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18007EDNEWS You Can USE- 2 August- Math Education Special

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  • S. E. Anderson
    Jul 26, 2014
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      We're Teaching To The Test — Not Students' Futures

      <b></b>
      Gina Barreca
      Not That I'm Bitter 
      July 22, 2014- courant.com
       

      I'm worried that we're no longer teaching students how to think critically or to write well.

      Everything I'm hearing from teachers, students and parents suggests that, with the standardized testing epidemic sweeping through our nation's public schools, what we're teaching the next generation is how to fill in the blanks and work from templates.

      Success, innovation and productivity rarely rely on answers derived from a multiple-choice format. Think about it for a minute: Is it ever the good guys who ask, "Do you want: a) Your money? b) Your life?"

      • Gina Barreca
      • Gina Barreca

        We're producing answer-givers when what we need are problem-solvers. The most important question a child asks of his or her teacher shouldn't be, "Is this going to be on the test?"

        American students are forfeiting creativity, inspiration and contextual understanding in order to do better on high-stakes exams. It's a meretricious trade.

        If students learn exclusively what can be measured, what can't be measured will no longer be taught.

        Think writing. Think critical thinking. Think music, art, public speaking. Think citizenship.

        I fear the next generation of American students will end up like those impaired souls on reality television who think that Mozart was a writer, that "arugula" is what's being chanted in the background of "The Lion Sleeps Tonight" and that "From each according to his ability, to each according to his needs" is from the U.S. Constitution.

        Rigorous independent schools, which have always been quite literally the playgrounds of the privileged, know this. They recognize the artisanal nature of teaching. Unfettered by the common or the core, their students reach for the extraordinary and the cutting edge. Their instructors are encouraged to have students dig deep, go far and come up with their own answers.

        Don't public school students also deserve to have their curiosity inspired instead of managed?

        If the next generation of public school students fails, in part it will be because we made them spend 12 years playing a scholastic version of "Mad Libs," throwing random words into the air in the hope that some will land in an appropriate spot. As Les Perelman — the former director of undergraduate writing at MIT— famously put it: "You're getting teachers to train students to be bad writers."

        It's called high-stakes testing, by the way, because, like gambling, it appears to offer a fair shot at winning while the odds remain against those who come in with their pockets nearly empty.

        No coach, no test prep, no tutors, no money to keep retaking the test, no small, individualized classes? No luck.

        Yet fans of fanatical testing argue that only what is measured can be improved; it's like Weight Watchers for the mind. There are a lot of scales, but there's no accounting for taste.

        The real point is this: Can you measure education? Does it come in ounces, in diplomas, in the number of assessments per semester, in density, in money earned after graduation or in eureka moments?

        And who decides?

        This is not a multiple-choice question. You need to provide a defense of your central argument and an innovative conclusion.

        As they are taught now, students have bits and pieces of information but no internalized means permitting them to comprehend or discover patterns. True, they will know how to look up facts and they'll be able to accumulate data. This is limiting. They'll think they only need to know enough geography to use the navigation system in their car.

        In truth, they'll need a world map.

        Our students — our children — should be able to make themselves understood in the global community and not just take a stab at vocabulary words. Neither a Frommer's travel guide nor "An Idiot's Guide To The Future" will help.

        Those who test well sometimes can't articulate their own ideas; those who communicate with originality and grace sometimes can't fill in the right bubble.

        We know it's essential to read between the lines to get a job and to keep one. Those who can only read the writing on the wall when it has a single, concrete meaning will be unable to survive in the increasingly competitive international economy.

        There are no short cuts to learning. If we don't teach our students to write well, our nation's history will soon be written by others.

        Gina Barreca is an English professor at the University of Connecticut and a feminist scholar who has written eight books. She can be reached through her website at http://www.ginabarreca.com.

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        Don't Send Your Kid to the Ivy League:

        The nation's top colleges are turning our kids into zombies

        By William Deresiewicz

        In the spring of 2008, I did a daylong stint on the Yale admissions committee. Wethat is, three admissions staff, a member of the college dean’s office, and me, the faculty representativewere going through submissions from eastern Pennsylvania. The applicants had been assigned a score from one to four, calculated from a string of figures and codesSATs, GPA, class rank, numerical scores to which the letters of recommendation had been converted, special notations for legacies and diversity cases. The ones had already been admitted, and the threes and fours could get in only under special conditionsif they were a nationally ranked athlete, for instance, or a “DevA,” (an applicant in the highest category of “development” cases, which means a child of very rich donors). Our task for the day was to adjudicate among the twos. Huge bowls of junk food were stationed at the side of the room to keep our energy up.

        The junior officer in charge, a young man who looked to be about 30, presented each case, rat-a-tat-tat, in a blizzard of admissions jargon that I had to pick up on the fly. “Good rig”: the transcript exhibits a good degree of academic rigor. “Ed level 1”: parents have an educational level no higher than high school, indicating a genuine hardship case. “MUSD”: a musician in the highest category of promise. Kids who had five or six items on their list of extracurricularsthe “brag”were already in trouble, because that wasn’t nearly enough. We listened, asked questions, dove into a letter or two, then voted up or down.

        With so many accomplished applicants to choose from, we were looking for kids with something special, “PQs”personal qualitiesthat were often revealed by the letters or essays. Kids who only had the numbers and the résumé were usually rejected: “no spark,” “not a team-builder,” “this is pretty much in the middle of the fairway for us.” One young person, who had piled up a truly insane quantity of extracurriculars and who submitted nine letters of recommendation, was felt to be “too intense.” On the other hand, the numbers and the résumé were clearly indispensable. I’d been told that successful applicants could either be “well-rounded” or “pointy”outstanding in one particular waybut if they were pointy, they had to be really pointy: a musician whose audition tape had impressed the music department, a scientist who had won a national award.

        “Super People,” the writer James Atlas has called themthe stereotypical ultra-high-achieving elite college students of today. A double major, a sport, a musical instrument, a couple of foreign languages, service work in distant corners of the globe, a few hobbies thrown in for good measure: They have mastered them all, and with a serene self-assurance that leaves adults and peers alike in awe. A friend who teaches at a top university once asked her class to memorize 30 lines of the eighteenth-century poet Alexander Pope. Nearly every single kid got every single line correct. It was a thing of wonder, she said, like watching thoroughbreds circle a track.

        These enviable youngsters appear to be the winners in the race we have made of childhood. But the reality is very different, as I have witnessed in many of my own students and heard from the hundreds of young people whom I have spoken with on campuses or who have written to me over the last few years. Our system of elite education manufactures young people who are smart and talented and driven, yes, but also anxious, timid, and lost, with little intellectual curiosity and a stunted sense of purpose: trapped in a bubble of privilege, heading meekly in the same direction, great at what they’re doing but with no idea why they’re doing it.

        When I speak of elite education, I mean prestigious institutions like Harvard or Stanford or Williams as well as the larger universe of second-tier selective schools, but I also mean everything that leads up to and away from themthe private and affluent public high schools; the ever-growing industry of tutors and consultants and test-prep courses; the admissions process itself, squatting like a dragon at the entrance to adulthood; the brand-name graduate schools and employment opportunities that come after the B.A.; and the parents and communities, largely upper-middle class, who push their children into the maw of this machine. In short, our entire system of elite education.

        I should say that this subject is very personal for me. Like so many kids today, I went off to college like a sleepwalker. You chose the most prestigious place that let you in; up ahead were vaguely understood objectives: status, wealth“success.” What it meant to actually get an education and why you might want oneall this was off the table. It was only after 24 years in the Ivy Leaguecollege and a Ph.D. at Columbia, ten years on the faculty at Yalethat I started to think about what this system does to kids and how they can escape from it, what it does to our society and how we can dismantle it.

        ADVERTISEMENT
         

        A young woman from another school wrote me this about her boyfriend at Yale:

        Before he started college, he spent most of his time reading and writing short stories. Three years later, he’s painfully insecure, worrying about things my public-educated friends don’t give a second thought to, like the stigma of eating lunch alone and whether he’s “networking” enough. No one but me knows he fakes being well-read by thumbing through the first and last chapters of any book he hears about and obsessively devouring reviews in lieu of the real thing. He does this not because he’s incurious, but because there’s a bigger social reward for being able to talk about books than for actually reading them.

        I taught many wonderful young people during my years in the Ivy Leaguebright, thoughtful, creative kids whom it was a pleasure to talk with and learn from. But most of them seemed content to color within the lines that their education had marked out for them. Very few were passionate about ideas. Very few saw college as part of a larger project of intellectual discovery and development. Everyone dressed as if they were ready to be interviewed at a moment’s notice.

        Look beneath the façade of seamless well-adjustment, and what you often find are toxic levels of fear, anxiety, and depression, of emptiness and aimlessness and isolation. A large-scale survey of college freshmen recently found that self-reports of emotional well-being have fallen to their lowest level in the study’s 25-year history.

        So extreme are the admission standards now that kids who manage to get into elite colleges have, by definition, never experienced anything but success. The prospect of not being successful terrifies them, disorients them. The cost of falling short, even temporarily, becomes not merely practical, but existential. The result is a violent aversion to risk. You have no margin for error, so you avoid the possibility that you will ever make an error. Once, a student at Pomona told me that she’d love to have a chance to think about the things she’s studying, only she doesn’t have the time. I asked her if she had ever considered not trying to get an A in every class. She looked at me as if I had made an indecent suggestion.

        There are exceptions, kids who insist, against all odds, on trying to get a real education. But their experience tends to make them feel like freaks. One student told me that a friend of hers had left Yale because she found the school “stifling to the parts of yourself that you’d call a soul.”

        It's About Capital Gains & Profits- Not Intellectual Development

        “Return on investment”: that’s the phrase you often hear today when people talk about college. What no one seems to ask is what the “return” is supposed to be. Is it just about earning more money? Is the only purpose of an education to enable you to get a job? What, in short, is college for?

        The first thing that college is for is to teach you to think. That doesn’t simply mean developing the mental skills particular to individual disciplines. College is an opportunity to stand outside the world for a few years, between the orthodoxy of your family and the exigencies of career, and contemplate things from a distance.

        Learning how to think is only the beginning, though. There’s something in particular you need to think about: building a self. The notion may sound strange. “We’ve taught them,” David Foster Wallace once said, “that a self is something you just have.” But it is only through the act of establishing communication between the mind and the heart, the mind and experience, that you become an individual, a unique beinga soul. The job of college is to assist you to begin to do that. Books, ideas, works of art and thought, the pressure of the minds around you that are looking for their own answers in their own ways.

        College is not the only chance to learn to think, but it is the best. One thing is certain: If you haven’t started by the time you finish your B.A., there’s little likelihood you’ll do it later. That is why an undergraduate experience devoted exclusively to career preparation is four years largely wasted.

        Elite schools like to boast that they teach their students how to think, but all they mean is that they train them in the analytic and rhetorical skills that are necessary for success in business and the professions. Everything is technocraticthe development of expertiseand everything is ultimately justified in technocratic terms.

        Religious collegeseven obscure, regional schools that no one has ever heard of on the coastsoften do a much better job in that respect. What an indictment of the Ivy League and its peers: that colleges four levels down on the academic totem pole, enrolling students whose SAT scores are hundreds of points lower than theirs, deliver a better education, in the highest sense of the word.

        At least the classes at elite schools are academically rigorous, demanding on their own terms, no? Not necessarily. In the sciences, usually; in other disciplines, not so much. There are exceptions, of course, but professors and students have largely entered into what one observer called a “nonaggression pact.” Students are regarded by the institution as “customers,” people to be pandered to instead of challenged. Professors are rewarded for research, so they want to spend as little time on their classes as they can. The profession’s whole incentive structure is biased against teaching, and the more prestigious the school, the stronger the bias is likely to be. The result is higher marks for shoddier work.

        It is true that today’s young people appear to be more socially engaged than kids have been for several decades and that they are more apt to harbor creative or entrepreneurial impulses. But it is also true, at least at the most selective schools, that even if those aspirations make it out of collegea big “if”they tend to be played out within the same narrow conception of what constitutes a valid life: affluence, credentials, prestige.

        Experience itself has been reduced to instrumental function, via the college essay. From learning to commodify your experiences for the application, the next step has been to seek out experiences in order to have them to commodify. The New York Times reports that there is now a thriving sector devoted to producing essay-ready summers, but what strikes one is the superficiality of the activities involved: a month traveling around Italy studying the Renaissance, “a whole day” with a band of renegade artists. A whole day!

        I’ve noticed something similar when it comes to service. Why is it that people feel the need to go to places like Guatemala to do their projects of rescue or documentation, instead of Milwaukee or Arkansas? When students do stay in the States, why is it that so many head for New Orleans? Perhaps it’s no surprise, when kids are trained to think of service as something they are ultimately doing for themselvesthat is, for their résumés. “Do well by doing good,” goes the slogan. How about just doing good?

        If there is one idea, above all, through which the concept of social responsibility is communicated at the most prestigious schools, it is “leadership.” “Harvard is for leaders,” goes the Cambridge cliché. To be a high-achieving student is to constantly be urged to think of yourself as a future leader of society. But what these institutions mean by leadership is nothing more than getting to the top. Making partner at a major law firm or becoming a chief executive, climbing the greasy pole of whatever hierarchy you decide to attach yourself to. I don’t think it occurs to the people in charge of elite colleges that the concept of leadership ought to have a higher meaning, or, really, any meaning.

        The irony is that elite students are told that they can be whatever they want, but most of them end up choosing to be one of a few very similar things. As of 2010, about a third of graduates went into financing or consulting at a number of top schools, including Harvard, Princeton, and Cornell. Whole fields have disappeared from view: the clergy, the military, electoral politics, even academia itself, for the most part, including basic science. It’s considered glamorous to drop out of a selective college if you want to become the next Mark Zuckerberg, but ludicrous to stay in to become a social worker. “What Wall Street figured out,” as Ezra Klein has put it, “is that colleges are producing a large number of very smart, completely confused graduates. Kids who have ample mental horsepower, an incredible work ethic and no idea what to do next.”

        For the most selective colleges, this system is working very well indeed. Application numbers continue to swell, endowments are robust, tuition hikes bring ritual complaints but no decline in business. Whether it is working for anyone else is a different question.

        It almost feels ridiculous to have to insist that colleges like Harvard are bastions of privilege, where the rich send their children to learn to walk, talk, and think like the rich. Don’t we already know this? They aren’t called elite colleges for nothing. But apparently we like pretending otherwise. We live in a meritocracy, after all.

        Ivy League "Diversity": Smoke & Mirrors for the Elite Status Quo

        The sign of the system’s alleged fairness is the set of policies that travel under the banner of “diversity.” And that diversity does indeed represent nothing less than a social revolution. Princeton, which didn’t even admit its first woman graduatestudent until 1961a year in which a grand total of one (no doubt very lonely) African American matriculated at its collegeis now half female and only about half white. But diversity of sex and race has become a cover for increasing economic resegregation. Elite colleges are still living off the moral capital they earned in the 1960s, when they took the genuinely courageous step of dismantling the mechanisms of the WASP aristocracy.

        The truth is that the meritocracy was never more than partial. Visit any elite campus across our great nation, and you can thrill to the heart-warming spectacle of the children of white businesspeople and professionals studying and playing alongside the children of black, Asian, and Latino businesspeople and professionals. Kids at schools like Stanford think that their environment is diverse if one comes from Missouri and another from Pakistan, or if one plays the cello and the other lacrosse. Never mind that all of their parents are doctors or bankers.

        That doesn’t mean there aren’t a few exceptions, but that is all they are. In fact, the group that is most disadvantaged by our current admissions policies are working-class and rural whites, who are hardly present on selective campuses at all. The only way to think these places are diverse is if that’s all you’ve ever seen.

        Let’s not kid ourselves: The college admissions game is not primarily about the lower and middle classes seeking to rise, or even about the upper-middle class attempting to maintain its position. It is about determining the exact hierarchy of status within the upper-middle class itself. In the affluent suburbs and well-heeled urban enclaves where this game is principally played, it is not about whether you go to an elite school. It’s about which one you go to. It is Penn versus Tufts, not Penn versus Penn State. It doesn’t matter that a bright young person can go to Ohio State, become a doctor, settle in Dayton, and make a very good living. Such an outcome is simply too horrible to contemplate.

        This system is exacerbating inequality, retarding social mobility, perpetuating privilege, and creating an elite that is isolated from the society that it’s supposed to lead. The numbers are undeniable. In 1985, 46 percent of incoming freshmen at the 250 most selective colleges came from the top quarter of the income distribution. By 2000, it was 55 percent. As of 2006, only about 15 percent of students at the most competitive schools came from the bottom half. The more prestigious the school, the more unequal its student body is apt to be. And public institutions are not much better than private ones. As of 2004, 40 percent of first-year students at the most selective state campuses came from families with incomes of more than $100,000, up from 32 percent just five years earlier.

        The major reason for the trend is clear. Not increasing tuition, though that is a factor, but the ever-growing cost of manufacturing children who are fit to compete in the college admissions game. The more hurdles there are, the more expensive it is to catapult your kid across them. Wealthy families start buying their children’s way into elite colleges almost from the moment they are born: music lessons, sports equipment, foreign travel (“enrichment” programs, to use the all-too-perfect term)most important, of course, private-school tuition or the costs of living in a place with top-tier public schools. The SAT is supposed to measure aptitude, but what it actually measures is parental income, which it tracks quite closely. Today, fewer than half of high-scoring students from low-income families even enroll at four-year schools.

        The problem isn’t that there aren’t more qualified lower-income kids from which to choose. Elite private colleges will never allow their students’ economic profile to mirror that of society as a whole. They can’t afford tothey need a critical mass of full payers and they need to tend to their donor baseand it’s not even clear that they’d want to.

        And so it is hardly a coincidence that income inequality is higher than it has been since before the Great Depression, or that social mobility is lower in the United States than in almost every other developed country. Elite colleges are not just powerless to reverse the movement toward a more unequal society; their policies actively promote it.

        Is there anything that I can do, a lot of young people have written to ask me, to avoid becoming an out-of-touch, entitled little shit? I don’t have a satisfying answer, short of telling them to transfer to a public university. You cannot cogitate your way to sympathy with people of different backgrounds, still less to knowledge of them. You need to interact with them directly, and it has to be on an equal footing: not in the context of “service,” and not in the spirit of “making an effort,” eitherswooping down on a member of the college support staff and offering to “buy them a coffee,” as a former Yalie once suggested, in order to “ask them about themselves.”

        Instead of service, how about service work? That’ll really give you insight into other people. How about waiting tables so that you can see how hard it is, physically and mentally? You really aren’t as smart as everyone has been telling you; you’re only smarter in a certain way. There are smart people who do not go to a prestigious college, or to any collegeoften precisely for reasons of class. There are smart people who are not “smart.”

        Options to Elite Colleges & Universities

        I am under no illusion that it doesn’t matter where you go to college. But there are options. There are still very good public universities in every region of the country. The education is often impersonal, but the student body is usually genuinely diverse in terms of socioeconomic background, with all of the invaluable experiential learning that implies.

        U.S. News and World Report supplies the percentage of freshmen at each college who finished in the highest 10 percent of their high school class. Among the top 20 universities, the number is usually above 90 percent. I’d be wary of attending schools like that. Students determine the level of classroom discussion; they shape your values and expectations, for good and ill. It’s partly because of the students that I’d warn kids away from the Ivies and their ilk. Kids at less prestigious schools are apt to be more interesting, more curious, more open, and far less entitled and competitive.

        If there is anywhere that college is still collegeanywhere that teaching and the humanities are still accorded pride of placeit is the liberal arts college. Such places are small, which is not for everyone, and they’re often fairly isolated, which is also not for everyone. The best option of all may be the second-tiernot second-ratecolleges, like Reed, Kenyon, Wesleyan, Sewanee, Mount Holyoke, and others. Instead of trying to compete with Harvard and Yale, these schools have retained their allegiance to real educational values.

        Not being an entitled little shit is an admirable goal. But in the end, the deeper issue is the situation that makes it so hard to be anything else. The time has come, not simply to reform that system top to bottom, but to plot our exit to another kind of society altogether.

        The education system has to act to mitigate the class system, not reproduce it. Affirmative action should be based on class instead of race, a change that many have been advocating for years. Preferences for legacies and athletes ought to be discarded. SAT scores should be weighted to account for socioeconomic factors. Colleges should put an end to résumé-stuffing by imposing a limit on the number of extracurriculars that kids can list on their applications. They ought to place more value on the kind of service jobs that lower-income students often take in high school and that high achievers almost never do. They should refuse to be impressed by any opportunity that was enabled by parental wealth. Of course, they have to stop cooperating with U.S. News.

        More broadly, they need to rethink their conception of merit. If schools are going to train a better class of leaders than the ones we have today, they’re going to have to ask themselves what kinds of qualities they need to promote. Selecting students by GPA or the number of extracurriculars more often benefits the faithful drudge than the original mind.

        The changes must go deeper, though, than reforming the admissions process. That might address the problem of mediocrity, but it won’t address the greater one of inequality. The problem is the Ivy League itself. We have contracted the training of our leadership class to a set of private institutions. However much they claim to act for the common good, they will always place their interests first. The arrangement is great for the schools, but is Harvard’s desire for alumni donations a sufficient reason to perpetuate the class system?

        I used to think that we needed to create a world where every child had an equal chance to get to the Ivy League. I’ve come to see that what we really need is to create one where you don’t have to go to the Ivy League, or any private college, to get a first-rate education.

        High-quality public education, financed with public money, for the benefit of all: the exact commitment that drove the growth of public higher education in the postwar years. Everybody gets an equal chance to go as far as their hard work and talent will take themyou know, the American dream. Everyone who wants it gets to have the kind of mind-expanding, soul-enriching experience that a liberal arts education provides. We recognize that free, quality K–12 education is a right of citizenship. We also need to recognizeas we once did and as many countries still dothat the same is true of higher education. We have tried aristocracy. We have tried meritocracy. Now it’s time to try democracy.

        William Deresiewicz is the author of Excellent Sheep: The Miseducation of the American Elite and The Way to a Meaningful Life, coming out August 19 from Free Press. He taught at Yale from 1998 to 2008.

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        Don’t Teach Math, Coach It

         
        Credit Tomi Um

        MADISON, Wis. — PEOPLE ask me all the time how they can get their kids excited about math. That ought to be a softball for me, because I teach math for a living. I wake up excited about math.

        But it’s not that simple. With the college students I teach, it’s a straightforward transaction. They’re paying me to teach them math, and my job is to cajole or incentivize them into doing the work that’s necessary to learn the subject, whether they feel like it or not.

        It’s a different story with your own children. None of us want to be Leo Wiener. Yes, Wiener helped shape his son, Norbert, into a child prodigy who got a Ph.D. at Harvard at 18, and who later became a groundbreaking mathematician. But this was how Norbert recalled the process:

        “He would begin the discussion in an easy, conversational tone. This lasted exactly until I made the first mathematical mistake. Then the gentle and loving father was replaced by the avenger of the blood. ... Father was raging, I was weeping, and my mother did her best to defend me, although hers was a losing battle.”

        No parents want this story told in their child’s memoirs. But how can we encourage kids in a difficult task like math without doing so in a way they’ll come to resent?

        I found an answer in something my 8-year-old son, C. J., likes even better than math: baseball. Let me be clear here. My level of skill at baseball — actually, with every kind of ball — is pretty much the opposite of my mastery of math. I’ve reached 40 and I still throw in the way that we used to call, before they started showing college softball on TV, “like a girl.”

        But C. J. is a baseball fanatic. He lives and dies with the Milwaukee Brewers and he’s pretty set on being one of them when he grows up. He plays Little League with a fierce concentration I seldom see at home. And I’ve learned a lot about what kind of math parent I want to be from an unexpected source — his coaches.

        Baseball is a game. And math, for kids, is a game, too. Everything for them is a game. That’s the great thing about being a kid. In Little League, you play hard and you play to win, but it doesn’t actually matter who wins. And good coaches get this. They don’t get mad and they don’t throw you off the team. They don’t tell you that you stink at baseball, even if you do — they tell you what you need to do to get better, which everybody can do.

        What does it mean to coach math instead of teaching it? For C. J., it means I give him a “mystery number” to think about before bed. “I’m thinking of a mystery number, and when I multiply it by 2 and add 7, I get 29; what’s the mystery number?” And already you’re doing not just arithmetic but algebra.

        For his little sister, who’s 4, that’s too formal. But say we’re at the grocery store and we need four cans of soup and she brings me two, and I say, “so we need three more, right?” and she says “No, Daddy!” That’s really funny when you’re 4. It’s a game, and it’s math.

        Lots of games are math. There are the classics you know about: chess, which builds the ability to follow a series of logical steps; Monopoly, which demands basic arithmetic and probabilistic reasoning; and Rubik’s Cube, which is fundamentally an exercise in geometry and group theory.

        But there are new classics, too, that weren’t around when you were a kid: Rush Hour, a board game about search algorithms; Set, a study in higher-dimensional geometry in the form of a viciously competitive card game; and DragonBox, an app for phone or tablet that teaches the formalisms of algebra. Every one of these games shows kids mathematical ideas in a spirit of play, which is a big and often hidden part of the true spirit of math.

        These games are difficult, but also, for many kids, kind of addictive. Which means they also teach sitzfleisch, the ability to focus on a complicated skill for the length of time it takes to master it. Math needs that. (Baseball does, too.) It fits with the research of the psychologist Carol Dweck, which suggests that mentors should emphasize effort over native ability. We can’t really teach kids to do things; we can only teach them to practice things.

        There are many things we’d like to coach our kids to do. And we can’t help playing favorites to some extent. I’ll admit, I’d rather C. J. aimed to be a mathematician than a shortstop. I tried to open his eyes to some more realistic careers that could still satisfy his hunger for the major leagues. “You know,” I told him, “you really like math, and all the teams now have people who work for them analyzing the players’ statistics. You’d probably enjoy that!”

        At this suggestion he became agreeably eager. “Daddy, that’s a really good idea,” he said. “Because almost all major league players have to retire by the time they’re 40 — so then I could get a job analyzing the statistics!”

        Well, I tried.

        Jordan Ellenberg, a professor of mathematics at the University of Wisconsin, is the author of “How Not To Be Wrong: The Power of Mathematical Thinking.”

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        Why Do Americans Stink at Math?

        Credit Photo illustration by Andrew B. Myers. Prop stylIst: Randi Brookman Harris. Calculator icons by Tim Boelaars.

        When Akihiko Takahashi was a junior in college in 1978, he was like most of the other students at his university in suburban Tokyo. He had a vague sense of wanting to accomplish something but no clue what that something should be. But that spring he met a man who would become his mentor, and this relationship set the course of his entire career.

        Takeshi Matsuyama was an elementary-school teacher, but like a small number of instructors in Japan, he taught not just young children but also college students who wanted to become teachers. At the university-affiliated elementary school where Matsuyama taught, he turned his classroom into a kind of laboratory, concocting and trying out new teaching ideas. When Takahashi met him, Matsuyama was in the middle of his boldest experiment yet — revolutionizing the way students learned math by radically changing the way teachers taught it.

        Instead of having students memorize and then practice endless lists of equations — which Takahashi remembered from his own days in school — Matsuyama taught his college students to encourage passionate discussions among children so they would come to uncover math’s procedures, properties and proofs for themselves. One day, for example, the young students would derive the formula for finding the area of a rectangle; the next, they would use what they learned to do the same for parallelograms. Taught this new way, math itself seemed transformed. It was not dull misery but challenging, stimulating and even fun.

        Takahashi quickly became a convert. He discovered that these ideas came from reformers in the United States, and he dedicated himself to learning to teach like an American. Over the next 12 years, as the Japanese educational system embraced this more vibrant approach to math, Takahashi taught first through sixth grade. Teaching, and thinking about teaching, was practically all he did. A quiet man with calm, smiling eyes, his passion for a new kind of math instruction could take his colleagues by surprise. “He looks very gentle and kind,” Kazuyuki Shirai, a fellow math teacher, told me through a translator. “But when he starts talking about math, everything changes.”

        Takahashi was especially enthralled with an American group called the National Council of Teachers of Mathematics, or N.C.T.M., which published manifestoes throughout the 1980s, prescribing radical changes in the teaching of math. Spending late nights at school, Takahashi read every one. Like many professionals in Japan, teachers often said they did their work in the name of their mentor. It was as if Takahashi bore two influences: Matsuyama and the American reformers.

        Takahashi, who is 58, became one of his country’s leading math teachers, once attracting 1,000 observers to a public lesson. He participated in a classroom equivalent of “Iron Chef,” the popular Japanese television show. But in 1991, when he got the opportunity to take a new job in America, teaching at a school run by the Japanese Education Ministry for expats in Chicago, he did not hesitate. With his wife, a graphic designer, he left his friends, family, colleagues — everything he knew — and moved to the United States, eager to be at the center of the new math.

        As soon as he arrived, he started spending his days off visiting American schools. One of the first math classes he observed gave him such a jolt that he assumed there must have been some kind of mistake. The class looked exactly like his own memories of school. “I thought, Well, that’s only this class,” Takahashi said. But the next class looked like the first, and so did the next and the one after that. The Americans might have invented the world’s best methods for teaching math to children, but it was difficult to find anyone actually using them.

        It wasn’t the first time that Americans had dreamed up a better way to teach math and then failed to implement it. The same pattern played out in the 1960s, when schools gripped by a post-Sputnik inferiority complex unveiled an ambitious “new math,” only to find, a few years later, that nothing actually changed. In fact, efforts to introduce a better way of teaching math stretch back to the 1800s. The story is the same every time: a big, excited push, followed by mass confusion and then a return to conventional practices.

        The trouble always starts when teachers are told to put innovative ideas into practice without much guidance on how to do it. In the hands of unprepared teachers, the reforms turn to nonsense, perplexing students more than helping them. One 1965 Peanuts cartoon depicts the young blond-haired Sally struggling to understand her new-math assignment: “Sets . . . one to one matching . . . equivalent sets . . . sets of one . . . sets of two . . . renaming two. . . .” After persisting for three valiant frames, she throws back her head and bursts into tears: “All I want to know is, how much is two and two?”

        Today the frustrating descent from good intentions to tears is playing out once again, as states across the country carry out the latest wave of math reforms: the Common Core. A new set of academic standards developed to replace states’ individually designed learning goals, the Common Core math standards a

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