Destroying American Math Education

Diversity is our strength. Our diverse and equitable and inclusive nation will naturally prevail against the authoritarian state that is China. You can see this thesis argued across the political spectrum. Unfortunately, it is rank nonsense, Prozac for the depressed American soul.

In truth, as most of us recognize, diversity quotas are destroying America. They are certainly destroying the minds of America’s schoolchildren. In the field of mathematics America is falling behind the world. The new mania about anti-racism training and social justice is going to make things worse, not better.

And, yes, I know that you have heard these basic ideas before, at times on this blog. And yet, I want to emphasize the importance of a Quillette article, written by three senior, and decorated mathematicians: Percy Deift, Svetlana Jitomirskaya, and Sergiu Klainerman.

They are sounding the alarm against critical race theory and the rest, especially as it has been dumbing down children’s ability to learn math. And as math goes, so goes science.

The authors remark that great achievements in math and science have sustained America’s past greatness. As it happens, many of the leaders in the field were immigrants from Europe, refugees from World War II and the Cold War.

To their minds, our dominance in math is now under siege:

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.

Of course, the problem begins in elementary and high schools. Aside from the horrors visited on children by the teachers’ unions, we have the simple fact that teachers’ colleges are getting it all wrong. What other lesson could we have drawn from the kerfuffle over Jill Biden’s calling herself a doctor. Graduates of teachers’ colleges learn some pedagogical techniques, but while they are doing so they are not learning how to do math.

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.

A not-so-minor detail-- the best American college students in math are not exactly the products of America’s K-12 educational system. How many are Asian American, the products of a rigorous community culture? How many of them, being Asian immigrants, will graduate and return to their home countries, where they will not be burdened by empty-headed rants about critical race theory:

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.

Of course, the war on merit, now being conducted under the guise of reducing racial disparities is merely dumbing down the discipline, so that underachievers will not feel so bad.

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.

Now, a diverse America is having trouble competing with other countries for top talent. Many foreign students come here because the educational system is of higher quality than what they have at home. Now, however, the Chinese are doing everything in their power to improve their colleges and universities:

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.

As for the numbers, American students are world class laggards:

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.

The authors show us how a state like California is dumbing down the teaching of math in school.

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.

California proposes to dumb down math by making it a function of data science. Unfortunately, it eliminates most algebra courses, and this, the authors note, makes children unqualified to do most advanced STEM work.

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).

Deift, Jitomirskaya, and Klainerman respond:

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.

Since skin color is now all that matters, universities in California will be hiring for diversity, but not for merit.

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.

Of course, China is taking their math training in an entirely different direction:

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 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.

The signs of American decline are manifest:

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.

Have a nice day!