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Math education — or not

Summary:
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 ...

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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: 

[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.

Policy

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).  


John H. Cochrane
In real life I'm a Senior Fellow of the Hoover Institution at Stanford. I was formerly a professor at the University of Chicago Booth School of Business. I'm also an adjunct scholar of the Cato Institute. I'm not really grumpy by the way!

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