Smartest Kids in the World: American Schools

Part of The Smartest Kids in the World: And How They Got That Way concerns American schools. Unfortunately it is mostly to contrast them with effective schools elsewhere.

Amanda Ripley identifies the following major problems with American schools:

  • people who are poorly educated are hired as schoolteachers
  • teachers have limited autonomy (partly as a result of their low level of knowledge and ability)
  • schools have multiple missions, only one of which is education, which leads to a loss of focus
  • teachers and administrators dwell on student and family backgrounds so as to build up a catalog of excuses for poor educational outcomes
  • parents are complacent regarding the low expectations set for their children

Here are some excerpts from this interesting book:

Scott Farmer had just been appointed the town’s first new superintendent in twenty years. He had short brown hair and a boyish face. The state of Oklahoma had 530 superintendents like him, each with their own fiefdom. There were about as many superintendents in Oklahoma as there were members of Congress for the entire country.

This tradition of hyperlocal control, hard-wired for inefficiency, hinted at one reason that the United States spent so much more than other countries on education. Farmer made about $100,000 per year, which made him one of the top earners in Sallisaw. He had an assistant superintendent, too, along with eight director-level managers and a school board. It was quite an operation for a district that included just four schools. But it was hardly unusual. Compared to the rest of the state, in fact, Sallisaw was one of the more efficient school districts in Oklahoma.

That, too, was a common refrain among educators all over the United States. Whatever the problem, it was, it seemed, largely outside their control.

Sallisaw had plenty of good students, too. Other than the destitute and the dropouts, Sallisaw High School had its success stories, like every town. About half the kids who graduated from Sallisaw enrolled in public colleges and universities in Oklahoma. Others went to out-of-state colleges or looked for jobs. What happened to these success stories after they left? Their colleges tested their basic skills and found them wanting. More than half these students were promptly placed into remedial classes at Oklahoma public colleges. That meant that some of Sallisaw’s best students were paying good money for college, often in the form of student loans, but they weren’t getting college credit.

I asked Principal Martens about all the Sallisaw alumni who were retaking math or English. “That really doesn’t bother me,” he said, “because at least they are trying.”  The main goal was to go to college. Whether his graduates succeeded there was out of his control, or so it seemed. The fact that those kids had spent four years in his school preparing to get to college—and that he’d given them a diploma that was supposed to mean they were ready—did not seem relevant.

American teachers taught with textbooks that were written to appease thousands of districts and many states all at once, as education researcher William Schmidt has documented in detail. That meant that American textbooks tended to be far too long—covering (and repeating) way too many topics in too little depth. Internationally, the average eighth grade math textbook was 225 pages long; in the United States, eighth grade math texts averaged 800 pages. That was about 300 pages longer than all thirteen volumes of Euclid’s Elements.

The end result was that American students ended up learning about, say, fractions every single year, from first to eighth grade, while their peers in smarter countries covered fractions in grades three through six.

By eighth grade, seven out of ten kids went to schools that did not even offer algebra courses with the kind of content that was standard in most other countries. It was only logical that American kids were behind their peers in the smart-kid countries; they were essentially taking remedial math, whether they needed it or not.

Aside from the high cash compensation, three months of summer vacation, and secure pension, what motivates Americans to work in an environment where failure is almost guaranteed?

… consider Kim’s math teacher back home, Scott Bethel. He’d decided to become a teacher mostly so that he could become a football coach. In America, this made sense. As a student at Sallisaw High School, he was an all-state quarterback in 1989. “My dad taught at a school about ten miles from here,” Bethel told me. “He was also a football coach, and I was always good at sports, and I thought, ‘You know what, I’d like to become a coach.’ ”

If you too wanted to be a high school sports coach/math teacher, what would you have to do?

Although Bethel hadn’t taken calculus in high school, he’d always been pretty good at math. So, he figured the best way to become a coach was to become a math teacher. Bethel was one of several coaches that Kim had as teachers over the years, a hybrid job that would be considered bizarre in Finland and many countries, where sports lay beyond the central mission of schools. In Oklahoma alone, Bethel could choose from nearly two dozen teacher-training programs—almost three times as many as in all of Finland, a much bigger place. Oklahoma, like most states, educated far more teachers than it needed. At most U.S. colleges, education was known as one of the easiest majors. Education departments usually welcomed almost anyone who claimed to like children. Once students got there, they were rewarded with high grades and relatively easy work. Instead of taking the more rigorous mathematics classes offered to other students, for example, education majors tended to take special math classes designed for students who did not like math. Bethel did his training at Northeastern State University, like the Sallisaw superintendent and many Oklahoma teachers, including Kim’s mom. The university prepares more teachers than any other institution in the state and has a good reputation. However, it also has a 75 percent acceptance rate, which means that it admits, on average, students with much weaker math, reading, and science skills than Finnish education schools.

During his sophomore year at Northeastern State University, Bethel had applied to the university’s education college. Here was another chance for the university to select its best and brightest to become teachers. But to be admitted, Bethel had to have a grade-point average of just 2.5 or higher (out of 4). He would have needed a higher GPA to become an optometrist at the same university today. To be a teacher, he also had to have at least a C grade in freshman English and a C in speech or a class called the fundamentals of oral communication. He also needed a score of 19 or higher on the ACT, a standardized test like the SAT. The national average for the ACT back then was 20.6. Let’s consider what this meant: It was acceptable to perform below average for the country on a test of what you had learned throughout your educational career if you aspired to dedicate your career to education.

At the education college, Bethel discovered that he didn’t have to major in math to become a high-school math teacher. So he didn’t. Nationwide, less than half of American high-school math teachers majored in math. Almost a third did not even minor in math.

Bethel liked math, but his primary goal was to become a coach, so he majored in physical education and minored in math. When he took the required test for high school math teachers in Oklahoma, he passed easily. Most of the material was at a tenth or eleventh grade level, and he didn’t find it difficult. However, if he had, he would have been allowed to retake the test until he passed.

When researchers tested thousands of aspiring teachers in sixteen countries, they found that future middle-school math teachers in the United States knew about as much math as their peers in Thailand and Oman. They had nowhere near the math competence of teachers-in-training in Taiwan, Singapore, or Poland.

Maybe American teachers get more practical training to compensate for their weak college experience?

In Oklahoma, Bethel’s student teaching experience helped him learn to plan lessons and manage a classroom. But it lasted just twelve weeks, compared to the year-long residency typical in Finland. Nationwide, U.S. teacher-training colleges only require an average of twelve to fifteen weeks of student teaching,

Has any state ever tried to “pull a Finland” and restrict teacher education and hiring to those who were reasonably good students?

Why hadn’t that evolution ever happened in the United States—or in most other countries? Had anyone even tried? The examples were few but revealing. As the new education commissioner in Rhode Island, one of Deborah Gist’s first acts was to raise the minimum test scores for teachers-to-be in 2009. At the time, Rhode Island allowed lower scores than almost any state in the nation. She had the power to change this unilaterally, and she did, taking one small step in the direction of Finland by requiring new teachers to score significantly higher on the SAT, ACT, and the Praxis, a teacher certification test. Immediately, critics called her elitist, lobbing the same accusations critics had used against reformers in Finland in the 1970s. Some argued that a teacher who struggled in school was actually a better teacher, because that teacher could relate to students who were failing.

Others worried that higher standards would lead to a teacher shortage. Yet Rhode Island’s teacher colleges already churned out 1,000 teachers a year, about 800 more than the school system needed to hire.

Because this was America, a diverse country with a long history of racism in colleges, public schools, and every other institution, Gist’s efforts were also attacked as discriminatory. Higher education leaders warned that the new standards would prevent minority students, who tended to score lower on tests, from becoming teachers.

It was interesting to note that higher standards were seen not as an investment in students; they were seen, first and foremost, as a threat to teachers. Rhode Island’s teacher-preparation programs produced five times more teachers than Rhode Island’s public schools actually hired each year. The only institution benefiting from this system seemed to be the colleges themselves, but college leaders still complained that they would lose too many students if the standards were higher. They voiced this concern to newspaper reporters, and reporters quoted them without irony.

Under the new, higher standards, about 85 percent of Rhode Island College’s education students would not make the cut, the dean threatened. Coming from the college that produced more Rhode Island teachers than any other, this was an astounding statistic, one that should have been a source of deep shame, but was not. Gist did not back down, however. “I have the utmost confidence that Rhode Island’s future teachers are capable of this kind of performance,” she said. She did agree to phase in the higher cut score gradually over two years and to allow colleges to ask for waivers for highly promising candidates who did not make the cut score. Three years later, she had not received any waiver requests. At Rhode Island College, the percentage of minority students studying to be teachers went from 8.8 percent to 9.24 percent, remaining essentially unchanged despite all predictions to the contrary.

What does a good American high school look like to a Finnish teenager?

Elina discovered one important difference about America. Back home, she’d been a good student. In Colon, she was exceptional. She took Algebra II, the most advanced math class offered at Colon High. On her first test, she got 105 percent. Until then, Elina had thought it was mathematically impossible to get 105 percent on anything. She thought she might have more trouble in U.S. history class, since she was not, after all, American. Luckily, her teacher gave the class a study guide that contained all the questions—and answers—to the exam.

Elina was unsurprised to see she’d gotten an A. She was amazed, however, to see that some of the other students had gotten Cs. One of them looked at her and laughed at the absurdity. “How is it possible you know this stuff ?” “How is it possible you don’t know this stuff ?” Elina answered.

I talked to Elina after she had left the United States and gone to college in Finland. She was planning to work in foreign affairs one day. Now that some time had gone by, I wondered if she had a theory about what she’d seen in her American school. Were the students too coddled? Or the opposite—too troubled? Too diverse? Maybe they were demoralized by all the standardized testing? Elina didn’t think so. In her experience, American kids didn’t study much because, well, they didn’t have to. “Not much is demanded of U.S. students,” she said. In Finland, her exams were usually essay tests, requiring her to write three or four pages in response. “You really have to study. You have to prove that you know it,” Elina told me about Finnish high school. In the United States, her tests were typically multiple choice. “It was like elementary school in Finland,” she said.

In my own survey of 202 foreign-exchange students, an overwhelming majority said their U.S. classes were easier than their classes abroad. (Of the international students who came to America, nine out of ten said classes were easier in the United States; of the American teenagers who went abroad, seven out of ten agreed.)

Don’t American schools do something well? Or at least intensively?

Sports were central to American students’ lives and school cultures in a way in which they were not in most education superpowers. Exchange students agreed almost universally on this point. Nine out of ten international students I surveyed said that U.S. kids placed a higher priority on sports, and six out of ten American exchange students agreed with them. Even in middle school, other researchers had found, American students spent double the amount of time playing sports as Koreans. Without a doubt, sports brought many benefits, including lessons in leadership and persistence, not to mention exercise. In most U.S. high schools, however, only a minority of students actually played sports. So they weren’t getting the exercise, and the U.S. obesity rates reflected as much. In many U.S. schools, sports instilled leadership and persistence in one group of kids, while draining focus and resources from academics for everyone.

In countries like Finland, sports teams existed, of course. They were run by parents or outside clubs. As teenagers got older, most of them shifted their focus from playing sports to academics or vocational skills—the opposite of the typical U.S. pattern. About 10 percent of Kim’s classmates played sports in Finland, and they did so in community centers separate from school. Many of them quit senior year so that they would have time to study for their graduation exam. When I asked Kim’s Finnish teacher if she knew any teachers who also worked as coaches, she could only think of one. “Teachers do a lot of work at school,” she said, “and that’s enough I guess.”

Where can teachers and students bond over the impossibility and lack of rationale for learning math? The U.S.!

There was much to be said for American teachers, who, in many schools, worked hard to entertain and engage their students with interactive classrooms. In my survey of 202 exchange students, I was struck by how many of them brought up their affection for their U.S. teachers. One German exchange student surveyed described the difference this way: “The teachers in the U.S. are way more friendly. They are like your friends. . . . In Germany, we know nothing about our teachers. They are just teachers. We would never talk to them about personal problems.”

What about learning about students’ home lives?

To find out how diversity changed the culture of rigor, I went to the Tiistilä school, just outside Helsinki, where a third of the kids were immigrants, many of them refugees. The school enrolled children aged six to thirteen. It was surrounded by concrete block apartment buildings that looked more communist than Nordic. In a second-floor classroom, Heikki Vuorinen stood before his sixth graders. Four were African; two wore headscarves. An Albanian boy from Kosovo sat near a Chinese boy. There was a smattering of white kids born in Finland. Vuorinen gave the class an assignment and stepped out to talk to me. Wearing a purple T-shirt, jeans, and small, rectangular glasses, Vuorinen proudly reported that he had kids from nine different countries that year, including China, Somalia, Russia, and Kosovo. Most had single parents. Beyond that, he was reluctant to speculate. “I don’t want to think about their backgrounds too much,” he said,

When pressed, he told me about one of his students in particular. She had six brothers and sisters; her father was a janitor and her mother took care of other people’s children. Money was very tight. But she was, he said, the top student in his class. Vuorinen was visibly uncomfortable labeling his students. “I don’t want to have too much empathy for them,” he explained, “because I have to teach. If I thought about all of this too much, I would give better marks to them for worse work. I’d think, ‘Oh, you poor kid. Oh, well, what can I do?’ That would make my job too easy.” He seemed acutely aware of the effect that expectations could have on his teaching. Empathy for kids’ home lives could strip the rigor from his classroom. “I want to think about them as all the same.”

[At Vuorinen’s school, all fifth graders had been tested in math two years earlier. Compared to the rest of Finland, the Tiistilä kids performed above average.]

I’d never heard a U.S. teacher talk that way. To the contrary, state and federal laws required that teachers and principals think about their kids as different; they had to monitor their students’ race and income and report that data to the government. Schools were judged by the test scores of kids in each category. Most principals knew their ratios of low-income and minority kids by heart, like baseball players knew batting averages.

Diane Ravitch, one of the most popular education commentators in the United States, had insisted for years that Americans should think about our students’ backgrounds more, not less. “Our problem is poverty, not schools,” she told a roaring crowd of thousands of teachers at a D.C. rally in 2011. Kids were not all the same, in other words, and their differences preceded them. In Finland, Vuorinen said the opposite of what Ravitch was saying in America. “Wealth doesn’t mean a thing,” he said. “It’s your brain that counts. These kids know that from very young. We are all the same.” The more time I spent in Finland, the more I started to think that the diversity narrative in the United States—the one that blamed our mediocrity on kids’ backgrounds and neighborhoods—was as toxic as funding inequities.

It was becoming obvious to me that rigor couldn’t exist without equity. Equity was not just a matter of tracking and budgets; it was a mindset. Interestingly, this mindset extended to special education in Finland, too. Teachers considered most special ed students to have temporary learning difficulties, rather than permanent disabilities. That mindset helped explain why Finland had one of the highest proportions of special education kids in the world; the label was temporary and not pejorative. The Finns assumed that all kids could improve. In fact, by their seventeenth birthday, about half of Finnish kids had received some kind of special education services at some point, usually in elementary school, so that they did not fall farther behind. During the 2009 to 2010 school year, about one in four Finnish kids received some kind of special education services—almost always in a normal school, for only part of the day. (By comparison, about one in eight American students received special education services that year.)

As I watched Vuorinen talk with his students, I thought back to a Washington, D.C., public school at which I’d spent time a few years before. The school was in a poor part of the city, and many of the families were struggling. One veteran teacher I met had a warm manner and a bright, tidy classroom. She’d paid for classroom supplies with her own money. However, when she’d talked about her fourth grade students’ backgrounds, she’d stressed their disadvantages above all else. She’d talked about her kids’ families as if they were a lost cause: “Our parents on this side don’t have the know-how to raise their children,” she’d said. “They’re not sure what it takes for their child to make it.” She’d felt genuinely sorry for her students, but what good had come from her sympathy? After a year in her class, her students were farther below grade level in reading than they’d been when they’d first met her. They’d performed worse than other low-income kids who’d started the year at the same level in the very same city. Yet she’d seemed oddly sanguine about those results. The diversity narrative explained everything, even when it didn’t.

15 thoughts on “Smartest Kids in the World: American Schools

  1. Clearly, the failures of American public schools are the fault of George Bush’s “No Child Left Behind” debacle, right?

  2. I want to add another international perspective to on excessive sports. Australia sees itself as a sports mad nation. I teach medical students here in Australia including a couple of US students. A case we were working through had an 18 year who was heavily into his sport and trained trained twice weekly with his team. The Americans in the group who played football at high school were surprised that 2 afternoons a week was considered a lot. They trained every afternoon. When asked why they thought for two seconds and replied “to stop us doing drugs in the afternoon”. This is not generally considered the schools job after about 3:30 here…

  3. >Because this was America, a diverse country with a long history of racism in colleges, public schools, and every other institution, Gist’s efforts were also attacked as discriminatory. Higher education leaders warned that the new standards would prevent minority students, who tended to score lower on tests, from becoming teachers.

    In many minority communities, the schools are considered to be an important jobs program for locals. Teachers, administrators, school maintenance personnel, etc. are the backbone of the black middle class. Whether these people are effective in their jobs is considered to be largely besides the point.

    The bottom line again, is this – in America, the entire educational system has to be seen thru a racial lens, whether you like it or not. Even if you would like to be color-blind, there are many vested interests and legal structures that will prevent you from doing so. So comparisons to Finland, Korea and other racially homogeneous societies are just not useful. What “works” over there cannot work over here and if you even try to apply the same remedies, you will get dragged into America’s racial morass.

  4. Phil,
    Like you, I am in my second half-century of life with a daughter who is not yet school-age. It is a major focus of her mother and I to find the very best educational opportunity for our daughter, however stuff like this only adds to the worries.
    I have five cousins who were all public school teachers in central and southern Virginia and they all opine that our public school systems (in America) are shot.
    Separately, I spoke with a recently retired school administrator who was/is considered among the best in his field and he stated that he wouldn’t consider using our public school systems if he had young children and he went so far as to state many private schools in the U.S. weren’t much better.
    He seemed to support the growing trend of home-schooling, as long as the parents had the ability. Which makes me think that you, Phil, would be a superb home-school teacher for your kids.

  5. bobzibub,

    I think it’s less the poverty factor and more the parental influence factor that drives kids to success (or failure).
    I was orphaned as an infant and my adoptive parents were very poor, yet that fact didn’t prevent me from enjoying success in school. Although from modest means, my parents lectured me on being the best I could be. Today it seems that many families don’t employ that outlook.

  6. I’ll bet the author didn’t visit the (private) high school my kids attended. Their classwork and homework loads were huge, much larger than anything my wife and I had ever seen. It made the college transition easier.

    Oh, and sports after school were mandatory.

  7. Here is the text on the “normal failures” of the U.S. school system

    http://www.amazon.com/Systemantics-Systems-Work-Especially-They/dp/0812906748

    The master narrative is that systems, once in existence, act to perpetuate itself.

    Our school district just got a massive tax hike that was justified, in a letter to the editor, because of the high pension and health care costs. (Tell me you care about my pension and health care costs and maybe I’ll care.)

    It’s true that the union gets them good health insurance (sometimes it is scary to go visit a union worker and see the drug cabinet with huge quantities of every kind of controlled and uncontrolled substance that they get with no co-pay.) but the union does nothing for quality of life. Most of the public school teachers I know have nights where they come home crying because of the stress. One reason why “too many teachers” are trained is that half of them refuse to do the work after they see what a human meat grinder it is.

    On top of that, teaching certificates are not, in general, portable between states. For instance Nevada will take a certificate from NY, but not the other way around. Some states, like Connecticut, have “boot camp” programs that will get you teaching math and science after a summer session and an academic season of internship, but most states don’t.

    One funny thing about sports is the private schools in the anglophone zone have long had an emphasis on universal sports participation; it’s often been seen as something that “builds character”.

  8. Regarding the math teacher/coach thing: my father was a math teacher in a small-town junior high school for many years. He was very unusual in that he _wasn’t_ a coach. In fact, there was a joke among teachers: “What do you call a math teacher? Coach.”

    Keep in mind that in sports-dominated American schools, it’s normal for the jocks to torment anyone with an interest in math (or science, or just reading for fun). Curiously, none of the people fussing about poor math performance by American students ever seems to stop and consider whether people interested in math might have that interest impacted by putting the leaders of their tormentors in charge of teaching math.

  9. According to Wikipedia, Finland does not officially record statistics on ethnicity (and, apparently, race; what are they hiding?) But, according to Wikipedia and the CIA world Factbook, in 1990 there were zero Africans in Finland (and, presumably zero American blacks). In 2013, there were 15,789 Africans from Somalia in Finland (out of 5.45 million residents; or just 0.29%). Zero other Africans. Finland reports a 100% literacy rate.

    According to the CIA World Factbook, the US is 13% black.

    Finland and Finland’s educational system cannot be compared to the US.

  10. Ken,
    After giving this some thought, I recall exactly zero of my coaches teaching anything but PE and or a rudimentary, lower level class that was not considered to be even remotely similar to the more difficult courses.
    In short, they were all dumb jocks teaching classes that didn’t require much brain power.
    Also, I recently learned that a classmate of mine is teaching US history in a local, public high school and this poor guy was among the worst students in my graduating class!! Seriously, he was barely past our special education students, yet here he is teaching!! ??

  11. E: Assuming that you are American, by concentrating on the skin color of the students you are proving the author’s thesis, i.e., that Americans lead the world in making up excuses for why they can’t educate children. In any case, Ripley was ready for criticisms like yours. Because the U.S. does so obsessively track student performance sorted by skin color, she was able to include in her book the fact that white American students do worse than Finnish students of all skin colors. And white American students in private schools also do worse. Ripley finds plenty of schools in the U.S. with lavish funding, spectacular facilities, an overwhelming white/comfortable student body and mediocre educational outcomes.

  12. Phil,

    Part of the problem is that America’s racial politics complicate whatever you try to do. So, if for example, you want to raise teacher standards, you have to take into account that may have a “disparate impact” on black teachers. If you want to go to an admission-by-test system, your university may end up like Stuyvesant High, with 75% Asian students and very few blacks and Hispanics. Etc. You can’t impose Finnish type solutions in a vacuum. These are not excuses, this is the reality of what happens when you try to do thing in the real world with vested interests lined up against you. Race does not explain 100% of the problems in the American school system, but it explains at least some of them and it explains why it is so hard to fix these problems or even discuss them without stepping on all sorts of political third rails.

    BTW, why is it with American troubled primary and secondary system, that American universities are widely considered the best in the world?

  13. BTW, Here is exactly the kind of pressure I was just talking about:

    http://www.nytimes.com/2014/06/23/opinion/new-york-citys-top-public-schools-need-diversity.html?src=rechp

    Here is a school that is a proven example of excellence in a sea of mediocrity. A school that educates thousands of immigrant strivers and puts them on the path to the American Dream (1/2 the students are eligible for free lunches due to poverty at home). But because of America’s racial politics (the school is already mostly minority but they are mostly the “wrong” minority – Asian), the urge is to “fix” it.

  14. Speaking from my personal experience, I loved American high school education. It was not too demanding but just demanding enough for those who were motivated to go to top-tier national universities. It allowed me to play different sports each season as professionally as a high school kid could play (e.g., free coaching, free transportation, free uniforms with my own number … you name it!) without having to give up academics. In some countries with higher test scores than America, kids may face “either this or that” type of choices from a very young age (e.g., sports vs. academics, math/science vs. liberal arts, etc.). Not in America. Looking back at my own experience, most American high school students are just kids – they rarely have to think and act like adults, e.g., no responsibilities of having to support families like, for example, many Guatemalan kids have to. In that sense, American high schools afford its students opportunities to be who they are (kids!).

    For me, university was where “real” academic education started in America. American universities cost a lot, but if one goes to a decent one (and it’s much easier to go to a decent university in America if one wanted to!), he/she will get a lot out of it, too. They have tremendous resources and afford many opportunities, which may be why the smartest and the brightest from many countries (want to) come to America for higher education. And even “real’er” education happened when I entered work force because I think American work place is extremely demanding productivity-wise compared to other countries.

    Of course American students could benefit a lot more from more guidance. And I agree that the standard for becoming teachers in America should be more rigorous (… especially if they’ll be guaranteed their jobs for life … with early retirement pensions!). But maybe American parents should play more active role in guiding their kids because teachers can only do so much. Students are, at the end of the day, not their own kids. But in my high school days and afterwards, I often felt that some of those around me could be so much better off if their parents cared more. Some parents straight up felt like they just didn’t care to provide too much guidance to their kids … but that may be because I came from a fairly conservative society that generally had different family structures (at least back then) than America, where both parents often work, were divorced, etc.

    In any case, I don’t have any conclusions, but I think American system isn’t YET as doomed as what many say. The system allows American kids to enjoy their high school days like kids, go to world-famous universities if they wanted to, and they’re more likely to have long-term careers that are commensurate with the efforts that they had put in, etc. (Of course, all relatively speaking.) But, yes, the system can always benefit from improvements.

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