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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.