar Lewin, 2012, Instruction for masses knocks down campus walls. New York Times, March 4.
• Algebra, from the University of California, Irvine;
• Calculus: Single Variable, from the University of Pennsylvania;
• Analytic Combinatorics, from Princeton University; and
• Machine Learning, from the University of Washington.7
More recently, Harvard and MIT announced a joint partnership called edX “to offer online learning to millions of people around the world. EdX will offer Harvard and MIT classes online for free.”8 The press release9 accompanying that announcement notes that online students may receive “certificates of mastery” if they demonstrate adequate knowledge of the course material. It also states that “edX will release its learning platform as open-source software so it can be used by other universities and organizations that wish to host the platform themselves.” The press release goes on to say that Harvard and MIT faculty will use data from edX “to research how students learn and how technologies can facilitate effective teaching both on-campus and online . . . [to study] which teaching methods and tools are most successful.”
At the same time that mathematics and statistics departments are feeling these pressures, there is also the challenge noted at the beginning of Chapter 5: the belief in some circles that more lower-division mathematics should be taught by other departments. The 2012 report of the President’s Council of Advisors on Science and Technology on STEM education at the undergraduate level recommended that this hypothesis be actively explored through a set of perhaps 200 experiments across the nation. As stated in Chapter 5, the committee agrees that the existing mathematics curriculum would benefit from a significant updating of both content and teaching techniques. There is a real chance that if mathematicians do not do this, others will, and that could exacerbate the erosion in mathematics service teaching that is likely to occur due to cost pressures.
Another important trend of concern to all STEM disciplines is that graduate enrollments from overseas are likely to go down over time as the quality of overseas universities improves, because employment opportunities now exist worldwide for mathematical sciences talent. Over half (52 percent in the 2009-2010 academic year) of the Ph.D. degrees awarded annually in the mathematical sciences by U.S. universities are to non-U.S. citizens.10 Until now, a large fraction of them have continued their careers in the United States, and the nation has benefited greatly in recent decades
9 Available at http://web.mit.edu/press/2012/mit-harvard-edx-announcement.html. Accessed May 2, 2012.
10 R. Cleary, J.W. Maxwell, and C. Rose, 2010, Report on the 2009-2010 new doctoral recipients. Notices of the AMS 58(7):944-954.
because of its ability to attract such people, many of whom stay to contribute to U.S. science, technology, and business.
However, as economic and scientific conditions improve in other countries—especially in China and India—it may be more difficult to keep foreign-born graduates in the United States; already, other nations are aggressively recruiting talented individuals, especially those born there but who are now in the United States. Increasingly, there are reports of more Chinese graduate students electing to return to China after their Ph.D. work, and the opportunities for rewarding research careers in the mathematical sciences are improving in China and elsewhere overseas. Publication counts also suggest that other locations are increasingly productive in mathematics. From 1988 through 2003, the number of publications in mathematics worldwide increased by 40 percent—from 9,707 to 15,170— while the number of mathematics publications with at least one U.S. author increased by only 8 percent—from 4,301 to 4,651.11 U.S. policies regarding work visas and immigration are an important factor here, too. A decline in the ability of the United States to attract and retain top international students will have a serious negative effect on U.S. graduate training and on the production of young mathematical scientists to meet the demand of U.S. academic institutions, industry, and government exactly at the time of increasing demand for such people.
To the extent possible, NSF policies should be aligned with the goals of continuing to attract top foreign talent to our shores and inducing talented foreigners, especially those who pass through our educational system, to choose to make their careers here. Policies that encourage the growth of the U.S.-born segment of the mathematical sciences talent pool should clearly continue, but they need to be supplemented by programs to attract and retain mathematical scientists from other countries, especially for graduate school and continuing as feasible into early careers. This goal leads directly to questions about immigration policies, which are, of course, beyond the control of NSF. Mathematical scientists who are concerned about the future vitality of our profession should recognize the important role played by immigration policies and perhaps weigh in on related political discussions.
One particular aspect deserves mention here in connection with the stresses on academic finances: The ratio of federal support to institutional support for graduate students in the mathematical sciences is very low relative to the same ratio for students of other sciences, as shown in Figure 6-1. The support model for graduate students in the mathematical sciences is overly reliant on teaching assistantships, which extends time to degree, and is especially burdensome at a time when the amount that a graduate student in the mathematical sciences must learn is expanding. Overreliance on teaching assistantships is also worrisome because the changing business model for mathematics departments makes this source of support especially vulnerable to cutbacks, as discussed above. As a community, the mathematical sciences must be proactive in shifting this balance, because innovations in the delivery of the classes that support teaching assistants could erode that means of support much faster than the number of research assistantships could ramp up. A first step is for mathematical science researchers to be more aggressive in seeking research assistantships for their students, in recognition of the need for graduate students today to gain more research experience and to lessen departments’ dependency on teaching assistantships.
11 Derek Hill, Alan I. Rapoport, Rolf F. Lehming, and Robert K. Bell, 2007, Changing U.S. output of scientific articles: 1988-2003. Report 07-320, Appendix Table 2. National Science Foundation, Division of Science Resources Statistics, Arlington, Va.
FIGURE 6-1 Fraction of graduate students supported (above) by federal programs (primarily for research assistantships) and (below) by their academic institutions (primarily for teaching assistantships). In 2007, Graduate Student Support (GSS)-eligible fields were reclassified, newly eligible fields were added, and the survey was redesigned to improve coverage and coding of GSS-eligible units. “2007 new” presents data as collected in 2007; “2007 old” reflects data as they would have been collected under 2006 methodology. SOURCE: National Science Foundation/ National Center for Science and Engineering Statistics, 2009, NSF-NIH Survey of Graduate Students and Postdoctorates in Science and Engineering, Table 38. Available at http://www.nsf.gov/statistics/nsf12300/content.cfm?pub_id=4118&id=2.
One additional pressure of particular relevance to the mathematical sciences is the movement toward more multidisciplinarity in research, as emerging fields require mathematics and statistics expertise in order to move forward. At one extreme, this could lead to situations in which more mathematical scientists are members of the departments in which their work is applied, so that mathematics or statistics departments lose critical mass. If the mathematical sciences were to become dispersed in this way, the coherence and unity of the field would be threatened. Forging links to other departments will help in advancing this process. Such links would include cross-listing of courses, collaboration with other departments in planning courses, and having cross-disciplinary postdoctoral students and courtesy appointments. Creating appropriate methods to evaluate those engaged in interdisciplinary research is overdue.
The multitude of existing configurations of mathematical sciences departments at academic institutions often reflect the particular history at each institution rather than what is optimal. In view of the changing academic environment there is an opportunity to reconsider such arrangements and departmental divisions, in order to enhance the cohesiveness of the mathematical sciences and enable intradisciplinary and cross-disciplinary research and educational collaborations.
Recommendation 6-1: Academic departments in mathematics and statistics should begin the process of rethinking and adapting their programs to keep pace with the evolving academic environment, and be sure they have a seat at the table as online content and other innovations in the delivery of mathematical science coursework are created. The professional societies have important roles to play in mobilizing the community in these matters, through mechanisms such as opinion articles, online discussion groups, policy monitoring, and conferences.