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5 People in the Mathematical Sciences Enterprise INTRODUCTION The growth and broadening of research opportunities described in Chapters 3 and 4 necessitate changes in the way students are prepared, along with planning about how to attract a sufficient number of talented young people into the discipline. From its discussions with representatives from industry and government who hire mathematically trained individu- als, plus other information cited in Chapters 3-4, the committee concludes that demand for people with strong mathematical science skills is already growing and will probably grow even more. The range of positions that require mathematical skills is also expanding, as more and more fields are presented with the challenges and opportunities of large-scale data analysis and mathematical modeling. While these positions can be filled by indi­ viduals with a variety of postsecondary degrees, all of them will need strong skills in the mathematical sciences. This has implications for the math- ematical sciences community in its role as educators with a responsibility to prepare students from many disciplines to be ready for a broad range of science, technology, engineering, and mathematics (STEM) careers. Indeed, producing an adequate number of people with expertise in the mathemati- cal sciences at the bachelor’s, master’s, and Ph.D. levels and an adequate pipeline of well-trained students emerging from grades K-12 is necessary if the STEM fields are to thrive. 116

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PEOPLE IN THE MATHEMATICAL SCIENCES ENTERPRISE 117 CHANGING DEMAND FOR THE MATHEMATICAL SCIENCES At its meeting in December 2010, the committee heard from four people in sectors of industry that are becoming increasingly reliant on the mathematical sciences: • Nafees Bin Zafar, who heads the research division at DreamWorks Animation, • Brenda Dietrich, vice president for Business Analytics and Math- ematical Sciences at IBM’s T.J. Watson Research Center, • Harry (Heung-Yeung) Shum, head of Core Search Development at Microsoft Research, and • James Simons, head of Renaissance Technologies. The goal of this discussion was to gain insight about some of the topi- cal areas in which the mathematical sciences are critical. Speakers brought knowledge of the demand for the mathematical sciences in the financial sector and the growing demands in business analytics, the entertainment sector, and the information industry. Because Dr. Shum had been a founder of Microsoft Research–Asia, in Beijing, he was also able to comment on the growing mathematical science capabilities in China. The focus of these interactions was to learn about current and emerging uses of mathemati- cal sciences skills, whether or not carried out by people who consider themselves to be mathematical scientists. The financial sector, for example, employs thousands of financial engineers, only a fraction of whom have a terminal degree in mathematics or statistics. (Many are trained in physics or economics, and many have M.B.A. training.) Understanding the demand for mathematical science skills per se is critical for two reasons: (1) the demand for those skills, especially where it is increasing or moving in new directions, requires college and university education that in part relies on academic mathematical scientists and (2) the demand for those skills implies at least the possibility that the nation would benefit from a larger number of master’s or Ph.D.-level mathematical scientists, especially if their training were designed with consideration of the emerging career options. Dr. Simons noted that Renaissance Technologies has carried out all of its trading through quantitative models since 1998; it now works with several terabytes of data per day from markets around the world. The company has about 90 Ph.D.s, most in the research group but some in the programming group. Some of these people have backgrounds in mathemat- ics, but others have degrees in astronomy, computer science, physics, or other disciplines that provide strong mathematical science skills. He listed a number of financial functions that rely on mathematical science skills: prediction, valuation, portfolio construction, volatility modeling, and so

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118 THE MATHEMATICAL SCIENCES IN 2025 on. Even though the financial sector hires a large number of people with strong mathematical science expertise, he thinks the level of mathematical knowledge in the finance world is still lower than it should be. As an ex- ample, he said that many people do not know the distinction between beta (the difference between an instrument’s performance and that of a relevant market) and volatility; they are related but different. He thinks finance will continue to be permeated by quantitative methods. Some of the skills that are necessary, in Dr. Simons’s view, include statistics (though not normally at the level of new research) and optimization, and good programming skill is essential. Dr. Simons is concerned about the pool of U.S.-born people with strong skills in the mathematical sciences. The majority of people hired by R ­ enaissance are non-Americans. Most are from Europe, China, and India, though most have gone through a U.S. graduate program, and the fraction of U.S.-born people hired is declining. He thinks he probably could have found an adequate number of U.S.-born people if pressed, but it would have required a lot of work. He worries that high school teaching in the United States is simply not good enough, even though our economy is in- creasingly dependent on mathematical models and data analysis. Dr. Dietrich described the kinds of mathematical science opportunities she sees and the kind of people IBM-Watson would like to hire. She said that much of IBM’s business has become data-intensive, and numerical lit- eracy is needed throughout the corporation. The mathematical sciences are increasingly central to economics, finance, business, and marketing, includ- ing areas such as risk assessment, game theory, and machine learning for marketing. But she noted that it is difficult to find enough people who have the ability to deal with large numerical data sets plus the ability to under­ stand simple concepts such as range and variability. Many mathematical scientists at IBM must also operate as software developers, and they must be flexible enough to move from topic to topic. She listed some qualifications that are especially valuable in her divi- sion, which employs over 300 people worldwide. It needs people with statistical expertise who are also are very computational. They should not rely on existing models and toolkits and should be comfortable working with messy data. The division needs people who are strong in discrete mathematics and able to extract understanding from big data sets. In her experience, most employees do not need to know calculus, and she would like to see more emphasis in the undergraduate curriculum on stochastic processes and large data. Programming ability is essential. Mr. Bin Zafar presented impressions about the mathematical science skills that are important to the movie industry. (Similar skills are presum- ably important for the creation of computer games and computer-based training and simulation systems.) He showed the committee an example of

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PEOPLE IN THE MATHEMATICAL SCIENCES ENTERPRISE 119 a lengthy computer-generated sequence, from a major film release, that sim- ulates the destruction of Los Angeles by a tsunami. Mathematical model­ ng i was behind realistic images of wave motion and of building collapses, down to details such as the way windows would shatter and dust would rise and swirl. A great deal of effort is expended in creating tools for animation and computer-generated effects, both generic capabilities and particular instantiations. Mr. Bin Zafar reported that of the several hundred people working in R&D at DreamWorks, about 13 percent have Ph.D.s and 34 percent have master’s degrees. Just over half of the R&D staff have backgrounds in computer science, 19 percent in engineering, and 6 percent in a math- ematical science. He mentioned that he does not receive many applications from mathematical scientists, and he speculated that perhaps they are not aware of the mathematical nature of work in the entertainment sector. He observed that creating robust and maintainable software is essential in his business—most software must be reliable enough to last perhaps 5 years— and that very few of their applicants develop that skill through education. Their schooling seems to assume that actual code creation is just an “imple- mentation detail,” but Mr. Bin Zafar observed that the implementation step often exposes very deep details that, if caught earlier, would have led the developer to take a different course. Dr. Shum spoke first of his experience in helping Microsoft Research to establish a research laboratory in Beijing, beginning in 1999. He reported that there is plenty of raw talent in China, “every bit as good as MIT,” so in setting up the research center in Beijing, a conscious effort was made to include some training opportunities that would enable the laboratory to de- velop that raw talent. By the time Dr. Shum left Beijing in 2006, Microsoft Research–Asia employed about 200 researchers, a few dozen postdoctoral researchers, and 250 junior workers. Speaking more generally about Microsoft Research’s needs, Shum men- tioned three mathematical science areas that are of current importance to his search technology division of over 1,000 people: • Auction theory, including mechanism design. The problem of mechanism design (see Chapter 2) is critical, and people with backgrounds in the mathematical theory are necessary. He has a few dozen people working on this topic. • Graphs, including research that helps us manage enormous graphs such as Internet traffic patterns and research to understand social graphs, entity graphs, and click graphs (which show where users clicked on a hyperlink). His team at Microsoft Research includes many people with theoretical and mathematical backgrounds.

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120 THE MATHEMATICAL SCIENCES IN 2025 • Machine learning, which is a core foundation for advancing search technologies. His division includes perhaps 50 people working on aspects of machine learning. More than half the people in Dr. Shum’s division have backgrounds in computer science, and he has also hired engineers who have strong pro- gramming skills. Perhaps 5-10 percent of the people in his division received their final degrees in mathematics or statistics. Not too many of these people have Ph.D.s, though he has recently hired some Ph.D. statisticians. This anecdotal information gathered by the committee is echoed in a more thorough examination by the McKinsey Global Institute.1 That report estimated that U.S. businesses will need an additional 140,000-190,000 employees with “deep analytical talent” and a high level of quantitative skills by 2018. On p. 10, the report points out that “a significant constraint on realizing value from big data will be a shortage of talent, particularly of people with deep expertise in statistics and machine learning,” to carry out analyses in support of corporate decision making. Preparing enough professionals to address this need constitutes both an opportunity and a challenge for the mathematical sciences. The careers examined by that report are those that deal with business analytics, especially as driven by large-scale data. Most of the people who fill those slots will need very strong mathematical science backgrounds, whether or not they actu- ally receive a graduate degree in mathematics or statistics. And academic mathematical scientists must prepare to educate these additional people, regardless of what degrees they actually pursue. The McKinsey report goes on to say (p. 105) that “although we conducted this analysis in the United States, we believe that the shortage of deep analytical talent will be a global p ­ henomenon. . . . Countries with a higher per capita production of deep analytical talent could potentially be attractive sources of these skills for other geographies either through immigration or through companies off- shoring to meet their needs.” This McKinsey result supplements a well-known observation from Google’s chief economist, Hal Varian, who was quoted in the New York Times as saying “the sexy job in the next 10 years will be statisticians . . . and I’m not kidding.”2 In addition to new careers spawned by the avail- ability of large amounts of data and the information industry, many other fields—e.g., medicine—are also experiencing a growing need for profes- sionals with sophisticated skills in the mathematical sciences. 1  James Manyika, Michael Chui, Jacques Bughin, Brad Brown, Richard Dobbs, Charles Roxburgh, and Angela Hung Byers, 2011, Big Data: The Next Frontier for Innovation, Com- petition, and Productivity. McKinsey Global Institute, San Francisco. 2  “For Today’s Graduate, Just One Word: Statistics,” New York Times, August 5, 2009.

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PEOPLE IN THE MATHEMATICAL SCIENCES ENTERPRISE 121 Throughout its study, the committee heard many expressions of con- cern about the supply of home-grown talent in the mathematical sciences. That is, of course, a concern shared across all STEM disciplines. For a long time, the U.S. STEM workforce has been dependent on the flow of talented young people from other countries and on the fact that many of them are interested in building careers in the United States. Our country cannot de- pend on that situation continuing. In recent years, there has been a great advance in our ability to quan- tify. But even top undergraduates too often have little or no experience and intuition about probability or concepts such as the central limit theorem, the law of large numbers, or indeterminacy. In order to prepare students for today’s opportunities in the mathematical sciences, we need to push earlier on these skills. Our high schools focus on getting people prepared for calculus, and that influences even the elementary school curriculum. But we do little to teach statistics, probability, and uncertainty, instead acting as though students can just pick this up in the course of other learning. This is one of the biggest issues facing U.S. mathematical sciences; it is also a big problem in terms of national competitiveness. The statistics profession might learn from the physics profession’s atti­ tude with regard to training. Physicists who have been trained as theoreti- cians may often then gain postdoctoral experience in experimental work (often in a different field). But statisticians are more rigid in their attitudes. For example, it is rare that statistics departments embrace a broad range of theoreticians, applied statisticians, and experimentalists. The latter category is important: When statisticians collect their own data, as some do, they are less likely to be relegated to supporting roles in scientific investigations, as can sometimes happen. Students educated in such an environment would have innate understanding of how to work in an interdisciplinary setting. However, statisticians may have difficulty obtaining funding to support data collection, and so the field cannot change in this direction unless fund- ing programs evolve as well. The mathematical sciences community plays a critical role in edu- cating a broad range of students. Some will exhibit a special talent in mathematics from a young age and may remind successful researchers of their youthful selves. But there are many more whose interest in the mathematical sciences arises later and perhaps through nontraditional pathways, and these latter students constitute a valuable pool of potential majors and graduate students. A third cadre consists of students from other disciplines who need strong mathematical sciences education. All three pools of students need expert guidance and mentoring from suc- cessful mathematical scientists, and their needs are not identical. The mathematical sciences must successfully attract and serve all three of these cadres of students.

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122 THE MATHEMATICAL SCIENCES IN 2025 The challenge of producing an adequate number of people for STEM careers is of interest far beyond the mathematical sciences, of course. For example, a recent report3 from the President’s Council of Advisors on Sci- ence and Technology (PCAST) “provides a strategy for improving STEM education during the first two years of college that [it believes] is respon- sive to both the challenges and the opportunities that this crucial stage in the STEM education pathway presents,” according to the cover letter to the President that accompanies the report.4 That cover letter goes on to recount the reason why STEM fields receive this attention: Economic forecasts point to a need for producing, over the next decade, approximately 1 million more college graduates in STEM fields than expected under current assumptions. Fewer than 40% of students who enter college intending to major in a STEM field complete a STEM degree. Merely increasing the retention of STEM majors from 40% to 50% would generate three-quarters of the targeted 1 million additional STEM degrees over the next decade.5 That PCAST report goes on to recommend, among other steps, a “multi-campus 5-year initiative aimed at developing new approaches to re- move or reduce the mathematics bottleneck that is currently keeping many students from pursuing STEM majors.” This proposed initiative might in- volve approximately 200 “experiments” exploring a variety of approaches, including the following: (1)  Summer and other bridge programs for high school students entering college; (2)  remedial courses for students in college, including approaches that rely on computer technology; (3)  college mathematics teaching and curricula developed and taught by faculty from mathematics-intensive disciplines other than math­ ematics, including physics, engineering, and computer science; and (4)  new pipeline for producing K-12 mathematics teachers from under- a graduate and graduate programs in mathematics-intensive fields other than mathematics. It is critical that the mathematical sciences community actively engage with STEM discussions going on outside the mathematical sciences com- 3  PCAST, 2012, Engage to Excel: Producing One Million Additional College Graduates with Degrees in Science, Technology, Engineering, and Mathematics. The White House, Washington, D.C. 4  Available at http://www.whitehouse.gov/sites/default/files/microsites/ostp/pcast-engage-to-   excel-final_2-25-12.pdf. 5  Ibid.

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PEOPLE IN THE MATHEMATICAL SCIENCES ENTERPRISE 123 munity and not be marginalized in efforts to improve STEM education, especially since those plans would greatly affect the responsibilities of mathematics and statistics faculty members. This committee knows of no evidence that teaching lower-division college mathematics and statistics or providing a mathematical background for K-12 mathematics teachers can be done better by faculty from other subjects but it is clear that the mathematics-intensive disciplines are full of creative people who constitute a valuable resource for innovative teaching ideas. The need to create a truly compelling menu of creatively taught lower-division courses in the mathematical sciences tailored to the needs of twenty-first century students is pressing, and partnerships with mathematics-intensive disciplines in de- signing such courses are eminently worth pursuing. The traditional lecture-homework-exam format that often prevails in lower-division mathematics courses would benefit from a reexamination. One aspect of the changes PCAST would like to see is explained in its report: Better teaching methods are needed by university faculty to make courses more inspiring, provide more help to students facing mathematical chal- lenges, and to create an atmosphere of a community of STEM learners. Traditional teaching methods have trained many STEM professionals, including most of the current STEM workforce. But a large and grow- ing body of research indicates that STEM education can be substantially improved through a diversification of teaching methods. These data show that evidence-based teaching methods are more effective in reaching all students—especially the ‘underrepresented majority’—the women and members of minority groups who now constitute approximately 70% of college students while being underrepresented among students who receive undergraduate STEM degrees (approximately 45%). In an appendix to the report, some of the methods the PCAST work- ing group would like to see explored are (1) active learning techniques; (2) motivating learning by explaining how mathematics is used and making courses more relevant for students’ fields of specialization; (3) creating a community of high expectations among students; and (4) expanding op- portunities for undergraduate research. The PCAST report should be viewed as a wake-up call for the math- ematical sciences community. While there have been numerous promising experiments within the community for addressing the issues it raises—­ especially noteworthy has been the tremendous expansion in opportunities for undergraduate research in the mathematical sciences—at this point a community-wide effort is called for. The professional societies should work cooperatively to spark this. Change is unquestionably coming to lower-division undergraduate mathematics, and it is incumbent upon the

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124 THE MATHEMATICAL SCIENCES IN 2025 mathematical sciences community to ensure that it is at the center of these changes and not at the periphery. THE TYPICAL EDUCATIONAL PATH IN THE MATHEMATICAL SCIENCES NEEDS ADJUSTMENTS Chapter 3 showed exciting emerging opportunities for anyone with expertise in the mathematical sciences. The precise thinking and conceptual abilities that are hallmarks of mathematical science training continue to be an excellent preparation for many career paths. However, it is apparent that an ability to work with data and computers is a common need. An under­ standing of statistics, probability, randomness, algorithms, and discrete mathematics are probably of greater importance than calculus for many students who will follow such careers, and indeed students with this train- ing will be much more employable in those areas. The educational offerings of typical departments in the mathematical sciences have not kept pace with the changes in how the mathematical sciences are used. A redesigned offering of courses and majors is needed. Although there are promising ex- periments, a community-wide effort is needed in the mathematical sciences to make its undergraduate courses more compelling to students and better aligned with needs of user departments. The 2012 report of the Society for Industrial and Applied Mathematics (SIAM) on mathematical sciences in industry6 adds support for this, with regard to those students who would like to work in industry. The SIAM report makes the following statement about useful background for such people: Useful mathematical skills include a broad training in the core of math- ematics, statistics, mathematical modeling, and numerical simulation, as well as depth in an appropriate specialty. Computational skills include, at a minimum, experience in programming in one or more languages. Specific requirements, such as C++, a fourth-generation language such as MATLAB, or a scripting language such as Python, vary a great deal from company to company and industry to industry. Familiarity with high-­ erformance computing (e.g., parallel computing, large-scale data p mining, and visualization) is becoming more and more of an asset, and in some jobs is a requirement. . . . In general, the student’s level of knowl- edge [of an application domain] has to be sufficient to understand the language of that domain and bridge the gap between theory and practical implementation.7 6  SIAM, 2012, Mathematics in Industry. Society for Industrial and Applied Mathematics, Philadelphia, Pa. Available at http://www.siam.org/reports/mii/2012/index.php. 7  Ibid., p. 2 of Summary.

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PEOPLE IN THE MATHEMATICAL SCIENCES ENTERPRISE 125 TABLE 5-1  Enrollment (in 1000s) in Undergraduate Courses Taught in the Mathematics or Statistics Departments of Four-Year Colleges and Universities, and in Mathematics Programs of Two-Year Colleges, for Fall 1990, 1995, 2000, 2005, and 2010 Discipline Fall 1990 Fall 1995 Fall 2000 Fall 2005 Fall 2010 Mathematics 1,621 1,471 1,614 1,607 1,971 Statistics 169 208 245 260 371 SOURCES: CBMS, 2007, 2012. It may be that students are already “voting with their feet.” According to data from the Conference Board of the Mathematical Sciences (CBMS), the number of enrollments in mathematics courses in 1990-2010 remained generally flat, while the number of enrollments in statistics courses in- creased by 120 percent.8,9 The raw numbers are shown in Table 5-1. The four industry leaders who spoke with the committee, and whose observations were recounted earlier in this chapter, raised the need for more people who focus on real problems—rather than on models that omit too much of the messiness of reality—and who are able to work with com­ puters, statistics, and data so as to test and validate their modeling. Theory alone is not the best preparation for, say, careers at IBM, Renaissance ­ Technologies, or DreamWorks Animation. But an optimistic lesson to draw from these discussions is that industry has an increasing need for students with mathematical science skills, whether or not the skills are explicitly labeled that way. The role of the mathematical sciences in science, engineering, medicine, finance, social science, and society at large has changed enormously, at a pace that challenges the university mathematical sciences curriculum. This change necessitates new courses, new majors, new programs, and new educational partnerships with those in other disciplines, both inside and outside universities. New educational pathways for training in the math- ematical sciences need to be created—for students in mathematical sciences departments, for those pursuing degrees in science, medicine, engineering, business, and social science, and for those already in the workforce need- ing additional quantitative skills. New credentials may be needed, such as professional master’s degrees for those about to enter the workforce or 8  CBMS, 2007, Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States; Fall 2005 CBMS Survey, Table S.1. Available at http://www.ams.org/ profession/data/cbms-survey/full-report.pdf. 9  CBMS, 2012, Draft of the Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States; Fall 2010 CBMS Survey. Table S.1. Available at http://www.ams.org/profession/ data/cbms-survey/cbms2010-work.

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126 THE MATHEMATICAL SCIENCES IN 2025 already in it. The trend toward periodic acquisition of new job skills by those already in the workforce provides an opportunity for the mathemati- cal sciences to serve new needs. Most mathematics departments still tend to use calculus as the gate- way to higher-level coursework, and that is not appropriate for many stu- dents. Although there is a very long history of discussions about this issue, the need for a serious reexamination is real, driven by changes in how the mathematical sciences are being used. For example, someone who wants to study bioinformatics ought to have a pathway whereby he or she can learn probability and statistics; learn enough calculus to find maxima and minima and understand ordinary differential equations, get a solid dose of discrete mathematics; learn linear algebra; and get an introduction to algorithms. Space could be made in their curriculum by deemphasizing such topics as line integrals and Stokes’s theorem, epsilons and deltas, abstract vector spaces, and so on. Different pathways are needed for students who may go on to work in bioinformatics, ecology, medicine, computing, and so on. It is not enough to rearrange existing courses to create alternative curricula. As one step in this direction, colleges and universities might encourage AP statistics courses as much as they do AP calculus. Such a move would also help those in secondary education who believe that teaching of probability, statistics, and uncertainty should be more common. The dramatic increase over the past 20 years in the number of NSF Research Experience for Undergraduate (REU) programs has, in the ex- perience of members of the study committee, been a noticeable force for attracting talented undergraduates to major in a mathematical science while also providing a stronger foundation for graduate study.10 Another striking trend over the past decade or two is the increase in double majors. This increase means that undergraduates who might otherwise pursue a non­ athematical sciences major gain exposure to a broader array of m mathematics and statistics courses and, in essence, keep more career op- tions open. Double or flexible majors have also enabled some departments in mathematics and statistics to increase the number of undergraduates in their programs and keep them strongly involved at least through their bachelor’s degrees. Many graduate students will end up not with traditional academic jobs but with jobs where they are expected to deal with problems much less well formulated than those in the academic setting. They must bring their math- 10  PCAST, 2012, Engage to Excel: Producing One Million Additional College Graduates with Degrees in Science, Technology, Engineering, and Mathematics. The White House, Washington, D.C. Appendix G of this report recounts some anecdotal evidence of the value of undergraduate research experiences for building student commitment to STEM fields and retaining it.

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134 THE MATHEMATICAL SCIENCES IN 2025 enterprise must improve its ability to attract and retain a greater fraction of talented young people. As indicated in the introduction to this chapter, this is a high-priority national issue. What Can Be Done? There have been some notable successes in attracting and retaining more under-represented minorities in the mathematical sciences. For ex- ample, William Vélez of the University of Arizona at Tucson has success- fully increased minority enrollment. He offered the following advice for recruiting all types of students: • Provide timely information to students. Help them to understand the system and future opportunities. Even good students need a ­ ttention and advice. • Examine ways to ease the transition from high school to college or university. • Encourage students who are interested in science and engineering to have a second major in mathematics. • Pay more individual attention to talented students by having fac- ulty reach out to them directly. • Communicate the necessity of studying mathematics.20 While these suggestions are not unique, the practices are often not implemented. They can be broadly applied to all students, regardless of race or gender, to increase the population of undergraduate majors in the mathematical sciences. Despite the small numbers of underrepresented minorities entering the mathematical sciences, there are a number of programs across the country that are quite successful at achieving greater participation. They have es- tablished practices that work and which could be replicated elsewhere. A recent report from the National Academies21 presents a thorough examina- tion of approaches for tapping this talent. The NSF-supported mathematical science institutes have also been active in efforts to reach out to underrepresented groups. For example, the Insti­ tute for Mathematics and its Applications (IMA) and the Institute for Pure and Applied Mathematics (IPAM) offer workshops in professional devel­ 20  William Yslas Vélez, 2006, “Increasing the number of mathematics majors,” FOCUS Newsletter, Mathematical Association of America, March. 21  Institute of Medicine, National Academy of Sciences, and National Academy of Engi- neering, 2011, Expanding Underrepresented Minority Participation: America’s Science and Technology Talent at the Crossroads. The National Academies Press, Washington, D.C.

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PEOPLE IN THE MATHEMATICAL SCIENCES ENTERPRISE 135 opment aimed at mathematical scientists from under-represented groups. At the K-12 level, IPAM, IMA, and other institutes have offered week-long programs for middle and high school girls. In rotation, the institutes offer the Blackwell-Tapia conferences, which aim to increase the exposure of underrepresented groups to mathematics. Some efforts of the Mathematical Sciences Research Institute (MSRI) aim at increasing the participation of women and minorities: • Connections for Women workshops, 2-day workshops that aim to showcase women’s talent in the field and that sometimes offer an intensive minicourse on fundamental ideas and techniques; • MSRI-UP, a program for undergraduates aimed at increasing the participation of underrepresented groups in mathematics graduate programs; and • The Network Tree, a project to compile names and contact infor- mation for mathematicians from underrepresented groups. Colette Patt from the Science Diversity Office of the University of California, Berkeley, and Deborah Nolan and Bin Yu from the Statistics Department at that university shared with the committee the following lists of issues (adapted by the committee) they compiled that academic depart- ments should consider when determining how to improve their recruitment and retention of women and other underrepresented groups. Issues That Affect Recruitment and Retention at the Undergraduate Level •  ffordability of undergraduate education and awareness of assistance A programs, such as Research Experiences for Undergraduates and sup- port for travel to conferences; •  wareness of and motivation to enter the mathematical sciences, such A as information about career options made possible by mathematical science coursework or majors and comparison of those options to some more common career paths; •  dequacy of mentoring, including encouragement, coaching, and strate- A gic advising; •  ccess to, and encouragement to participate in, a variety of research A opportunities; •  he possibility of boosting confidence by departmental approaches to T structuring the curriculum and course pedagogies, such as confidence, study habits, sense of community, and so on; •  cademic requirements, structure of courses and majors, academic sup- A port, choice of gateway courses, teaching effectiveness, and classroom practices; •  ampus climate and department culture. C

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136 THE MATHEMATICAL SCIENCES IN 2025 Issues That Affect Recruitment and Retention at the Graduate Level • A  vailability of role models; • N  eed for a sense of belonging and community to avoid possible isolation; • P  ossible harassment, peer interactions, and climate issues; • A  vailability and skill of mentoring; • O  pportunities for professional development and socialization; • P  sychological factors that possibly can be boosted by departments’ ap- proaches to structuring the graduate curriculum, courses, and tests to influence factors such as confidence, self-concept, science identity, and the threats of being stereotyped. •  onitoring and possible intervention to assist at the critical transition M from the graduate to postdoctoral positions; •  ssistance in goal-setting and evaluation. A Issues That Affect Recruitment and Retention of Underrepresented Faculty •  nderstanding and countering the drop-off of women and minorities U at the critical transition from postdoctoral years to faculty careers; •  nderstanding and countering the difficulties of achieving a life-work U balance, which tends to affect women more than men; •  dentifying perceptions that are gender differentiated and can affect I seemingly objective measures—for example, gender bias in letters of recommendation, teaching evaluations, perceptions of leaders; •  pportunities for leadership; O •  ifferential recognition, awards, and the accumulation of cultural capi- D tal in the field. Many of these issues have been the subject of published studies that document their impact on the recruitment and retention of women and other underrepresented groups, and most should be familiar to anyone who has spent time in academic departments. Statistics departments have been quite successful in recent years in at- tracting and retaining women, and it would be very helpful to understand better how the broader mathematical sciences community can learn from this success. A similar observation has been made with regard to attracting women to application-oriented computer science (CS) programs.22 Overall, there has been progress in attracting women and minorities to the mathematical sciences. Unfortunately, the accumulation of small dis­ advantages women and minorities face throughout their career can add up to a significant disadvantage and can cause the leaking of the pipeline that 22  See Christine Alvarado and Zachary Dodds, 2010, Women in CS: An evaluation of three promising practices. Proceedings of SIGCSE 2010 March 10-13. Association for Computing Machinery, Milwaukee, Wisc.

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PEOPLE IN THE MATHEMATICAL SCIENCES ENTERPRISE 137 is documented above. Beyond this, one or more egregious incidents can tip the balance for an individual. This is an important issue for the mathemati- cal sciences to address. Recommendation 5-4: Every academic department in the mathemati- cal sciences should explicitly incorporate recruitment and retention of women and underrepresented groups into the responsibilities of the faculty members in charge of the undergraduate program, graduate program, and faculty hiring and promotion. Resources need to be pro- vided to enable departments to monitor and adapt successful recruiting and mentoring programs that have been pioneered at many schools and to find and correct any disincentives that may exist in the department. Appendix E lists some of the organizations and programs that are committed to improving participation by women and minorities in the mathematical sciences at all levels of education. THE CRITICAL ROLE OF K-12 MATHEMATICS AND STATISTICS EDUCATION The extent to which size of the pipeline of students preparing for math- ematical science-based careers can be enlarged is fundamentally limited by the quality of K-12 mathematics and statistics education. The nation’s well-being is dependent on a strong flow of talented students into careers in STEM fields, but college students cannot even contemplate those careers unless they have strong K-12 preparation in the mathematical sciences. Absent such preparation, most are unlikely to be interested. Those state- ments are even more apt with respect to young people who could become mathematical scientists per se. The K-12 pipeline is an Achilles heel for U.S. innovation. Fortunately, a lot of innovation is taking place in K-12 mathematics and statistics education, and the mathematical sciences com- munity has a role to play in strengthening and implementing the best of these efforts. This section gives a brief overview of the issues and pointers to the relevant literature. It is beyond the mandate of the current study to recommend actions in response to this general national challenge. There are a large number of K-12 schools, both public and private, that perform at a high level year after year across the United States. Annual ­ rankings of the best U.S. high schools document the top few on the basis of student performance parameters and other criteria.23 Most states employ 23  For example, US News and World Report, America’s Best High Schools, November 29, 2007; Newsweek, Best High Schools in the U.S., June 19, 2011; Bloomberg Business Week, America’s Best High Schools 2009, January 15, 2009.

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138 THE MATHEMATICAL SCIENCES IN 2025 information systems that keep detailed public school records for students, teachers, and school administrators on the basis of parameters established for mandatory statewide use. Public schools are subject to state-enforced sanctions when a school fails to meet the mandated performance criteria. But overall, particularly in the sciences and mathematics, U.S. K-12 students con- tinue to perform substantially below average in international comparisons. Education Secretary Arne Duncan’s report on December 7, 2010, pre- sented on the occasion of the release of the 2009 results of the Program for International Student Assessment (PISA) of the Organisation for Economic Co-operation and Development (OECD), did not contain encouraging news about the performance of U.S. 15-year-olds in mathematics.24 U.S. students ranked 25th among the 34 participating OECD nations, the same level of performance as 6 years earlier in 2003. The results were not encouraging in reading literacy either, with U.S. students placing 14th, effectively no change since 2000. The only improvement noted was a 17th place rank- ing in science, marginally better than the 2006 ranking. Secretary Duncan added that the OECD analysis suggests the 15-year-olds in South Korea and Finland are, on average, 1 or 2 years ahead of their American peers in math and science. The picture is not improving. In September 2011, the College Board reported that the SAT scores for the U.S. high school graduating classes of 2011 fell in all three subject areas tested: reading, writing, and mathemat- ics. The writing scores were the lowest ever recorded.25 A report from Harvard’s Program on Education Policy and Governance in August of 2011 revealed that U.S. high school students in the Class of 2011 ranked 32nd in mathematics among OECD nations that participated in PISA for students at age 15. The report noted that 22 countries significantly outperform the United States in the share of students who reach the “proficient” level in math (a considerably lower standard of performance than “advanced”).26 In September 2007 McKinsey & Co. produced what it called a first-of- its-kind approach that links quantitative results with qualitative insights on what high-performing and rapidly improving school systems have in com- mon.27 McKinsey studied 25 of the world’s school systems, including 10 of the top performers. They examined what high-performing school systems have in common and what tools they use to improve student outcomes. They concluded that, overall, the following matter most: 24  Available at http://www.ED.gov, December 7, 2010. 25  Wall Street Journal, “SAT Reading, Writing Scores Hit New Low,” September 15, 2011. 26  Paul E. Peterson, Ludgar Woessmann, Eric A. Hanushek, and Carlos X. Lastra-Anadon, 2011, Globally Challenged: Are U.S. Students Ready to Compete. Harvard Kennedy School of Government, August. 27  McKinsey & Co., 2007, How the World’s Best Performing School Systems Came Out on Top.

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PEOPLE IN THE MATHEMATICAL SCIENCES ENTERPRISE 139 • Getting the right people to become teachers (the quality of an edu- cation system cannot exceed the quality of its teachers); • Developing them into effective instructors (the only way to im- prove outcomes is to improve instruction); and • Ensuring that the system is able to provide the best possible in- struction for every child (high performance requires every child to succeed). The McKinsey report concludes: “The available evidence suggests that the main driver of the variation in student learning at school is the quality of the teachers.” Three illustrations are provided to support this conclusion: • Ten years ago, seminal research based on data from the Tennessee Comprehensive Assessment Program tests showed that if two aver- age 8-year-old students were given different teachers—one of them a high performer, the other a low performer—the students’ perfor- mance diverged by more than 50 percentile points within 3 years.28 • A study from Dallas showed that the performance gap between stu- dents assigned three effective teachers in a row and those assigned three ineffective teachers in a row was 49 percentile points.29 • In Boston, students placed with top-performing math teachers made substantial gains, while students placed with the worst teachers ­ r ­ egressed—their math actually got worse. The McKinsey report further concluded as follows: Studies that take into account all of the available evidence on teacher effective­ ess suggest that students placed with high-performing teachers will n progress three times as fast as those placed with low-performing teachers. The second McKinsey report (2010) addresses the teacher talent gap by examining the details of teacher preparation and performance in three top-performing countries: Singapore, Finland, and South Korea.30 These 28  W. Sanders and J. Rivers, 1996, Cumulative and Residual Effects of Teachers on Future Student Academic Achievement. University of Tennessee, Value-Added Research and Assess- ment Center, Knoxville, Tenn. 29  Heather R. Jordan, Robert L. Mendro, and Dash Weerasinghe, 1997, “Teacher Effects on Longitudinal Student Achievement: A Report on Research in Progress,” Presented at the CREATE Annual Meeting Indianapolis, Ind. Available at http://dallasisd.schoolwires.net/ cms/lib/TX01001475/Centricity/Shared/evalacct/research/articles/Jordan-Teacher-Effects-on- Longitudinal-Student-Achievement-1997.pdf. 30  Byron Auguste, Paul Kihn, and Matt Miller, 2010, “Closing the talent gap: Attracting and retaining top-third graduates to careers in teaching.” McKinsey & Company, September.

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140 THE MATHEMATICAL SCIENCES IN 2025 three countries recruit 100 percent of their teacher corps from the top third of their college graduate academic cohort, then screen for other important qualities as well. By contrast, in the United States only 23 percent of new K-12 teachers come from the top third, and in high poverty schools, the fraction is only 14 percent. The report concludes that Finland, Singapore, and South Korea “use a rigorous selection process and teacher training more akin to medical school and residency than a typical American school of education.” It goes on to examine what an American version of a “top third” strategy might entail and concludes that “if the U.S. is to close its achievement gap with the world’s best education systems—and ease its own socio-economic disparities—a top-third strategy for the teaching profession must be a part of the debate.” Undoubtedly, a part of closing this gap must address the situation that most teachers of mathematics and science in U.S. public middle and high schools do not have degrees or other certification in mathematics or science.31 ENRICHMENT FOR PRECOLLEGE STUDENTS WITH CLEAR TALENT IN MATHEMATICS AND STATISTICS While, as noted above, the current study does not have a mandate to examine the broad question of K-12 mathematics education, the math- ematical sciences community does have a clear interest in those precollege students with special talent for and interest in mathematics and statistics. Such students may very well go on to become future leaders of the re- search community, and in many cases they are ready to learn from active re­ earchers while still in high school, or even earlier. s A 2010 paper32 reported on two studies into the relationship between precollegiate advanced/enriched educational experiences and adult accom- plishments in STEM fields. In the first of these studies, 1,467 13-year-olds were identified as mathematically talented on the basis of scores of at least 500 on the mathematics section of the Scholastic Assessment Test, which puts them in the top 0.5 percentile. Their developmental trajectories were studied over 25 years, with particular attention being paid to accomplish- ments in STEM fields, such as scholarly publications, Ph.D. attainment, tenure, patents, and types of occupation(s) over the period. The second study profiled, retrospectively, the adolescent advanced/enriched educa- 31  NRC, 2010, Rising Above the Gathering Storm, Revisited: Rapidly Approaching Cat- egory 5. The National Academies Press, Washington, D.C. 32  Jonathan Wai, David Lubenski, Camilla Benbow, and James Steiger, 2010, Accomplish- ment in science, technology, engineering, and mathematics (STEM) and its relation to STEM educational dose: A 25-year longitudinal study. Journal of Educational Psychology 102 (4).

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PEOPLE IN THE MATHEMATICAL SCIENCES ENTERPRISE 141 tional experiences of 714 top STEM graduate students and related their experiences to their STEM accomplishments up to age 35. In both longitudinal studies, those with notable STEM accomplish- ments had been involved in a richer and more robust collection of advanced precollegiate educational opportunities in STEM (“STEM doses”) than the members of their cohorts with lower levels of STEM-related professional achievement. This finding holds for students of both sexes. The types of “STEM doses” noted in these studies include advanced placement (AP) and early college math and science courses, science or math project competi- tions, independent research projects, and writing articles within the disci- plines. Of these mathematically inclined students, those who participated in more than the median number of science and math courses and activities during their K-12 school years were about twice as likely, by age 33, to have earned a doctorate, become tenured, or published in a STEM field than were students who participated in a lower-than-average number of such activities. The differences in achieving a STEM professional occupation or securing a STEM patent between the “low dose” and “high dose” students were evident but not as pronounced. Note, however, that these results are merely an association and do not imply a cause-and-effect relationship. For example, those with the most interest and abilities in STEM fields might self-select for the enrichment programs. Nevertheless, it does fit with the individual experiences of many members of this committee that early ex- posure to highly challenging material in the mathematical sciences had an impact on their career trajectories. One means by which the mathematical sciences professional commu- nity contributes to efforts to attract and encourage precollege students is through Math Circles. Box 5-1 gives an overview of this mechanism, which has proved to be of real value in attracting and encouraging young people with strong talent in the mathematical sciences. From 1988 to 1996, the National Science Foundation (NSF) sponsored a Young Scholars Program that supported summer enrichment activities for high school students who exhibited special talent in mathematics and science.33 It was begun at a time when the United States was worried about the pipeline for scientists and engineers just as it worries now. By 1996, the NSF was “funding 114 summer programs that reached around 5,000 students annually [and about] 15% of the Young Scholars programs were in mathematics.”34 Some of the successful funding of mathematics programs through this mechanism included programs at Ohio State Uni- versity, Boston University, and Hampshire College. The committee believes 33  This description is drawn from Allyn Jackson, 1998, The demise of the Young Scholars Program. Notices of the AMS, March. 34  Ibid.

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142 THE MATHEMATICAL SCIENCES IN 2025 BOX 5-1 Mathematical Circles: Teaching Students to Explorea In 2006, an eighth-grade home-schooled student named Evan O’Dorney came to an evening meeting of the Berkeley Mathematics Circle with his mother. For an hour he listened to the director, Zvezdelina Stankova, talk about how to solve ­ eometry problems with a technique called circle inversion. Then, during a g 5-minute break, he went back to his mother and told her, “Mom, there are prob- lems here I can’t do!” It’s not something that O’Dorney has said very often in his life. By the time he graduated from high school, he had become as famous for academic excellence as any student can be. In 2007, he won the National Spelling Bee. From 2008 to 2010 he participated in the International Mathematics Olympiad (IMO) for the U.S. team three times, winning two silver medals and a gold. And in 2011 he won the Intel Science Talent Search with a mathematics project on continued fractions. President Barack Obama called O’Dorney personally to congratulate him after his IMO triumph, and the two met in person during the Intel finals. It would be easy to say that a student as talented as O’Dorney probably would have achieved great things even without the Berkeley Math Circle. But that would miss the point. For 5 years, the mathematics circle gave him direction, inspiration, and advice. It put him in contact with university professors who could pose problems difficult enough to challenge him. (As a ninth-grader, he took a university course on linear algebra and found a solution to a previously unsolved problem.) By the time he was a high-school senior, he was experienced enough and confident enough to teach sessions of the Berkeley Mathematics Circle himself. The experience helped him develop the communication skills he needed to win the Intel Science Talent Search. Not all students can be O’Dorneys, of course. But the math circle concept, imported from Eastern Europe, has begun to find fertile ground in the United States. The National Association of Math Circles now counts 97 active circles in 31 states, most of them based at universities and led by university professors. As is the case in Eastern Europe, math circles have become one of the most effec- tive ways for professional mathematicians to make direct contact with precollege students. In math circles, students learn that there is mathematics beyond the school curriculum. And yes, they discover problems that might be too hard for them to solve. But that is exactly the kind of problem that a student like O’Dorney wants to work on. Gifted students are often completely turned off by the problems they see in their high-school classes, which for them are as about as challenging as a game of tic-tac-toe. Dr. Stankova, who was then a postdoctoral fellow at the Mathematical Sciences Research Institute at Berkeley (she now teaches at Mills College in ­ akland), O b ­ egan the Berkeley Math Circle in 1998, hoping to replicate the experience she had as a grade-school student in Bulgaria. In Bulgaria and throughout Eastern E ­ urope, math circles are found in most grade schools and many high schools. Just as students with a talent for soccer might play on a school soccer team, students with a talent for mathematics go to a math circle. This does not mean that the continued

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PEOPLE IN THE MATHEMATICAL SCIENCES ENTERPRISE 143 BOX 5-1 Continued school’s regular math curriculum is insufficient or inadequate; it simply recognizes that some students want more. Dr. Stankova was surprised that a similar system did not exist in the United States. (The first math circle in the United States was founded at Harvard by R ­ obert and Ellen Kaplan in 1994; Stankova’s was the second.) Originally the Berkeley Math Circle was intended as a demonstration for a program that would move into secondary schools. But the United States turned out to be different from Eastern Europe in important ways. Here, very few secondary school teachers had the knowledge, the confi- dence, or the incentive to start a math circle and keep it going. This was different from the situation in Bulgaria, where schoolteachers were compensated for their work with math circles. Although some U.S. math circles have flourished without a university nearby (for example, the math circle in Payton, Illinois), most have de- pended on leadership from one or more university mathematicians. For example, the Los Angeles Math Circle has very close ties to the math department at UCLA. Other differences showed up over time. With circles based at universities, l ­ogistics—getting kids to the meeting, and finding rooms for them to meet in— became more difficult. At present the Berkeley Math Circle, with more than 200 students, literally uses every seminar room available within the UC Berkeley math department on Tuesday nights. Most universities offer little or no support to the faculty who participate. Administrators do not always realize that the high-school students who attend the math circles are potential future star students at their universities. In fact, some of them are already taking courses at the university. Stankova has often had to alert UC Berkeley faculty members to expect a tenth- grader in their classes who will outshine the much older college students. One part of the math circles philosophy has, fortunately, survived its trans- plantation from Eastern Europe to America. Math circles encourage open-ended exploration, a style of learning that is seldom possible in high-school curricula that are packed to the brim with mandatory topics. Problems in a math circle are defined as interesting questions that one does not know at the outset how to answer—the exact opposite of “exercises.” They introduce students to topics that are almost never taught in high school: for example, circle inversion, complex numbers, continued fractions (the subject of O’Dorney’s Intel project), cryptology, topology, and mathematical games like Nim and Chomp. Many participants in math circles have gone on to success in scholastic math competitions, such as the USA Mathematical Olympiad (USAMO) and the IMO. For example, Gabriel Carroll, from the Berkeley Math Circle, earned a silver medal and two golds in the IMO, including a perfect score in 2001. He participated in the Intel Science Talent Search and finished third. As a graduate student in economics at MIT, Carroll proposed problems that were selected for both the 2009 and 2010 IMO events. Ironically, the latter problem was the only one that stumped O’Dorney. But not all students are interested in competitions. Victoria Wood participated in the local Bay Area Math Olympiad but did not like having to solve problems in a limited time. She liked problems that required longer reflection (as real research continued

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144 THE MATHEMATICAL SCIENCES IN 2025 BOX 5-1 Continued problems almost always do). She started attending the Berkeley Math Circle at age 11, matriculated at UC Berkeley at age 13, and is now a graduate student with several patents to her name. Some math circles, such as the Kaplans’ original math circle in Boston, deliberately avoid preparing students for math competitions. Others do provide preparation for competition, but it is far from being their main emphasis. In 2006, the American Institute of Mathematics (AIM) began organizing math teachers’ circles, designed specifically for middle-school teachers. After all, why should students have all the fun? By exposing teachers to open-ended learning, and encouraging them to view themselves as mathematicians, the organizers hope to have a trickle-down effect on thousands of students. At present, AIM lists 30 active teachers’ circles in 19 states. Despite their very promising start, it remains to be seen whether math circles will become a formal part of the American educational system or remain a poorly funded adjunct that depends on the passion and unpaid labor of volunteers. Clearly they have already provided an invaluable service to some of America’s brightest youngsters. Conceivably, if teachers’ circles take root, or if enough teachers come to observe math circles with their students, they could begin trans- forming American schools in a broader way, so that mathematical competence is expected and mathematical virtuosity is rewarded. aThe committee thanks Dana Mackenzie for drafting the text in this box. that reviving this sort of program would contribute in exciting ways to the mathematical sciences (or STEM) pipeline. Recommendation 5-5: The federal government should establish a n ­ ational program to provide extended enrichment opportunities for students with unusual talent in the mathematical sciences. The program would fund activities to help those students develop their talents and enhance the likelihood of their pursuing careers in the mathematical sciences. In making this recommendation, the committee does not intend in any way to detract from the important goal of ensuring that every student has access to excellent teachers and training in the mathematical sciences. The goal of growing the mathematical sciences talent pool broadly is synergistic with the goal of attracting and preparing those with exceptional talent for high-impact careers in the mathematical sciences.