Monday, August 23, 2021

Math education -- or not

Percy Deift, Svetlana Jitomirskaya, and Sergiu Klainerman have a well-informed essay at Quillette on the state of math education in the US and China. Italics are mine throughout. I did not copy over the links, but the article is full of documentation. 

The most interesting part is the economics and politics of math education: 

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”). ...

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....

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,”...

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). ...

"Equity" programs will end up hurting the disadvantaged most.  

I went to a mostly black public high school in Chicago. It had 5 tracks.  The upper track featured about 50/50 the kids of white liberal professors and smart black kids from throughout the south side. We got a great education including math and STEM, through AP calculus and physics. (Thank you Ms. Stein, Mrs. Gordon, Mr. Sherrill and especially Mr. Hofslund, my physics teacher.) I learned to program.  In a Chicago public school. In 1974. It got me in to MIT. I spent some time in the lowest tracks, thanks to a scheduling snafu, which was an eye-opening and empathy-raising experience. Had all the classes mixed, the results would have been disastrous, especially for those smart black kids who went on to professional careers.  

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 and calculus should be considered basic math, not advanced math! It's still amazing to me, who uses both in every working day, that the US puts off teaching these central skills until late in high school. If, now, at all.  

...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).

Equity gone mad is spreading 

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.


[China] 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. ...

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. ... 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.


Reversing America’s slide in STEM education will require many policy changes...

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.

... 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....

... 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.

Maybe a little bit of Cold War III threat has some side benefits of keeping the US a little sharp. Competition is always a good thing. So long as it doesn't involve actual shooting. Maybe there is a space race we could start with the Chinese instead? 

They start with an interesting observation: The US got good in the first place by attracting the best from around the world, and stayed on top by a meritocracy that keeps attracting foreigners. Which is a good thing, considering how miserable our own educational system is 

The United States has been dominant in the mathematical sciences since the mass exodus of European scientists in the 1930s. ...

...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 same is true in finance and economics. Looking up and down the hallways, I am proud that almost everyone came from somewhere else -- the US attracts the worlds' best. (And thankful for universities' exemption to the H1B visa limits! Too bad more productive enterprises don't have similar sweet deals.) But it is a stark sign of how awful US stem education is. 

As you watch this amazing AI demo (Marginal Revolution), do not fail to note that two out of three seem to be immigrants, who got math training outside the US. 

A minor disagreement: 

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. 

Everyone likes to talk up their own book, and advocate "be like me." I like applied math, and I hate pure math. I was no good at it. I need to see things, not prove theorems. I learn things from simple example to more general example, and finally to theorem that encompasses a full set of examples. I loved physics, and hated the math olympiad questions. I hate number theory.  

The skills of a research mathematician are not the skills that 99% of stem users need! We need to demystify applied math, the race to proving theorems in elegant generality. That's a great skill for those who have it, but neither necessary nor sufficient (!) for producing a generation of stem users. Indeed, I think math education goes haywire far too soon by trying to teach people to be "research mathematicians" and weed out that talent, rather than teach people to be competent math users (like me).  


  1. A very nice post. I agree with most of what you said.

    However, please take note that recently China banned the use of tutors outside of school. Their propaganda uses arguments similar to the equity argument in the U.S. (They say that it's unfair for the rich to hire tutors while the poor can't afford it).


  2. Ultimately, if a society doesn't accept the possibility (reality) that different population groups have different average genetic ability/predisposition for something and instead assumes that all abilities (particularly mental: iq, maths, etc.) MUST be identical, then 'equity' narrative will be a natural outcome of the dialectic as the cause of different outcomes must be some veiled form of unjust treatment or 'supremacy' or legacy thereof.

    Trying to fight the 'equity' narrative without accepting and driving home the obvious fact that maybe, JUST maybe, not all population groups have identical average IQ after tens of thousands (sometimes hundreds of thousands) of years of different selection pressures on evolution, is a losing play.

    Which explains most of the losing actions of the 'conservatives' over the past fifty years (longer?). Because if you establish equal 'opportunity', then with different natural abilities you'll get very different outcomes with massive 'disparate impact.' This is obvious in say, the 100m sprint finalists in the Olympics, or Marathon winners, or NBA, or starting cornerbacks in the NFL. But when it comes to say, Fields Medalists or Fortune 500 CEOs, or more broadly, average SAT scores, income, and so on, everyone loses their mind.

    1. > different population groups have different average genetic ability/predisposition

      There is no race. Its an invalid concept based on arbitrarily selected properties, as if height or weight created a race. IQ is poorly understood. Innate ideas is the mystical absurdity that man knows reality prior to knowing reality. Different population groups (code for race) increase IQ test scores when influenced by rational cultures. There is no race. Man is a being of self-made soul, [Aristotle], not a "racial" beast. Left and Right are dragging us back to primitivism w/racism, rationalized by intuition-selected statistics, not by sense-based science.

      Return Of The Primitive-Ayn Rand

    2. Would be preferable if the writer of this comment presented facts rather than heated rhetoric. Heated rhetoric is usually indictive of a weak position. Aristotle was around close to 2,000 years before the scientific method was discovered so citing him as a authority on an empirical issue is unpersuasive.

    3. >Aristotle was around close to 2,000 years before the scientific method was discovered

      Aristotle discovered scientific method and, in his biology,was the first scientist. One part of his discovery, systematic deduction, remains an important part of science. Darwin called him the best biologist. Bacon was influential in returning science to Aristotelian inductive empiricism after centuries of stagnant, Scholastic deductivism. The Renaissance is the renaissance of his rational realism. In that intellectual context , math and systematic induction ,eg, Mill's Methods, were added to scientific method. Aristotle did not discover everything about scientific method that later philosophers of science discovered but he was the beginning. Read his biology for detailed, systematic descriptions and explanations of nature. Where in Zeus's name did you get the absurdity of ignoring Aristotle? Five seconds of online searching will identify Aristotle.

      Leap of Logic-David Harriman; an inductive history of science; induction as generalization from Aristotle's discovery of conceptualized concretes, not modern, non-inductive, enumerated concretes ,ie, the primitive mentality.

  3. "Maybe a little bit of Cold War III threat has some side benefits of keeping the US a little sharp. Competition is always a good thing. So long as it doesn't involve actual shooting. Maybe there is a space race we could start with the Chinese instead?"

    More war dog economist crap.

  4. This comment has been removed by the author.

    1. "Competition is always to be desired--it brings out the best."

    2. Two countries start with an endowment of some raw material (say iron ore).

      Country A - Starts with an endowment of 1 million tons of ore
      Country B - Starts with an endowment of 1.5 million tons of ore

      Both countries "compete" in the production and sale of motor vehicles. The vehicles produced by both countries are equivalent in terms of vehicle safety, fuel economy, etc.

      From it's endowment, Country A produces 800 thousand cars from it's endowment, Country B produces 1.1 million cars from it's endowment.

      Which country is more productive? Which country "won" the competition?

    3. Assuming there is global demand for 1.9 million cars, both countries 'won'.

    4. Anonymous,

      Some would say that country B "won" because it produced and sold more cars on an absolute basis (1.1 million > 800 thousand).

      Others would say that country A "won" because it produced and sold more cars per ton of allotted ore (0.8 cars per ton > 0.73 cars per ton).

      Rivalrous claims on output depend on what a country has in terms of resources and what it is willing to do to secure additional resources - John's lets start World War III with the Chinese.

      Even if no shots are fired, does it matter if property rights are violated in the waging of this war?

      Nonrivalrous claims on productivity improvement can be considered competition, however neither party has an incentive to go to war in search of resources.

      But I might as well be banging my head against a brick wall.

      So many war dog economists have been trained by so many prior war dog economists that the field of economics has become lost in the fog of war.

    5. Er, quite. I'm sure there's a brilliant insight in there somewhere, but exactly what it has to do with ensuring calculus is in the high school mathematics curriculum seems destined to remain a mystery.

      Perhaps it's time to give that brick wall a rest?

    6. Coker,

      This was in reference to John's statement:

      "Maybe a little bit of Cold War III threat has some side benefits of keeping the US a little sharp. Competition is always a good thing. So long as it doesn't involve actual shooting. Maybe there is a space race we could start with the Chinese instead."

      As well as Old Eagle Eye's statement:

      "As to China, that conflict is in the offing--perhaps as near as two years out, but not likely longer term than 5 to 7 years away."

      Your inquiry:

      "...but exactly what it has to do with ensuring calculus is in the high school mathematics curriculum seems destined to remain a mystery."

      The question (directed to JC and OEE) is why do you think you need a war to motivate and/or justify improvement in math education?

    7. From another former University of Chicago graduate:

      "A new consciousness is developing which sees the earth as a single organism and recognizes that an organism at war with itself is doomed. We are one planet. One of the great revelations of the age of space exploration is the image of the earth finite and lonely, somehow vulnerable, bearing the entire human species through the oceans of space and time."

      Carl Sagan

    8. > We are one planet.

      It's certainly good to know that astronomer Sagan doesnt think that the Earth is many planets.

      >somehow vulnerable

      This is Christianity, not science.

  5. I see the US in decline, and China as a cypher, but possibly rising. Too soon to tell with CCP going heavy-handed.

    Curiously the reasons for possible Sino ascendance seem to be genetic and cultural, not what macroeconomists talk about (although China created huge export markets through state direction).

    The entire Far East features variations of dirigiste economies, none more than Singapore.

    Might have to wait 100 years to see how it turns out.

  6. I found Steve Levitt's critiques of US math curricula to ring true. In a nut shell, too much solving or esoteric problems and too little applied math.

  7. "Algebra and calculus should be considered basic math, not advanced math! It's still amazing to me, who uses both in every working day, that the US puts off teaching these central skills until late in high school. If, now, at all."

    Professor Cochrane is ignoring the fact that the average IQ is 100, not 115 and 130, and that some U.S. schools have students with average IQ of 85.

    1. Also, almost no job requires calculus in day-to-day work.

    2. A computer can do math better than you can. High school algebra is in practice a completely useless subject except for students specifically interested in math.

      Unusual people like Mr. Cochran don't need to learn math in school, but can instead teach themselves.

    3. Algebra is definitely a useful subject for almost everyone. Geometry and calculus, and trigonometry, those can be skipped by most people. Algebra though, that's critical for just setting up questions, and basic algebra is within reach of anyone who can do arithmetic and a little logic.
      Really abstract math isn't terribly useful, but like Prof Cochran said, applied math is much easier for most people. Applied algebra is teachable to primary school students.

  8. The statistics on the current CA proposal, which I believe comes up for review/decision in November is appalling contract to the "dumb down for equity" operational reasoning for the change. Currently a very high percentage of students qualify for 8th grade algebra, and students of color have high and increasing qualification rates. If think WSJ OpEd from late spring/summer may have references and numbers on these. The movie "Idiocracy" is too close to the truth already today, not something out in the future.

  9. Perhaps the new woke movement in education is making things worse, but I have to side with Bryan Caplan – education is mostly useless, and we produce too much of it. Back in the 1960s, Feynman made many of the same observations as the authors in the Quillette article about the poor quality of mathematics education. Part of the problem these mathematicians see today are rooted in too many people going to college, trying to get a signal, and as a result fewer and fewer students come well prepared. Education sorts more than it forms.

    Material poverty does not mean a lack of opportunity to learn mathematics, even in the inner city. The European transplants in the 1930s mostly came from really poor backgrounds. Many suffered under extreme antisemitism and formal educational restrictions. Culture matters far, far more than the school system. As Jim Heckman says, “Family is the source of life and growth. It’s politically incorrect to express the truth and go to the source of the problem. Schools can only partially compensate for the damage done to the children by dysfunctional families.” Of course we should do better rather than worse with our schools, more charter schools, more school choice, and the woke nonsense of devaluing merit is certainly worse, but everything outside the home and family culture is second order. What are the real cause-and-effect channels here?

    Beyond basic literacy, most people never use what they “learned”, even in K-12. I know all kinds of adults who can’t do fractions but do very well in life. Are they, as the Quillette authors claim, lacking the ability for successful participation in the economy? Not at all – you should see the size of some of their bank accounts. Woke education or not, I doubt the number of future adults who will be able to do fractions will change much. An alien from outer space looking at our high school curricula might be forgiven for thinking that typical American life has such an enormous demand for professional musicians, athletes, language translators, and mathematicians, that nearly everyone needs training in these areas from childhood. A lot of time is wasted on education, even at elite schools.

    People who will turn into brilliant mathematicians or experts in applied mathematical fields will almost always find a way. They teach it to themselves, they find their coaches and mentors. They have an irrepressible urge to understand relationships and to know. Take a look at the picture of the 1929 Solvay Conference. Those 29 people basically set the foundation of the modern world, some coming from what we would call near abject poverty. How many mediocre scientists and mathematicians writing careerist papers do we really need to train? And with the internet, it’s never been easier for the motivated to learn. Elite people don’t wait for someone to teach them calculus. Sure, let’s do better rather than worse with education, but let’s keep in mind the real prize: the diamonds of the world accrue to the United States because of what diamonds can accomplish in the United States. As long as that remains true, we’re fine.

    1. I agree with a lot of this, but the costs of weak mathematics backgrounds have become all too clear in recent public policy debates: too many of the mathematically illiterate don't know the difference between a t-statistic and a tea bag and so are ripe for the plucking by charlatans.

    2. I agree with you generally as well, but it worth noting that lowering the quality of math in school doesn't fix the education problem in the Caplan sense. Caplan is arguing against education as measured by economists and policy makers, which is just "years of education" or how long you were in school. That education is worthless because students don't learn anything. Letting students learn less math while still forcing them to waste time in school is making the problem worse, not better.

  10. Totally agreed: Physics is where absolutely all the intelligent people are. Maths is just a bunch of rules. And it is where all the bureaucrats, conformists, obedient people are.

    1. Part of modern science is Newtons application of math to science. Physics w/o math is a start but it doesnt discover universal gravity or get robots on Mars. Math is part of mans method of identifying reality.

  11. Should our best mathematical minds be in pure math, economics, geophysics, engineering? I'm not so sure I think the meritocracy currently does a great job of getting people into the right disciplines. And it does an abysmal job of keeping out the frauds and charlatans. In my opinion the marginal economics PhD student is very marginal (my former self included).

  12. I had the good fortune to attend an excellent private high school. The math teachers had to have a math degree, chemistry teachers a chemistry degree. An education degree generally disqualified you for employment as the administration considered an education degree to be a waste of time.

    1. That is good fortune!

      Comprachicos-Ayn Rand; Progressive ed. as deliberate
      Teaching Johnny To Think-Leonard Peikoff; close down education ......schools

  13. I had the good fortune to attend an excellent private high school. The math teachers had to have a math degree, chemistry teachers a chemistry degree. An education degree generally disqualified you for employment as the administration considered an education degree to be a waste of time.

  14. The Achilles Heal of our education politics is its being a prisoner of is employees, focusing on retaining administrative, budgetary, self-serving control over wages and benefits, at the expense of students, and the needs of the nation. So long as the inmates of the education Deep State continues, China will beat us in math and the sciences, the building block for innovation and invention. Oddly, there is a hope. We could import Chinese scientists with individual opportunities to be free from restrictions of central controls of China's command economy. Funny....our hope being dependent on Chinese government mistakes.

  15. Folks-

    Figure 1 from this Brookings study speaks volumes about DEI mandates at universities:

  16. 1) Even "STEM" jobs don't use much math. Academic economists might use calculus, but even software engineers, engineers, actuaries, and quantitative researchers usually never use calculus.

    2) Smart US-born students might be more valuable in jobs that don't require advanced mathematics. It's not a shame that so few US-born students go into math-oriented academia; they might be choosing better options.

    3) US students are choosing non-research careers, because they can afford to. Why bemoan their preferences?

    1. The issue is not whether everyone should learn calculus. The issue is whether anyone can learn calculus. Without some sort of tracking in which those that want to and can move ahead do so, nobody gets to calculus -- or only children of well informed wealthy parents who can arrange private education. Second, it is at least partly true that few jobs use calculus because few people know calculus. People who know calculus might find it useful.

    2. Is it really true that lack of calculus tracks wealth and not culture? What is the real cause-and-effect channel here? Look at the 1927 Solvay Conference. There were some desperately poor origin stories there, including the childhood of a rather poor Polish woman. Not a lot of state education tracking at that time. Do we really think that public high school mathematics education of any kind is going to get a lot more young people interested in calculus? Maybe some marginal effects here and there, but my bet is that after a lot of sound and fury no matter what we do, the same kinds of people will end up learning calculus. In the end, culture dominates.

    3. Math teaches method ,a critical part of education. Education is mind-training, ie, intellectual, not job training. Mind-training is a need of mans life. Its not arbitrary.

    4. Having worked in STEM for decades (including 20 years starting and leading technology teams at Intel, I used calculus a lot, and more importantly at conceptual levels in looking at differential data sets, as well as in combination with advanced statistics. That said John's reply is spot on, the question is not whether everyone should learn calculus (which was once an objective for undergrads at U Chicago), but more of access, and algebra is many times more valuable in daily life and even in our poorer than most CA public schools, high percentages of students are ready for it by 8th grade.. The conceptual frameworks of calculus are much more important than the details of how to use imaginary numbers to resolve some complex integral. The other important concept is competitively, i.e., the US education system is falling further behind EU, South and East Asia, especially in STEM, whether its math, physics, molecular genetics, AI deep learning, or advanced engineering.

    5. Speaking as a mechanical engineer of 17 years now, I really feel sorry for any student that goes to college pursue an and did not d engin to did not take calculusdrop out of it freshman year. This in a major where a ton of people drop out of it immediately freshman year.

  17. As a data scientist, it's so annoying to see it treated as the career choice everyone should be doing.

    For starters, not everyone likes math. Not everyone likes to code. And it's also a field that keeps evolving such that things you learn today can become obsolete in a matter of years.

    As an aside, I am fortunate that the US is a country of second and third chances. I was a pretty mediocre student in math for a long time and only in the latter half of my education did I embrace it. I worry that China's style of teaching math will discourage a lot of students who don't show early aptitude

  18. I read the article when published at Quillette. I was very ho-hum about it, for a couple of reasons:

    1. the truth of the matter is that sub-college education in the US has always been second or third rate. I graduated high school in 1965. Despite the post-Sputnik emphasis on science and math, the courses I took in high school taught me very little. The Biology teacher was an insurance agent on the side. he taught us that human cells had 48 chromosomes. (His surname was "Boring" really). We called the Chemistry teacher "Coach". That was his real job. He knew nothing about chemistry. The math teacher refused to teach calculus. he thought that we were not mature enough to learn it. I had a good physics course.

    I enrolled at the University of Chicago. I wanted to major in economics. the department had almost no undergraduate courses. My "adviser" had never heard of econometrics, did not know what it was. I took first year calculus and miraculously got an A. I talked to Paul Sally, whom I will wager, John knew. He persuaded me to take the upper level second year calculus course. I lasted about two weeks in that course, quit and never took another math course.

    My children went to the same High School 45-40 years later. Not much had changed. They were not well prepared for college in math and science.

    2. I agree that the popular racial ideology will impede any chance at reforming the American system, and may well extinguish islands of excellence like the specialized high schools in New York city. But, Tocqueville was right, intellectual excellence is an aristocratic virtue. Americans, as a people, have never had it, and won't pursue it. To that extent, racialist ideology is working with the grain, not pushing against it.

    China is also reverting to its national character. But, it will have no impact on great power competition. The arena for that is the next 30 years. Children in school today will not determine its outcome. For better or worse we are going to war with the army we have. The war over Taiwan has a time frame of 5-10 years. And we are stuck with the gang that couldn't shoot their way out of Kabul.

  19. China's PISA scores are manipulated and shouldn't be compared to other countries. I'm surprised the article left that detail out, since the authors must have known it.

  20. In the public school system I passed through (province of BC, 1970s and early 198s), algebra was introduced in 7th grade and calculus was formally discouraged (poorly taught high school calculus apparently made things harder for the provincial university instructors than it was worth). Students from schools with mediocre math programs (teachers) struggled with the pace if they aspired to honours STEM. Kids who had aptitude, interest, and opportunity to study calculus in school arrived prepared well enough to flourish in the difficult programs. Adding it up, it's a disservice to kids with high aptitude to deny them the challenge of advanced math and calculus in Gr 11/12. They will still do well when they hit uni, but they assuredly could do better. Dumbing down public school courses and measures of achievement just seems like the nomenklatura's way of reducing competition for their kids' entry into prestigious programs.

  21. This comment has been removed by the author.

    1. Meritocracy is a destructive, Marxist package-deal of politics and economics. I am not implying Eagle and John are Marxists. They are probably unknowingly influenced. The rational purpose of politics is individual rights, not the enforcement of undefined merit. Politics should protect whatever voluntary merit people value. Politics should protect the freedom to be moral, not morality.

      Education, ie, mind-training for mans survival, must, of course, be a meritocracy. In the present context, the first step must be the total abolition of our anti-mind, public schools. This will encourage private, pro-mind private schools competing with anti-mind private schools. The second step is knowledge of a pro-mind education, which seems to be lacking even in people who value it. As someone who suffered thru fours years in a university philosophy dept, few know the fundamentally abstract nature of the modern intellectual corruption. Its worse than false ideas. Its literal ,systematic mind-disintgration. Leftists want their minds disintegrated, eg, statistics instead of conceptualizeed concretes, "transexuality," egalitarianism. Rightists flee into the illusory safety of religion. But philosophy is basic. And reason is the identification and integration of perceptions.

      Comprachicos-Ayn Rand
      Teaching Johnny To Read-Leonard Peikoff.


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