All three of us are mathematicians who came to the United States as young immigrants, having been attracted by the unmatched quality and openness of American universities. We came, as many others before and after, with nothing more than a good education and a strong desire to succeed. As David Hilbert famously said, “Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.” Having built our careers in US academia, we are proud to call ourselves American mathematicians.
The United States has been dominant in the mathematical sciences since the mass exodus of European scientists in the 1930s. Because mathematics is the basis of science—as well as virtually all major technological advances, including scientific computing, climate modelling, artificial intelligence, cybersecurity, and robotics—US leadership in math has supplied our country with an enormous strategic advantage. But for various reasons, three of which we set out below, the United States is now at risk of losing that dominant position.
First, and most obvious, is the deplorable state of our K-12 math education system. Far too few American public-school children are prepared for careers in science, technology, engineering, and mathematics (STEM). This leaves us increasingly dependent on a constant inflow of foreign talent, especially from mainland China, Taiwan, South Korea, and India. In a 2015 survey conducted by the Council of Graduate Schools and the Graduate Record Examinations Board, about 55 percent of all participating graduate students in mathematics, computer sciences, and engineering at US schools were found to be foreign nationals. In 2017, the National Foundation for American Policy estimated that international students accounted for 81 percent of full-time graduate students in electrical engineering at U.S. universities; and 79 percent of full-time graduate students in computer science.
That report also concluded that many programs in these fields couldn’t even be maintained without international students. In our field, mathematics, we find that at most top departments in the United States, at least two-thirds of the faculty are foreign born. (And even among those faculty born in the United States, a large portion are first-generation Americans.) Similar patterns may be observed in other STEM disciplines.
The second reason for concern is that the nationwide effort to reduce racial disparities, however well-intentioned, has had the unfortunate effect of weakening the connection between merit and scholastic admission. It also has served (sometimes indirectly) to discriminate against certain groups—mainly Asian Americans. The social-justice rhetoric used to justify these diversity, equity, and inclusion (DEI) programs is often completely at odds with the reality one observes on campuses. The concept of fighting “white supremacy,” in particular, doesn’t apply to the math field, since American-born scholars of all races now collectively represent a small (and diminishing) minority of the country’s academic STEM specialists.
Third, other countries are now competing aggressively with the United States to recruit top talent, using the same policies that worked well for us in the past. Most notably, China, America’s main economic and strategic competitor, is in the midst of an extraordinary, mostly successful, effort to improve its universities and research institutions. As a result, it is now able to retain some of the best Chinese scientists and engineers, as well as attract elite recruits from the United States, Europe, and beyond.
In a 2018 report published by the Organization for Economic Cooperation and Development (OECD), China ranked first in mathematical proficiency among 15-year-olds, while the United States was in 25th place. And a recent large-scale study of adults’ cognitive abilities, conducted by the National Center for Education Statistics, found that many Americans lack the basic skills in math and reading required for successful participation in the economy. This poor performance can’t be explained by budgetary factors: When it comes to education spending per pupil, the United States ranks fifth among 37 developed OECD nations.
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There are numerous underlying factors that help explain these failures—including some that, as mathematicians, we feel competent to address. One obvious problem lies in the way teachers are trained. The vast majority of K-12 math teachers in the United States are graduates of programs that teach little in the way of substantive mathematics beyond so-called math methods courses (which focus on such topics as “understanding the complexities of diverse, multiple-ability classrooms”). This has been true for some time. But the trend has become more noticeable in recent years, as curricula increasingly shift from actual mathematics knowledge to courses about social justice and identity politics.
At the same time, math majors—who can arrive in the classroom pre-equipped with substantive mathematics knowledge—must go through the process of teacher certification before they can teach math in most public schools, a costly and time-consuming prerequisite. The policy justification for this is that all teachers need pedagogical training to perform effectively. But to our knowledge, this claim isn’t supported by the experience of other advanced countries. Moreover, in those US schools where certification isn’t required, such as in many charter and private schools, math majors and PhDs are in great demand, and the quality of math instruction they provide is often superior.
Even if some pedagogical training is desirable, particularly for elementary-school teachers, it is easier for a math specialist to pick up teaching skills on the job than it is for a trained teacher to acquire fundamental math knowledge. Based on our own experience, the best high school teachers are typically those who have solid mathematics backgrounds and enjoy teaching math.
An even bigger problem, in our view, is that the educational establishment has an almost complete lock on the content taught in our schools, with little input from the university math community. This unusual feature of American policymaking has led to a constant stream of ill-advised and dumbed-down “reforms,” which have served to degrade the teaching of mathematics to such an extent that it has become difficult to distinguish a student who is capable from one who is not.
Those who find that last assertion difficult to accept should peruse the revised Mathematics Framework proposed by California’s Department of Education. If implemented, the California framework would do away with any tracking or differentiation of students up to the 11th grade. In order to achieve what the authors call “equity” in math education, the framework would effectively close the main pathway to calculus in high school to all students except those who take extra math outside school—which, in practice, means students from families that can afford enrichment programs (or those going to charter and private schools). California is just one state, of course. But as has been widely noted, when it comes to policymaking, what happens in California today often will come to other states tomorrow.
The framework proposed for California’s 10,588 public schools and their six-million-plus students promotes “data science” as a preferred pathway, touting it as the mathematics of the 21st century. While this might sound like a promising idea, the actual “data-science” pathway described in the framework minimizes algebraic training to such an extent that it leaves students completely unprepared for most STEM undergraduate degrees. Algebra is essential to modern mathematics; and there is hardly any application of mathematics (including real data science) that is not based to a large extent on either algebra or calculus (with the latter being impossible to explain or implement without the former).
The authors write that “a fundamental aim of this framework is to respond to issues of inequity in mathematics learning”; that “we reject ideas of natural gifts and talents [and the] cult of the genius”; and that “active efforts in mathematics teaching are required in order to counter the cultural forces that have led to and continue to perpetuate current inequities.” And yet the research they cite to justify these claims has been demonstrated to be shallow, misleadingly applied, vigorously disputed, or just plainly wrong. Even the specific model lessons offered in the proposed framework fail to withstand basic mathematical scrutiny, as they muddle basic logic, present problems that can’t be solved by techniques described as being available to students, or list solutions without discussing the need for a proof (thus developing a false understanding of what it means to “solve” a problem—a misconception that university educators such as ourselves must struggle to undo).
The low quality of public K-12 math education in the United States has affected all demographic groups. But it has had a particularly strong negative effect on non-immigrant blacks and Hispanics, as well as young women of all races. This has led to a disappointing level of representation for these groups in STEM disciplines, which in turn has provoked understandable concern. We applaud efforts to address this problem, insofar as they help remove remaining obstacles and prejudices, and encourage more women and underrepresented minorities to choose careers in mathematics and other STEM disciplines. Indeed, partly as a result of such steps, the representation of women in our profession has increased dramatically over the last 50 years.
But what started as a well-meaning and sometimes beneficial effort has, over time, transformed into a bureaucratic machine whose goal has gone well beyond fighting discrimination. The new goal is to eliminate disparities in representation by any means possible. This is why education officials in some school boards and cities—and even entire states, such as California and Virginia—are moving to scrap academic tracking and various K-12 gifted programs, which they deem “inequitable.” Operating on the same motivations, many universities are abandoning the use of standardized tests such as the SAT and GRE in admissions.
This trend, which reaches across many fields, is especially self-defeating in mathematics, because declining standards in K-12 math education are now feeding into a vicious cycle that threatens to affect all STEM disciplines. As already noted, low-quality K-12 public-school education produces students who exhibit sub-par math skills, with underprivileged minorities suffering the most. This in turn leads to large disparities in admissions at universities, graduate programs, faculty, and STEM industry positions. Those disparities are then, in turn, condemned as manifestations of systemic racism—which results in administrative measures aimed at lowering evaluation criteria. This lowering of standards leads to even worse outcomes and larger disparities, thus pushing the vicious cycle through another loop.
The short-term fix is a quota system. But when applied to any supposedly merit-based selection process, quotas are usually counterproductive. Various studies, which accord with our own experience in academia, show that placing talented students from underrepresented groups in math programs that are too advanced for their level of preparedness can lead to discouragement, and often even abandonment of the field. Typically, these students would be better served by slightly less competitive, more nurturing programs that accord with their objectively exhibited levels of performance.
Unfortunately, the trend is pointing in the opposite direction. In fact, at many of our leading academic and research institutions, including the National Academies of Sciences, the American Academy of Arts and Sciences, the National Science Foundation, and the National Institutes of Health, scientific excellence is being supplanted by diversity as the determining factor for eligibility in regard to prizes and other distinctions. And some universities, following the example of the University of California, are now implementing measures to evaluate candidates for faculty positions and promotions based not only on the quality of their research, teaching, and service, but also on their specifically articulated commitment to diversity metrics. Various institutions have even introduced pathways to tenure based on diversity activities alone. The potential damage such measures can bring to academic standards in STEM is immense. And the history of science is full of examples that show how performative adherence to a politically favored ideology, easily faked by opportunistic and mediocre scientists, can lead to the devaluation of entire academic fields.
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Needless to say, China pursues none of the equity programs that are sweeping the United States. Quite the contrary: It is building on the kind of accelerated, explicitly merit-based programs, centered on gifted students, that are being repudiated by American educators. Having learned its lesson from the Cultural Revolution, when science and merit-based education were all but obliterated in favor of ideological indoctrination, China is pursuing a far-sighted, long-term strategy to create a world-leading corps of elite STEM experts. In some strategically important fields, such as quantum computing, the country is arguably already ahead of the United States.
As part of this effort, China is identifying and nurturing talented math students as early as middle school. At the university entrance level, China relies on a hierarchical, layered system based on a highly competitive, fairly administered, national exam. STEM disciplines are encouraged: According to the World Economic Forum, China has the highest number of STEM grads in the world—at least 4.7 million in 2016. (By comparison, the United States came in third at 569,000. And as noted previously, a large portion of these graduates are foreign nationals.) China also has vastly increased the quality of its top universities, with six now ranked among the best 100 in the world. Tsinghua and Peking (ranked 17th and 18th respectively) now narrowly outrank Columbia, Princeton, and Cornell. As visitors to these Chinese universities (including ourselves) can attest, the average math undergraduate is now performing at a much higher level than his or her counterpart at comparable US institutions.
One reason for this is the work of scientists such as Shing-Tung Yau, a prominent Harvard mathematician who has spent decades helping to build up research mathematics in China. A key feature of the selective and consequential undergraduate competitions he’s developed over the last 10 years is that students are encouraged to focus their studies precisely on the content they will need as research mathematicians. High placement in these competitions virtually guarantees a student a spot at a top graduate school, and the program thereby helps systematically attract talented people to mathematics.
More recently, another group of prominent mathematicians (including some based in the United States), acting with the help of the Alibaba technology conglomerate and the China Association for Science and Technology, have created a global undergraduate mathematics competition with similar features. High schoolers who excel in annual math olympiads also are fast-tracked into top university programs.
While China already produces almost twice as many STEM PhDs as the United States, its universities still lag their US counterparts with respect to the quality of their graduate education programs. This is why many talented Chinese scholars continue to enroll in US programs. But this talent flow will likely soon ebb, or even dry up completely, as Chinese universities are now actively attracting senior Chinese, US, and European scientists to their faculty. (And unlike their American institutional counterparts, they recruit on the merit principle, unhampered by ideologically dictated diversity mandates.) In some cases, we are seeing prominent mathematicians at good or even top US schools moving to Peking and Tsinghua Universities after long and successful US careers. Many of these scholars are Chinese, but some are not.
We do not wish to gloss over China’s status as an authoritarian country that exhibits little concern for personal freedoms. But acknowledging this fact only serves to emphasize the significance of the shift we are describing: The drawbacks of American education policies are so pronounced that US schools are now losing their ability to attract elite scholars despite the fact that the United States offers these academics a freer and more democratic environment.
Moreover, even America’s vaunted reputation as a welcoming land for immigrants has taken a hit thanks to the recent, highly-publicized wave of anti-Asian crimes—which, though small in scale, is scaring off some Chinese students and their parents. Of greater significance are the thinly disguised anti-Asian policies (masquerading as anti-racism mandates) that are implemented by top US schools as a means to exclude Asian students.
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Reversing America’s slide in STEM education will require many policy changes, not all of which fall within our expertise as mathematicians and academics. But at the very least, we recommend that American education authorities prioritize the development of comprehensive STEM curricula, at both basic and advanced levels, and allow outstanding mathematicians and other scientists to assist public servants in their design. Highly successful precedents such as the BASIS Charter School Curriculum and the Math for America teacher-development program supply examples of how such curricula might be developed. This should be coupled with a nationwide effort to identify and develop students who exhibit exceptional math talent.
American policymakers must also address the misplaced priorities of the education schools that train teachers. At the very least, math majors should be allowed to teach without following a full slate of accreditation procedures. And people who teach middle and high-school math should themselves be required to receive rigorous instruction in that subject.
Schools in urban areas and inner-city neighborhoods should be improved by following the most promising models. Such programs demonstrate that children benefit if they are challenged by high standards and a nurturing environment. Ideally, schools should operate in a manner that allows them to avoid year-to-year dependence on the vagaries of local funding and bureaucratic mandates.
More broadly, American educators must return to a process of recruitment and promotion based on merit, at all levels of education and research—a step that will require a policy U-turn at the federal, state, and local levels (not to mention at universities, and at tech corporations that have sought to reinvent themselves as social-justice organizations). Instead of implementing divisive policies based on the premise of rooting out invisible forms of racism, or seeking to deconstruct the idea of merit in spurious ways, organizations should redirect their (by now substantial) DEI budgets toward more constructive goals, such as funding outreach programs, and even starting innovative new charter schools for underprivileged K-12 students. Elite private universities, in particular, are well positioned to direct portions of their huge endowments and vast professional expertise in this regard. By doing so, they could demonstrate that it’s possible to help minority students succeed without sacrificing excellence.
The proposals we are describing here may sound highly ambitious—not to mention being at cross-currents with today’s ideological climate. But we also believe there will soon be an opportunity for change, as the rapid rise of China in strategically important STEM fields may help shock the American policymaking community into action—much like the so-called Sputnik crisis of the late 1950s and early 1960s, when it was Russia’s soaring level of technical expertise that became a subject of public concern. Then, as now, the only path to global technological leadership was one based on a rigorous, merit-based approach to excellence in mathematics, science, and engineering.
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