This is my response to an article by math professors with experiences at New York University, the Georgia Institute of Technology, the University of California in Irvine, and Princeton University. The authors are Percy Deift, Svetlana Jitomirskaya, and Sergiu Klainerman. The article was published in Quillette, which is generally a dubious source, but looking over several articles there, it seems like they sometimes get interesting and thoughtful contributions from serious thinkers. There are also plenty of articles that, it seems to me, are hack pieces written by ideologues. Readers can certainly choose among what they find at the website and find some worthwhile pieces. The article I’m responding to is one that I found worthwhile, and engaging.
Many of the articles at Quillette seem focused on attacking radical perspectives and policies. But, the critiques are typically more thoughtful than what one would find at many other conservative sources. I should say that the site seems to have a conservative Libertarian approach, but publishes less total garbage than what you might find at other Libertarian sources such as Reason or the Cato Institute. Back in 2019 Donna Minkowitz wrote a hack piece for the radical magazine the Nation about how horrible Quillette is, and her article illustrates some of the intellectual intolerance that turns me off while simultaneously making a damning critique of Quillette. Sure, Quillette pushes odious ideas and stupid articles, but “Fascist Creep”? Really?
Let’s take a look at the article “As US Schools Prioritize Diversity Over Merit, China Is Becoming the World’s STEM Leader” by Percy Deift, Svetlana Jitomirskaya, and Sergiu Klainerman, published on August 19th of 2021. https://quillette.com/2021/08/19/as-us-schools-prioritize-diversity-over-merit-china-is-becoming-the-worlds-stem-leader/
To start, I’ll disclose that I agree that math education in the United States is in trouble. The Program for the International Assessment of Adult Competencies (PIAAC) assesses how well American adults perform on tests of literacy, numeracy, and digital problem solving. Only 39% of American adults perform in the highest (of three) categories of numeracy, whereas the international average is 44%. Likewise, 28% of Americans are essentially illiterate with numeracy (lowest of three categories) while the international average is 23%. Top performing nations like Japan and Finland have 63% and 58% of their population in the highest level of numeracy, and only 8% and 13% in the lowest category. I think the authors make some good suggestions about how to improve math education. The authors are concerned about diversity values getting in the way of meritocracy values, and I think that is something we ought to be concerned about, but I doubt it is a substantial problem, and the article offers me no evidence that it is, and so I suspect that the authors’ concerns on that account are overwrought. However, I don’t have much evidence to disprove their claims (or, actually, conjectures), so I really don’t have a strong opinion about this, and I’d like to see more facts and evidence so I could draw a better-informed conclusion. It’s odd that authors with exceptionally good mathematical skills would publish an article like this that has so little quantitative evidence to support their claims.
The authors claim that we have deplorable K-12 math education. That may be so, but they support this claim with evidence that graduate students in mathematics, engineering, and computer science are mostly foreign nationals. They do not give any information about biology, medicine, chemistry, geology, or other scientific fields, but they make a good case that too few American students are attracted into graduate studies within mathematics, engineering, and computer science. To the extent that K-12 math education ought to inspire students into those disciplines and pull students into undergraduate programs that prepare them for graduate studies in those programs, this supports a claim that math education is “deplorable”. It does not tell us anything about whether K-12 math education is lacking in other respects. Are there any tests of basic mathematics literacy or the ability to apply mathematics and quantitative reasoning to real world problems given to 17-23 year-olds? There should be, and if there are, those would tell us something about the quality of math education in America in terms of what people are learning. The authors tell us that, “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 PIAAC results to which they direct readers tell us that “many” means about 28%, which is alarming, and worse than international comparison averages (23% of samples in comparison nations tend to be numerically illiterate).
However, if we examine the study with more care than the authors of this paper did, we can see an interesting thing. Persons my age or older (born in the late 1960s to early 1970s or earlier) did not experience education in an environment that emphasized diversity. Are the numeracy abilities of persons 45-54 or 55-65 better than the younger cohorts of 16-24 or 25-34 who have been subjected to all this diversity emphasis? No. I doubt there is a statistically significant difference. Average scores on numeracy in the 2017 PIAAC survey show 16-24 year-olds with 255, and 25-34 year-olds with 261. My cohort of 45-54 year-olds were scoring 251 and the 55-65 year old younger baby boomers were scoring 249. Maybe the fact that we who were studying math when (allegedly) merit was valued more than diversity, score lower on mathematical competence assessments (probably not significantly lower) than those kids who were subjected to an emphasis on diversity (allegedly over merit), is due to cognitive decline with aging?
Does the fact that most graduate students in mathematics, engineering, and computer science are immigrants and foreign-born tell us that mathematics education and knowledge in America is bad? America has a long tradition of bringing in people from other countries and making them into Americans to fill needs in many fields of our civilization. What percentage of students in mathematics or engineering were foreign-born or foreign students or children of immigrants in the 1920s-1930s, or the 1880s-1890s? Were immigrants overrepresented then, or is this a recent phenomenon? To understand whether a focus on diversity over merit has reduced interest in mathematics among non-immigrant American populations, I’d want the authors to establish that this lack of native-born Americans in those fields has significantly increased in recent years as the focus on diversity has increased. Other plausible explanations for why foreign-born students, native-born children-of-immigrants, and foreign students dominate these fields in the United States include:
- limits in language proficiency give those students a comparative advantage in those fields that require less nuanced fluency in English. They may be better than native-born Americans in all subjects, but they are lot better in fields that require less English fluency, so those fields attract them;
- graduate programs in the United States are global programs in which the top three million Americans in their twenties are competing against the top 30 million non-Americans in their twenties, and the Americans and non-Americans going into graduate studies know this, and tend to concentrate in fields where they have relative competitive advantages;
- Immigrants who do well in mathematics, computer science, and engineering are more survival-oriented in their value system, and therefore they seek out disciplines that promise higher economic reward in contrast to American native-born students, who may care more about self expression, or identity exploration, or having fun, and therefore study topics they find agreeable rather than considering which degrees are likely to lead to higher incomes.
The authors are correct that some diversity, equity, and inclusion initiatives have diminished the importance of merit, and this has in many cases been unfair to good students who should have been admitted or steered into mathematics, engineering, and computer sciences. The fact that this happens and is a problem is probably a consensus truth; it must certainly be happening somewhere, and we can find egregious anecdotes of it happening in specific places. Is this problem so widespread and pervasive that it can account for a significant portion of the explanation for why mathematics, computer science, and engineering graduate students and faculty are immigrants or foreign-born? The article claims so, but I’m unaware of any evidence that this is so, and the authors should have provided such evidence if it exists, but they didn’t. I’m not so interested in this that I’m going to go and find it for them.
A further point about merit. Decisions about admitting or hiring people force decision-makers into dichotomies between “admit" or “do not admit”; or “hire" or “do not hire”. These categorical decisions are placed on a real world that is not dichotomous. Some who are admitted or hired will not turn out to have been the best candidates, and some who are denied would have been better suited. Some mix of predictive indicators that are consciously referenced and used will combine with intuitive factors in the determination of many of these decisions. The quantitative predictive indicators tend to be good in making gross distinctions, but not very good at making subtle distinctions. While it is wise to be wary of professional intuition and unconscious decision-making, researchers in the field of decision-making such as Kenneth R. Hammond have convincingly argued that the best decisions require a mix of quantitative reasoning and intuition of experts. So, decisions about merit are imperfect (at least when making subtle distinctions), and such decisions usually include intuitive evaluations.
We also know that there is in many people an intuitive bias against low-income persons, or persons with African heritage. Since using some intuition in hiring and admissions decisions tends to give improved accuracy, and since we know that many of us have unconscious biases against certain people that would diminish the value of our intuitive thinking, it makes sense to me that there should be some conscious efforts to reduce our intuitive biases. Only a crazed fringe will want to entirely demolish meritocracy, but most advocates for anti-bias training and diversity-promotion are not attempting to demolish merit-based decisions (although a few outliers are). We are trying to improve our ability to detect merit when we incorporate an understanding that our conceptions of “merit" may involve both false dichotomy logical errors and unconscious bias against certain candidates, and also acknowledge that there is probably systematic error in our quantitative predictive indicators of merit (tending to overestimate merit of high status candidates and underestimate that of low status candidates). Thus, some attempts to enhance diversity may actually be good attempts at improving our accuracy in predicting merit of candidates, and not attempts to ignore merit. Perhaps the authors of this article know this, and had no space to acknowledge it or present nuance, but it wouldn't surprise me if they are instead ignorant of this, and are simply reacting to popular conceptions of “diversity” and "merit" that are not grounded in good empirical or theoretical work on these topics.
The authors claim that efforts to reduce racial disparities has weakened the connection between merit and scholastic admission. Is this a general phenomena? Can they point to specific examples? The Supreme Court and many state legislatures have made it illegal to use race as a broad criteria in admission, but race can be taken into consideration within a framework in which there is a “narrowly tailored use” that gives certain candidates an advantage (see Regents of The University of California v. Bakke (1978) and Gratz v. Bollinger (2003)). But, universities cannot abandon merit and replace it with race. In decisions among candidates that are close in merit, an advantage to candidates who will increase diversity is allowed. However, several states, including California, Washington, and Michigan have state laws forbidding their universities from considering race in admissions decisions. The authors ought to have provided some evidence that such states banning racial considerations in admissions decisions have seen more native-born American students enter graduate programs in mathematics, engineering, or computer science. That would have helped support their argument. I’m not feeling the need to look into it, but I doubt that there will be a big difference, because I don't think racial preferences in admissions are breaking the link between merit and admissions in any big way. If it turn out that there is a big difference, I would change my opinion.
The authors point out that the United States spends a lot per student (ranked 5th among 37 developed OECD nations). Those numbers on spending are crude. At my university, people actually in the classroom teaching students are getting about 42% of all the budget share directed toward salaried employees (and probably less than a third of the budget going to all paid employees, since there are many hourly wage-earning workers as secretaries, groundskeepers, student life staff, library staff, kitchen staff, and so forth). Inflation-adjusted per-student spending on salaries of persons doing direct instruction has decreased here in the 20+ years since I was hired, but overall spending has increased (we have many more highly paid administrators and executives than we did when I was hired). To help the authors, I'd qualify their claim that the problem “isn't budgetary”. We probably spend enough money to expect good math education, but we probably are not spending that money efficiently in ways that would get us the sort of math education we desire. So the problem is budgetary, but not a problem of total spending. Perhaps. America also invests a lot in spending on children with special needs, and that’s something that makes me proud. We also have children suffering with the traumas associated with living in areas of concentrated poverty and racial segregation, which drives up the needs of our children. Do comparison advanced economy nations have similar problems? There are complexities here that the authors did not have space to address.
The authors may be right about the quality of education for math teachers, which they claim is low. But, they do not offer any evidence for it. I know of anecdotal evidence that they are wrong.
One claim the authors make is that persons who train to be math teachers are poorly prepared because they spend too much time learning about diversity and social justice, and insufficient time learning about mathematics. They are therefore inadequate teachers of mathematics. The authors claim persons well-trained in mathematics who have received mere basic training in education would be equally good or superior in the classroom compared to those who received education degrees or certificates allowing them to be certified as math teachers. It so happens that my wife has a B.S. in mathematics and was one semester of student-teaching away from also having a B.A. in education with a teaching certificate when she decided the math degree was sufficient and abandoned her teacher education work. As she was not fully English-proficient, I read most of her written work in her education courses (to correct things like punctuation and verb tense issues—I never wrote anything for her), and I do not remember noticing too much emphasis on diversity or social justice in her training. She was well-trained in mathematics, and could have been (and still could be) a good secondary school math teacher.
Further, I have good friends who teach in teacher education, and I have had about two or three education students in my social work or liberal studies courses every year that I’ve been at the Springfield campus of the University of Illinois. These students always needed a degree in their field and they needed to pass tests of proficiency. If they were hoping to teach mathematics in high schools, they would need a mathematics degree in addition to their teacher education coursework leading to a secondary education teacher certification. There are many states where teacher education requirements demand that high school or middle school teachers have a solid grounding in the subject they specialize in teaching. Some states (Ohio, New York, Massachusetts) even require that teachers earn graduate degrees (in education), but to start teaching, many states must surely require considerable coursework in the field to be taught (social studies teachers must have taken courses in social sciences; science teachers must have taken courses in sciences; mathematics teachers must have taken courses in mathematics). Has anyone compared standardized math achievement tests of students from different states? The states that have stricter requirements for math education for their math teachers, or reduced requirements for education studies relative to their requirements for math studies, should, if the authors of this article are correct, have high math achievement scores for their students, right? Such studies would help us determine whether the claims of these authors that teacher education, with its focus on social justice and diversity, is harming education in STEM fields in the USA. Without evidence, I’m not just going to accept claims one way or the other on this question.
I believe many states (such as Illinois) have a system where students must have a degree in the field they will be teaching (at least at the secondary education level) and a teaching certificate. So, while education courses might have a lot of content about diversity and social justice, the students should still be getting a degree in mathematics that presumably has mostly math content and very little content about diversity and social justice. I agree with the authors that the standards for allowing people into the classroom as certified teachers may be too high, but I hope they would agree that some teaching preparation and child development or child psychology courses ought to be mandated for future teachers. That is, I do not oppose teacher certification requirements; I just think they should be relaxed a bit, and the authors clearly agree with me that teacher certifications ought to be easier to obtain. For example, my wife has taught as a bi-lingual educator in local public schools for several years, and taught in other settings as well, but Illinois could not certify her as a high school mathematics teacher, despite her B.S. in mathematics and her extensive course work and field practicum experience in education, and her years of teaching in classrooms as a bilingual educator. That seems ridiculous to me.
The middle and later part of the article is far more persuasive and correct. The criticisms of revised mathematics framework proposed for California seem sound, but I do not know whether the authors are fairly portraying that proposal. If they are, then it sounds like a real turd of a plan. My sister works in the state education bureaucracy in Oregon, and she has explained to me how sometimes Fox News pundits and Wall Street Journal editorial writers have completely mischaracterized things that happen in Oregon with education standards. If people believed that those sources were fairly and accurately explaining what was going on, it would be reasonable for them to be upset and worried about what Oregon was doing. However, those sources were essentially just lying about what was happening, and people were misled into a froth of anger about things that weren’t real. That makes me wonder if the authors are fairly and accurately presenting the revised mathematics framework that was proposed (was it adopted?) in California.
The authors support tracking, but tracking isn’t always good. It may be that tracking provides a satisfactory education only to the top 20%, when in fact the top 50% or top 60% could all benefit from an education matching what the high track gets. As the authors note later in the article, "Children benefit if they are challenged by high standards and a nurturing environment”. Some research I've seen from Denmark and Japan suggests that gifted students can achieve even higher mastery of a subject if they are involved with collaborative learning in which they help average students meet high standards, and these approaches are much better for average students, who learn from their teachers and their peers. As someone who scores three to four standard deviations above average in most assessments of reasoning and problem-solving, I can relate to the way it can be tedious and soul-crushing to be subjected to pedagogical or training practices designed for the full range of abilities (including persons who are well below-average in intelligence) or oriented toward average persons. But having been in settings (elite private schools; universities) where my intellectual power is mediocre compared to my peers and mentors, I’m well-aware that it’s possible to provide students with learning experiences where everyone can succeed and “gifted” students with higher abilities can be challenged and engaged while those who struggle with the learning tasks are pulled up to higher performance levels. I’m in favor of some tracking and some gifted programs, but feel cautious about those approaches, and fear that they give us the sort of results the authors deplore; where maybe 20% to 30% of Americans are mathematically competent, but an equal number are essentially mathematically illiterate. There is no excuse for having more than 15% of the adult population mathematically illiterate.
The authors are right to suggest that we take a pragmatic approach to math education and allow “models that work" to inform our practice. Most of their ideas for how to improve math education seem like common-sense and reasonable proposals. They do praise China for how well it does on international comparison tests. China has a long cultural tradition of valuing tests, and tests are used to sort students at an early age in many societies, including the United Kingdom, France, and Germany. American testing is usually at far lower stakes, and American students may tend to score lower on standardized testing used in international comparisons, whereas Chinese students may tend to score higher. There is probably some systematic bias there. Also, there may be sampling bias. Are all the schools in China doing so well, and are International comparisons using samples of Chinese students that are just as broad and representative as the samples of American students? American high school students also do not focus on particular areas of study so much, as our high school curricula tend to be general education all the way through high school graduation. In other societies, children often begin to concentrate their studies in focus areas while in secondary education to a degree that is unusual in the USA. So, while I agree that America could learn some lessons from the Chinese methods of education, I think we must be cautious about comparisons.
My sense is that persons who are trained very narrowly to be the top in their field are sometimes woefully foolish in other areas of inquiry or thought. I would like American engineers, computer scientists, and mathematicians to be well-trained in their fields, and they should be competent. But, they should also know something about the arts, literature, politics, biology, history, economics, philosophy, and society. Chinese society is in many respects horrible, and not worthy of emulation. It has its good points, of course. America likewise has its flaws and problems. My sense is that a great deal of the evil done in China results from people having narrow technical approaches to problems or goals.
One controversial point the authors make is that disparities in admissions into STEM fields between underprivileged minorities and others are blamed on systemic racism when in fact declining standards in the public schools where these underprivileged students attend account for much of the disparity. The authors do not understand the term “systemic racism” (which is hardly surprising, as they show little interest in understanding it beyond recognizing some of the ways the term and concept can be misused to harm students). Systemic racism would encompass exactly those problems they identify. If people have racially-biased ideas that girls or persons with African heritage need inferior alternative approaches to mathematics, or that such persons should be guided away from “difficult” subjects like math, engineering, and computer science, and institutions promote such attitudes in schools, that is exactly systemic racism. Combatting systemic racism and promoting diversity in STEM fields requires educators and school boards to hold students who are underprivileged minorities to the highest objective standards of accomplishment, and also requires educators and school boards to provide those students with the means to have realistic chances of actually meeting those standards. So, I'm saying in some extreme (outlier, I think) cases, the "anti-racist" solutions to problems are themselves examples of racism.
When it comes to achieving higher performance of disadvantaged minorities in the STEM fields, the authors seem to have a sense that we should be pragmatic and use what seems to work. Who could argue against that? If there are forms of “diversity education” that show good results in terms of giving underprivileged minorities an enhanced possibility of meeting high standards in STEM fields, those forms of diversity education ought to be promoted, not condemned. If there are forms of “diversity education” that fail to improve (or diminish) the chances of persons from underprivileged backgrounds to enter STEM fields, those forms of education should be discarded. The test should be pragmatic. Do these interventions work, or not? To answer that question, we need good-faith explorations of what seems to work and what doesn’t. The authors of this article don’t contribute much, because they aren’t giving evidence or even case studies or anecdotes about approaches that are working (or not working). They are simply claiming—and claiming without offering any good empirical observations or evidence—that an emphasis on diversity and social justice is diminishing the quality of mathematics education in our society.
The “emphasis on diversity” and “social justice” are broad concepts that are applied in diverse ways in the field of education. I hardly think it will be useful to make generalizations about how an emphasis on diversity or social justice is helpful or harmful in improving American education. We need actual research, good empirical evidence, detailed and fair case studies, and more specificity about which aspects of “emphasis on diversity” or “social justice” are failing or succeeding.
Well, they do point out that “less competitive” and “more nurturing” programs work better for some people than do competitive and abusive programs. Do the authors equate “high standards” with “more competitive”? Do they think that “more nurturing” (less abusive) programs are by definition programs with lower standards? If so, I think they are confusing “standards of excellence” with other aspects of teaching and learning (e.g., degree of nurturing going on in the process, degree of competition in the process).
Is “scientific excellence being supplanted by diversity as the determining factor” for eligibility and access to learning opportunities? The authors are correct that measuring adherence to ideologies or loyalty to group values or obedience to authority can poison science and engineering, and yield dystopian nightmare societies. But China, the country they hold out as an example of good educational techniques, is plagued with this problem. In China, to advance in universities or corporations, loyalty and obedience to those in superior positions of the hierarchy is of critical importance. Many good scientists are thwarted by their personal conflicts with superiors or Communist Party officials. Similar problems may exist in American academic or departmental politics, so perhaps this is a universal human problem.
In making their case that diversity is supplanting merit, the authors refer readers to the National Science Foundation’s Innovation Corps program, in which “provide opportunities to diverse communities of innovators” is listed as one of five areas of responsibility. That doesn’t seem like a risk to merit-based investment in innovation to me. Another source the authors use is a Wall Street Journal editorial by Heather MacDonald decrying the fact that the National Institute of Health will now want grant applications to explain how they will “enhance diverse perspectives” and include perspectives of traditionally underrepresented persons in biomedical fields. It seems to me that there is a general pattern in reality that diverse options and perspectives can provide us with a wider range of thoughts and ideas from which to choose, and thus increase the chances we have of finding or synthesizing an optimal solution or idea. So, I don’t see how forcing persons applying for research grants to consider how they will increase diversity representation in their work is likely to diminish the quality of science. The committees that allocate that money aren’t going to lower their standards to a point where they are funding more bad research than they already do. They are simply going to add to their already high standards a box to score how well the application addresses diversity. Is the score in that box going to get weighted higher than the scientific rigor of their research design? No. Since some of those grant-awarding committees have a certain intellectual incestuousness in them, lack of diversity in decision-making has been a problem already, hasn’t it?
I’m not going to deny that sometimes the emphasis on diversity creates inflated acclaim for some researchers. Sometimes the “superstar” scholars or authors getting lots of attention are really just good, and not actually so great. Sometimes they are promoted partly because of their interesting racial or class background, or the intriguing perspectives they have because of some aspect of their research topics, or subjects that seem unusual (involving diverse sorts of ideas or populations). I think people recognize this. The risk that the really great ideas are being ignored because some less-great ideas are coming from diverse scholars looking at diverse things is a real risk, but we already have a risk that we’re giving too much attention to “famous, great scholars” who had significant ideas years ago and are now promoting less valuable work. Or, we might be giving our attention to the people doing work in the fields that are the latest fashion or fad in our discipline, and ignoring the really significant work in some old-fashioned approach that no one cares about any more, or some esoteric subfield no one is paying any attention to. It seems to me that the things I’m describing are more likely to thwart good science and good thinking than too much emphasis on diversity or diverse scholars. This past year why have so many doctors been using Remdesivir instead of Ivermectin to treat COVID-19? Why are some literature reviews and studies of Ivermectin showing it to be highly effective, and other literature reviews showing Ivermectin to be of little or no use at all? That sort of bad science didn’t have anything to do with diversity, except maybe it was a bias against the randomized controlled studies suggesting Ivermectin is highly effective coming out of universities, hospitals, and countries that are not “high quality” (India, Latin America, Africa). I'm being sarcastic and suggesting there is a bias against poor country research in the mainstream medical research community.
It seems to me the greatest value of the article is its endorsement of the Math for America teacher-development and the BASIS Charter School Curriculum. I was unaware that those programs had demonstrated high effectiveness in improving student math abilities. It’s important that when programs have demonstrated success, their success is shared with teachers and teacher educators. The authors make some other recommendations that, for the most part, seem reasonable and likely to be helpful.
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