richard rusczyk founder of art of problem solving

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Tiger of the week richard rusczyk ’93 fosters resilience, curiosity through challenging math problems.

It’s a question that Richard Rusczyk ’93 has spent much of his life trying to solve.

“Every little child knows how to do it,” says Rusczyk — a former USA Math Olympiad champion, recipient of the Paul Erdős Award for innovation of math challenges, and founder of Art of Problem Solving (AoPS), a company that develops educational tools for math students. Preschoolers are surrounded by new problems, he explains — problems so overwhelmingly difficult that they sometimes yell and cry and throw tantrums. But they keep trying.

“A 4-year-old hasn’t learned to quit,” he says. “A big part of solving problems you’ve never seen before is retaining that resilience.”

Many of us abandon this approach when we grow older. Rusczyk attributes this in part to our education system, which incentivizes students to absorb and regurgitate material rather than master it. Hard-working students can ace their way through high school without confronting new problems — and when they finally face one, they often shy away from it.

Through AoPS, Rusczyk seeks to expose students of all ages to problems that challenge their understanding of fundamental concepts. His company provides demanding math curricula and instructors who encourage students to ask for help. It also offers a community of peers who are being similarly challenged, so that students learn to be comfortable stretching themselves.

“This is the sort of training one has to go through to get to the edges of any sort of intellectual discipline,” he says. “It’s not just math. It’s not just computer science or economics. It’s writing. It’s philosophy. It’s anything you want to do.”

Rusczyk began developing educational resources at Princeton, after he realized that the math competitions he had participated in during high school had prepared him well for the rigors of college. He and Sandor Lehoczky ’94 co-created national math competitions for high school students. And when the scores came back low, they decided that rather than make the tests easier, they would write a math textbook to help students prepare. By the time Rusczyk graduated, they had co-authored two textbooks — the first of many The Art of Problem Solving books they would write together.

Today, AoPS offers an online school, in-person learning centers, and a constellation of online applications, in addition to textbooks. It also boasts an active 300,000-member online community. The 2018 MIT admit class circulated a spreadsheet in which to share usernames for five social media platforms: Facebook, Instagram, Twitter, Snapchat, and AoPS. After 20 years without a win, the U.S. has won four of the past five International Math Olympiads — and all of the 22 members of those teams are or were AoPS students.

READ MORE Professor and Coach Po-Shen Loh *10 Challenges Rising Mathematicians

But while AoPS has done a great deal to advance top math students, Rusczyk is concerned that it remains inaccessible to talented students who lack resources or mentors.

“You see a growing gap between well-connected, high-ability, high-interest kids, and those high-ability, high-interest kids who are not well-connected,” he says. “We wanted to address this problem by trying to find a way to give those students access to the same sorts of materials and opportunities that had inspired us.”

In 2011, Rusczyk and Lehoczky started the Bridge to Enter Advanced Mathematics (BEAM), a program for gifted but underserved students. BEAM offers summer programs and mentors students through high school and the college application process. It is now partnering with schools and community organizations to offer AoPS online materials to elementary schoolers.

One of BEAM’s early students, Kadija Benoit ’23, just began her freshman year at Princeton.

“I didn’t think about college until I was with BEAM,” says Benoit, whose parents immigrated to the Bronx from Mali. “BEAM showed me that there was more to my capabilities, and more to life , than what I saw around me.”

Benoit feels grateful to BEAM for helping her explore her passion for STEM without placing a financial burden on her parents.

“It was really cool to be surrounded by a group of students who were also passionate about academic exploration,” she says. “To truly be yourself: your inner nerd.”

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Richard Rusczyk’s Worldwide Math Camp

At the start of a YouTube video titled “ Art of Problem Solving: Least Common Multiple ,” Richard Rusczyk invites viewers to play a game. Every twenty-four seconds, we’re supposed to clap; every forty-five seconds, we’re supposed to jump. The challenge is to keep going until we clap and jump at the same time. Rusczyk, who is dark-haired, clean-shaven, and boyish, gestures to a digital timer that appears in a corner of the screen. He starts the clock, stares at it, and fidgets. “Um, how long is this gonna take?” he asks, rolling his eyes like a teen-ager. “I hate waiting.”

When the timer hits twenty-four seconds, Rusczyk claps. When it reaches forty-five, he jumps. Meanwhile, on a digital blackboard, he starts trying to figure out when the clap and the jump will coincide. Over the course of a continuous seven-minute take, Rusczyk jumps and claps at the right times while scribbling equations. First, he tries writing out multiples of twenty-four, but gets bored. Then he tries expressing twenty-four and forty-five as products of their prime-number components: twenty-four is 2³ x 3¹, and forty-five is 3² x 5¹. “This is gonna work,” he says, clapping. Just as he concludes that it will take three hundred and sixty seconds for the clap and jump to converge, he claps and leaps simultaneously; as it happens, the timer has reached three hundred and sixty. It’s an exuberant, precise performance intended for middle-school kids, or younger ones, who are capable of doing advanced math.

Rusczyk, who lives near San Diego, founded Art of Problem Solving—or AoPS—eighteen years ago as a resource for budding math prodigies. Exceptionally gifted young math students often find classroom math unbearably easy and tedious; their parents can have difficulty obtaining sufficiently stimulating lessons. By offering online instruction in math that’s more complex than what’s in standard gifted-and-talented programs, AoPS has become a lifeline for math whizzes. Its free online forums also serve as a vital social network, allowing math prodigies to connect with kindred spirits every day.

Rusczyk began posting free videos more than a decade ago; he ad-libs without a written script. He made “Least Common Multiple,” with its quirky dramatization of a humdrum numerical concept, in 2011, at age forty. Some of his videos have garnered hundreds of thousands of views; occasionally, they feature his alter ego, a gravelly voiced character in dark shades and a black hoodie. Onscreen, Rusczyk conveys a playful, experimental fearlessness that sweeps young learners along. “It’s a slightly intangible quality that some people have, and he’s got it in spades,” the mathematician Sam Vandervelde, who is the head of Proof School, a private, math-centric liberal arts academy in San Francisco, told me.

Kristen Chandler, a former math teacher who is the executive director of MathCounts , a nonprofit that runs a popular middle-school math contest series, told me that Rusczyk is “a rock star at our competitions.” (Along with Raytheon Technologies, the Department of Defense STEM , and others, AoPS is a sponsor of the MathCounts program.) Pre-pandemic, Rusczyk attended the MathCounts national finals each May as an invited speaker; Chandler recalled how contestants and parents flocked to get his autograph and take selfies with him. One competitor asked Rusczyk to sign his forehead with a marker.

For years, AoPS grew gradually. It released print textbooks, Math Olympiad-prep materials, and an accredited online curriculum, including a free adaptive learning system containing thousands of hard math problems. In 2012, it began rolling out Beast Academy, an elementary-school curriculum in which advanced mathematical concepts are communicated to young math geeks by wisecracking comic-book monsters. It also opened ten brick-and-mortar learning centers across the country. By 2019, about thirty-six thousand math students from around the world were using its paid online curriculum or in-person courses, and tens of thousands more were consulting its textbooks for independent study.

In the spring of 2020, when schools shuttered , the company’s Web site traffic jumped five- to six-fold, and enrollments doubled. AoPS’s hundred employees began telecommuting, except for Rusczyk and four warehouse workers. On nights or weekends, Rusczyk and his wife, Vanessa, would go into the empty company headquarters—a two-story office building in the suburb of Rancho Bernardo—to help fill book orders. One Sunday when he was in the office, we connected over Zoom. He was dressed in a short-sleeved blue plaid shirt. Five feet seven, with cropped hair, Rusczyk has a quick, self-deprecating wit and sometimes laughs like a kid, almost doubled over. On a brief tour, he showed me stacks of book boxes in the warehouse and framed illustrations of Beast Academy monsters. In a dim hallway, the overhead fluorescent lighting had stopped working, except for one eerily flickering panel. “This is where the zombies are going to get me in the zombie apocalypse,” he said, grinning. (He read a lot of sci-fi and fantasy as a child.)

Now fifty, Rusczyk bonds easily with math-obsessed kids because he used to be one of them. Growing up, he was fast with calculations and showed a brilliant, intuitive grasp of geometric relationships. He had a competitive streak, and won many math competitions. But, at the same time, he experienced deflating setbacks that helped dissuade him from the academic pursuit of mathematics. He loved math—it had taught him about resilience, creativity, and the joys of finding one’s tribe. Still, he faced a conundrum: If you’re a math prodigy who doesn’t want to become a mathematician, what do you do with your life? Art of Problem Solving was his solution.

Rusczyk was born in Idaho Falls. He and his younger sister attended elementary schools in half a dozen states as their father, a U.S. naval officer and nuclear engineer, moved from one base to the next. Small but naturally athletic, Rusczyk played basketball and spouted pro baseball statistics—these “got him into numbers,” his mother, Claire, a former grade-school teacher, told me. In 1983, Claire read a newspaper article about the launch of the MathCounts program. Rusczyk, who was in seventh grade, signed up and did well; he loved being surrounded by dozens of teens who got a kick out of wrestling with numbers. Two years later, after the family had settled in Decatur, Alabama, he placed twenty-fourth at the MathCounts national finals.

Rusczyk became the star of his high school’s math team, which travelled to competitions around the Southeast. He also participated individually in the American Mathematics Competitions, a rigorous series organized by the Mathematical Association of America (M.A.A.). The contests built up to the U.S.A. Mathematical Olympiad, which back then was a five-question, three-and-a-half-hour examination. Rusczyk played tennis and ran cross-country, but he relished math and the company of his math buddies even more. His bookshelves were filled with math-contest ribbons and trophies. “I was definitely a trophy hunter,” he said. He spent hours practicing with old math-contest problems in his bedroom.

In June, 1987, after his sophomore year, he was invited to the M.A.A.’s Mathematical Olympiad Summer Program, reserved for those who’d placed in the top tier of the U.S.A. Mathematical Olympiad. The program was an intensive, monthlong math boot camp, held each year at either West Point or the Naval Academy, in Annapolis. (A redesigned program is now hosted by Carnegie Mellon University.) At West Point, Rusczyk was one of two dozen boot campers, nearly all boys. They stayed in spartan dorm rooms and were rousted early by the bugle call of reveille. Largely based on three exams in the first week—each roughly four hours long—six students would be chosen to represent the U.S. at the International Mathematical Olympiad, or I.M.O., in July.

Rusczyk arrived excited, expecting that he would be able to hold his own. On the first day, a professor stood at a blackboard and wrote “Counting” in chalk; the topic—“falling factorials”—was unfamiliar. Within minutes, Rusczyk was bewildered. It quickly became obvious that he wasn’t even close to being the brightest kid in the room. It was an unsettling feeling. Other students absorbed the math like sponges; some were clearly geniuses. Rusczyk couldn’t solve a single problem on the gruelling practice exams. Being outgunned by his cerebral classmates was inspiring but also terrifying. “I shut down by the end of the first week,” he recalled.

Still, the group was friendly, bantering over board games and Ultimate Frisbee. Rusczyk, who had brought his basketball, nimbly dribbled around the other campers. He formed strong friendships, including with Vandervelde, a fellow-Southerner. He noticed that Vandervelde and other top students—among them, the future mathematician and writer Jordan Ellenberg—appeared enthralled with pondering abstract numerical concepts and questions for their own sakes. Rusczyk realized that, for him, the appeal of math lay more in competition and camaraderie.

Rusczyk didn’t make the I.M.O. team; later he learned that a few other students were also struggling. The next summer, he attended the boot camp again, this time in Annapolis, and was still frequently perplexed. Nevertheless, he kept studying; in his senior year of high school, he began working through some mathematical proofs, attaining a more genuine grasp of the concepts. He graduated as valedictorian, was a winner of the U.S.A. Mathematical Olympiad—at that time, eight medals were awarded each year—and returned to the boot camp for a third summer. Although he didn’t qualify for the I.M.O. team that year, either—Vandervelde and Ellenberg did—he was picked as an alternate. He left the camp early after falling ill, ranked as one of the top eight high-school math students in the nation.

Rusczyk went to Princeton, famed for its powerhouse math department. But he was burned out. The boot camps had left him certain that he lacked the creativity to solve the great abstract mysteries of theoretical mathematics. (Paul Zeitz, an emeritus math professor at the University of San Francisco, told me that Rusczyk may have been too hasty in reaching this conclusion: performance in math contests, Zeitz said, has little to do with becoming a superb mathematician.) Rusczyk also doubted that he possessed the patience to devote a lifetime to math research. He decided to major in chemical engineering.

And yet he wasn’t quite ready to leave the math-contest world behind. Soon afterward, for fun, Rusczyk, Vandervelde, and Sandor Lehoczky, a younger Olympiad boot camper, created their own mail-in math contest. They called it the Mandelbrot Competition, named after Benoit Mandelbrot, the father of fractals. The trio ran into an issue: they found that the contest problems they came up with were too hard for the participants. Rusczyk discussed the problem with Lehoczky, who was also at Princeton. They concluded that opportunities to learn advanced math were scarce and unevenly distributed. Many young math enthusiasts didn’t know about competitions and élite summer programs; looking back at their Olympiad boot camp experiences, the pair saw that, although some of the mathletes were unquestionably smarter, others simply had earlier exposure to complex math, or access to university mathematicians, or had attended special schools with a high-octane math-team culture. “We should write a book,” Lehoczky declared; it could help democratize advanced math. The two went on to self-publish a two-volume textbook titled “ The Art of Problem Solving .” The book taught “not facts , but approaches ,” they wrote. “If you find yourself memorizing formulas, you are missing the point.”

In the fall of 1993, Rusczyk—newly married to Vanessa—started a Ph.D. in chemical engineering at Stanford. But research still struck him as unappealing. He dropped out after eight weeks. Meanwhile, orders for the math textbook were trickling in. He drove to local schools, hawking the book and hunting for a job as a math teacher. A small private high school hired him, but it wasn’t the right fit, either: he liked teaching, but it was tough to win over the students who abhorred math. Rusczyk figured that he could reach a thousand keen math students a year with the textbook. That summer, he quit the teaching job, too.

In the mid-nineties, Wall Street was emerging as a place where mathematical minds could excel. Rusczyk was recruited for a job at the hedge fund D. E. Shaw; during his interview, he ran into two math-competition geeks he knew. He enjoyed his time trading bonds, but still wanted to build something of his own. After the markets went sideways in 1998, he quit. The following year, he and Vanessa relocated to San Diego, where they bought a fixer-upper; the house was surrounded by national forest and came with three donkeys. For a while, the couple coasted, repairing the house and planting a garden. They became avid hikers. “If I let him choose the hike, it’s always whatever is the highest, whatever is the longest,” Vanessa told me. One of his hobbies was working on old Math Olympiad problems, which could leave him obsessed and cranky until he solved them. The Internet was still new; Rusczyk did some online math tutoring and began thinking about the possibilities.

In 2003, when he was thirty-one, Rusczyk launched artofproblemsolving.com . He used off-the-shelf forum software to set up a community message board and led interactive classes based on his and Lehoczky’s books. Word spread, and young math brainiacs from around the world joined the forum, sharing nerdy puns, posting intriguing problems, and spurring one another along. Yufei Zhao, an early community member from Canada who competed in the I.M.O. three times and is now a math professor at the Massachusetts Institute of Technology, recalled his routine after getting home from high school: “Logging onto this forum was the first thing I did,” he said.

In the twenty years from 1995 to 2014, teams from the U.S. never managed to rank first at the I.M.O. But since 2015 the U.S. has claimed four first-place victories there—an outcome partly attributable to AoPS. Many variables played a role in those successes—including other math enrichment programs and the tutelage of lead coach Po-Shen Loh—but all the members of those winning U.S. teams were AoPS’s students. They were among the first generation to grow up with access to its curriculum. In learning mathematics, just as with studying piano or playing tennis, the earlier that talented individuals start training, the more they may be able to attain. In Rusczyk’s view, this isn’t just a matter of acquiring mathematical knowledge. The pervasive stereotype of children who are labelled as “geniuses” or “gifted” at math assumes that their brilliance requires little effort; by that definition, a genius shouldn’t struggle to learn. (Rusczyk and many other math educators aren’t fans of those labels.) Rusczyk’s boot camp experiences, however, had prepared him for confronting tough, unfamiliar problems of any kind. By normalizing struggle and failure from an earlier age, AoPS was designed to show math prodigies that it was O.K. to stumble and grow.

When COVID-19 struck , AoPS, working pro bono, built a web platform to host the U.S.A. Mathematical Olympiad and other contests. In lieu of the MathCounts national finals, Chandler and her colleagues unofficially offered their 2020 state competition exam on the AoPS site. The day after the test, Rusczyk and David Patrick, a former math professor who is an AoPS curriculum director, reviewed some of the questions in an AoPS chat room before an audience of more than three thousand online students. Rusczyk moderated the chat from two large monitors at his standing desk at work; the walls around him displayed a letter from Benoit Mandelbrot and two delicately rendered oil paintings, by Vanessa, of white manzanita blossoms and red Indian paintbrush. Typing on his keyboard, he walked through the first problem, about an equilateral triangle. Each time he posted a question, a wave of replies came back; he grinned as the students chimed in. “They’re fast, and they all want to be first,” he told me. While discussing a subsequent problem, he laughed at a student’s message: “I got it before you did, Richard!”

While Patrick reviewed the next set of problems, Rusczyk sipped water from a stainless steel mug. I asked whether he had been like these kids.

“Honestly, we’re building stuff for the thirteen-year-old version of ourselves,” he said. “It turns out these kids are a lot like us. They find the same things neat. They find the same things beautiful.”

Many AoPS students learn from one another at the same time as they learn from Rusczyk and his team. Olivia, a precocious twelve-year-old who lives in the rural town of La Grande, Oregon, was able to intuit basic algebra concepts by age eight; last July, she began her first online course with AoPS, in algebra. At the initial weekly class session, the teacher posted the first problem to the chat room, and Olivia, unaccustomed to the text-chat format, copied it down with a pencil. When she glanced back up, other pupils had already submitted their answers. Their speed stunned her. “You could see this panic,” her mother, Angela D’Antonio, recalled. But Olivia soon became a frequent visitor to the online message board to work with other students on hard “challenge problems.” (The other kids were situated in Toronto, India, and Singapore, among other places.) She quickly became one of the first to answer problems during class. Olivia has “just grown by leaps and bounds,” D’Antonio said, and not just in math; on the AoPS boards, Olivia—who is usually shy—has discovered friends with whom she can talk about Dungeons & Dragons and cryptography.

AoPS’s paid resources aren’t cheap. An online high-school-level course with a textbook can cost more than six hundred dollars; the elementary-school-level Beast Academy print books run about a hundred and twenty dollars per set, and a subscription to the accompanying online platform costs ninety-six dollars a year. For much of the past twenty years, U.S. public school systems have mainly focussed on raising the academic proficiency of the weakest students; the families of math overachievers were forced to turn, when they could, to private enrichment programs—from math circles and summer camps to AoPS and newer Web sites, such as Brilliant and Expii. Still, around seventy public school districts, from Albuquerque, New Mexico, to Mankato, Minnesota, now buy AoPS materials for their advanced elementary-school students—a move accelerated by the pandemic.

Meanwhile, since 2011, the nonprofit that Rusczyk founded, the Art of Problem Solving Initiative, has supported a residential summer camp program for mathematically talented middle-school kids from low-income and historically marginalized communities. The camp is now known as Bridge to Enter Advanced Mathematics ( BEAM ) Summer Away, and is held in New York and Los Angeles. Led by a math educator named Daniel Zaharopol, it has provided more than six hundred students with long-term mentoring and support. This year, BEAM is also giving selected fifth-graders at around ten partnering schools across the U.S. free access to AoPS curricula and other supporting resources. In a separate experiment led by AoPS, this fall more than three hundred bright, math-curious pupils from underserved areas of Atlanta, Detroit, San Juan, and elsewhere have been participating in live-streamed AoPS classes for free.

In mathematics, a concept known as the random walk describes a meandering path that is determined, at each step, by a random process, such as tossing a coin. Say you’re standing at a street corner on Fifth Avenue and you flip two coins. If it’s two heads, you walk one block north; if it’s one head and one tail, you walk one block east, and so on. At each intersection, you repeat the process. According to a century-old theorem by a Hungarian mathematician named George Pólya, if you keep up this sort of exercise, after many, many coin flips, the probability of winding up where you started approaches a hundred per cent.

Rusczyk learned about random-walk theory as a teen-ager at a math-tournament lecture; Lehoczky was there, too. Later, while visiting an amusement park, they began flipping coins to decide where to go or what to do. Should they climb over a fence or take the long way around? Have hot dogs or pizza for lunch? The game became a lifelong tradition. Once, coin-flipping their way around Manhattan, the two friends wound up at a Tibetan restaurant; they never would have chosen it, but it turned out to be good.

Our major life choices aren’t purely random, of course, but they can feel like leaps of faith. In some ways, random-walk theory seems like an apt metaphor for Rusczyk’s peregrinations into and away from math. “I got pulled back to the origin,” he said. Creating AoPS was a return to his math-competition roots.

And yet he doesn’t see himself, or his company, as teaching mathematics. Its mission is “to discover, inspire, and train the great problem solvers of the next generation”; its real impact, Rusczyk said, might be “revealing to the kids themselves how much they can do” at something they love. Rusczyk hopes to expand Beast Academy—which is currently used with gifted kids in grades 2-5—into a full K-6 curriculum that public elementary schools can adopt for regular math classes. It would be a further step toward democratizing advanced learning. He figures that some kids are unaware that they are potential math whizzes. He wants to help students “find themselves” earlier than seventh grade, when he found himself. He hopes that the curriculum might help guide more young brainiacs toward lives in math, or outside of it—in science, finance, or Silicon Valley.

One Sunday, I Zoomed with Rusczyk while he and Vanessa worked a morning shift in the AoPS warehouse. They’d woken up early and sipped coffee in their garden as dawn broke, then unloaded hay to feed their donkeys. Rusczyk had driven his dark gray Tesla to the AoPS office, where he’d done a quick sanitizing wipe-down of surfaces in the second-floor break room and bathrooms. He printed out book-order invoices in the finance office, then ran down to unlock the front door for Vanessa, who had driven separately. A petite brunette with frizzy tresses, she walked in wearing flip-flops, shorts, and an olive-green tank top; Rusczyk, who was dressed in green cargo shorts and a red T-shirt, looked serious and a bit tired. His days were crammed with e-mails and video and phone meetings—the workaday business of shepherding his expanding firm in the middle of a pandemic.

In the shipping room, he grabbed Beast Academy books, which were stocked on metal shelves, and laid them atop a growing tower of crisscrossed book orders on a red plastic cart. Each time the cart filled up, he transferred the books to an array of tables. It was work he actually enjoyed, he told me. The textbooks were a direct link to the enthusiastic math learners who would soon be engrossed in their pages.

“Feels like we’re doing something real,” Vanessa said, working at her own book cart.

“Yeah—doing something real,” Rusczyk said. A couple thousand books would be boxed and shipped the next day.

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About the Art of Problem Solving Initiative, Inc.

Staff members.

Daniel Zaharopol

Chief executive officer.

Dan Zaharopol is the Founder of Bridge to Enter Advanced Mathematics (BEAM) , which works to create a realistic pathway for underserved middle school students to become scientists, mathematicians, engineers, and programmers. BEAM is a project of The Art of Problem Solving Initiative.

Previously, Dan was the Co-Founder and CEO of Learning Unlimited , an organization that helps college students create educational programs on their campuses. He also serves on the boards of directors of the Mathematics Foundation of America , which runs Canada/USA Mathcamp , and the New York Math Circle .

Dan graduated from MIT in 2004 where he studied mathematics, and earned dual master's degrees in mathematics (focusing on Algebraic Topology) and in mathematics education from the University of Illinois. He blogs at Consider Learning .

To view other staff members of the organization , please visit BEAM's website which has a full staff listing .

Board Members

Richard Rusczyk

President, board of directors.

Richard Rusczyk created the company Art of Problem Solving in 2003 to create interactive educational opportunities for avid math students, and expanded this work by founding the nonprofit Art of Problem Solving Initiative in 2004. He is one of the co-authors of the Art of Problem Solving classic textbooks, author of Art of Problem Solving's Introduction to Algebra, Introduction to Geometry, and Precalculus textbooks, co-author of Art of Problem Solving's Intermediate Algebra and Prealgebra, one of the co-creators of the Mandelbrot Competition , and a past Director of the USA Mathematical Talent Search . He was a participant in National MATHCOUNTS , a three-time participant in the Math Olympiad Summer Program , and a USA Mathematical Olympiad winner (1989). He graduated from Princeton University in 1993, and worked as a bond trader for D.E. Shaw & Company for four years. AoPS marks Richard's return to his vocation -- educating motivated students.

Darryl Hill, Ph.D.

Secretary, board of directors.

Darryl Hill is a senior program officer for measurement, learning and evaluation at the Bill & Melinda Gates Foundation. Previously he held roles in several school districts around the country, including as Assistant Superintendent of School Accountability and Governance for the Fulton County Schools in Atlanta, GA. He has a Ed.D. in Education Policy, Leadership, and Instructional Practice from Harvard University. Prior to attending Harvard, he built an outstanding mathematics team at Rickards High School in Florida, earning Mu Alpha Theta's most dedicated sponsor award.

Nanayaa Dadson

Treasurer, board of dirctors.

Nanayaa Dadson is a Managing Director at JPMorgan Chase & Co where she has worked since 1997. She was born and raised in Ghana, attended high school in the United Kingdom and moved to the United States to attend college. She holds a PhD, M.S. and B.S. in Engineering Sciences from Harvard University.

Member, Board of Directors; Chair, New York City Board

Ken Baron is currently a Managing Director and a Senior Research Scientist at Two Sigma Investments, where he has worked since 2008. Ken has been in the field of finance and investment management for over 25 years. He was born and raised in New York City attending NYC public schools, including Stuyvesant High School. Ken completed an undergraduate degree in Mathematics from the University of Chicago and a PhD in Statistics from Stanford University. He is the co-author of Parimutuel Applications in Finance, a mathematical finance book. Ken has been a volunteer with BEAM since 2017, including teaching an enrichment class at BEAM titled "Money and Investing".

Edray Goins

Member, board of directors; chair, los angeles board.

Edray Herber Goins is Professor of Mathematics at Pomona College. He has worked as a researcher at both Harvard and the National Security Agency; and has taught at both Caltech and Purdue. Professor Goins has published over 20 journal articles in areas such as applied mathematics, graph theory, number theory, and representation theory; and on topics such as Diophantine equations, elliptic curves, and African Americans in mathematics. He has acted as a referee for 20 different journals in mathematics, served on dozens of panels for the National Science Foundation, and has given more than 150 invited addresses on his research.

Jeff Hoffman

Member, board of directors.

Jeff Hoffman is a Principal Analytical Lead at Google based out of New York City. Prior to Google, he worked in analytically oriented roles at Amazon and Target. Jeff has a MBA from the Kellogg School of Management at Northwestern University and a BA in Mathematics and Economics from Washington University in St. Louis. He was inspired to pursue higher learning in mathematics at a young age and has worked as a math tutor since he was in middle school.

Kristin Kearns-Jordan

Kristin Kearns-Jordan is Chief Executive Officer of the Urban Assembly (UA), a network of 21 small public middle and high schools serving primarily low-income New Yorkers. Before coming to the UA she served as Executive Director of the Tortora Sillcox Foundation, a foundation advancing educational equity and excellence in New York City, from 2007 - 2016. From 2000 to 2007, she was the founder and director of the Bronx Preparatory Charter School, a classical, college preparatory middle and high school in the South Bronx. She became the founding executive director of the School Choice Scholarships Foundation in 1997 after beginning her career in education at the Student/Sponsor Partnership. She has extensive nonprofit governance experience, including board roles at the Student/Sponsor Partners, the READ Foundation, the Bronx Preparatory Charter School, the Urban Assembly (before becoming CEO), and the Cathedral School of St. John the Divine (for the last three years as President). She is a graduate of Phillips Exeter Academy and Brown University.

Kiran Kedlaya, Ph.D.

Kiran Kedlaya is Professor of Mathematics at the University of California, San Diego. He has served as a member of the USA International Mathematics Olympiad team, a deputy leader of the USA IMO team, a member of the IMO 2001 executive committee, a member of the USA Mathematical Olympiad committee, and a co-author of a book on the Putnam competition.

Sandor Lehoczky

Sandor Lehoczky works for Jane Street Capital, a financial firm in New York City. He co-authored the Art of Problem Solving with Richard Rusczyk and graduated from Princeton in 1994.

Susan Schwartz Wildstrom

Susan Schwartz Wildstrom is a mathematics teacher at Walt Whitman High Schoolin Bethesda, MD. She is involved in many national mathematical associations, including the American Mathematical Society and the Mathematical Association of America . She is also involved with the Committee on the American Mathematics Competitions and chair of the Committee on Local and Regional Competitions.

• State Policy

Straight Up Conversation: Math Guru Richard Rusczyk

Frederick Hess

Richard Rusczyk is the founder of the Art of Problem Solving (AoPS), a math curriculum and online learning community that supports students who excel in math. In the early 1990s, Richard started AoPS as a book series; it has grown into a 300,000-member online community with classes, video lessons, and an adaptive learning system. AoPS is also the go-to trainer for America’s Math Olympiad participants. I recently had a chance to chat with Richard about AoPS, how it works, and the effort to extend its reach to new kids.

Richard Rusczyk : AoPS develops educational resources for eager math students, including textbooks, an online school, in-person learning centers, and a constellation of online applications. We build the tools we wish we’d had when we were students.

RH : When did AoPS begin? Where did the idea come from, and how did you wind up getting started?

RR : As I was finishing college, back in 1993 to ’94, I co-wrote a two-volume series,  The Art of Problem Solving , for students preparing for math competitions. These texts are probably still the most widely used math contest prep books. I left grad school after a couple months because I wanted to teach high school. Then I learned how hard teaching is! It’s even harder when you’re 22 and look 13. I left teaching after a semester and traded bonds for a while. Then the internet came along, and I realized I could build a school online and let selection bias draw the students I could best serve: those who thirst for a greater challenge than they’re finding in their classrooms. We launched  artofproblemsolving.com  in 2003 and expanded from contest preparation to a full math curriculum.

RH : When a student participates in AoPS, what does that involve?

RR : It depends on which slice of AoPS the student is using. Students learn in many different ways, so we deliver our materials through a variety of media:  textbooks , an  adaptive learning system ,  videos , and an  online community . We weave these together in our  online school , though each can be used individually—and several are free. In the online school—which most students take in addition to their regular math classes—students meet weekly for a 75- to 120-minute conversation with instructors. Between classes, they read textbooks, watch videos, collaborate with instructors and other students in our online community, and tackle sets of difficult problems. Some of the problems require writing complete solutions on which students receive feedback on the accuracy and presentation of their work. Most students in the online school are taking math classes in their regular school in addition to ours; however, some students are able to replace to their school classes with ours. Our school is accredited, and we can provide grades and a transcript to students who need them.

RH : This is really striking. We hear a lot about gamification, video elements, and interactive technology, but it sounds like what you’re describing is old school, and then some. Is that right? Does this really work? And do students actually enjoy it?

RR : We have those modern elements—gamification, video, and our real-time classes are  extremely interactive because all the students can “talk” at any time. But the classroom is text-and-image only; you have to experience it to appreciate why we don’t use video and audio. The key part of the instruction comes from students solving hard problems themselves, which is the main old-school component. The online school works for some students. Nothing works for all students, so we deliver our material through multiple avenues. But many students keep coming back far past the age where they can say “no” to their parents. One mother recently told me that when she needs to get her son’s attention, she takes his AoPS  Precalculus  book away from him, and parents proudly send us pictures of their children’s creations celebrating their favorite  Beast Academy  characters from our elementary school curriculum.

RH : How do students get involved in AoPS?

RR : They or their parents find us. We have strong word-of-mouth in the communities we serve. If you have a math-focused child and start asking around online for suggestions for her, you’ll hear about us.

RH : How many students do you serve, and who are they?

RR : This year, we expect over 15,000 in our online school and over 3,000 in our in-person learning centers. Our online community has over 300,000 members, about half of whom are international. Our online learning system for middle school is nearing 100 million trials. While most students in our earliest classes are 10 or 11, we have some as young as 7 or 8. That age will get younger this summer when we launch  Beast Academy Online , our online learning system for elementary school. The students range through high school.

Most of our students have high interest and ability in math. At the very high end of the ability scale, the six members of the US team that won the 2015 International Math Olympiad—for the first time in over two decades—collectively enrolled in over 40 AoPS classes. We don’t collect data on income or race, but anecdotally speaking, many of our students have parents in math- or science-related fields, and probably most are in the top half of the income distribution. Many of our students’ parents are immigrants who can credit their own interest and ability in mathematics with allowing them to come to this country.

RH : Is there any alignment to curriculum or standards throughout AoPS? Can what students are doing on your platform help them in their math courses?

RR : While we reviewed various standards, we didn’t adhere precisely to any of them. The standards, like most of our K-12 education system, by necessity must target mathematical literacy, not mastery—they ensure that students reach a certain baseline level of understanding. AoPS’ target is different, it’s that of universities: the mastery required to be a STEM professional. Students who work through our curriculum usually find themselves extremely well-prepared for their regular school classes. They’re also far less likely to be shell-shocked when they take math or science classes in college, which is where we first see the gap between literacy- and mastery-focused educations as legions of students leave STEM-related majors. Those students may have notched high scores on their AP exams, but they hadn’t ever operated at the level they were asked to in their first university math and science classes, or at the level they’d need for internationally competitive careers.

RH : Can you talk a bit about the teaching side of all this? Who are the instructors? How do you find them and train them? How much time to they give to this? And how much are they paid?

RR : Some of our  instructors  are university professors or high-school teachers. Some are grad students at schools like MIT, Harvard, and Stanford. Some are professionals in software development or the financial industry. Some are on a break from their careers as they raise families. Teaching at AoPS allows them to share their love of math with eager students. We provide the students—we’ve essentially created a two-sided market where the teachers and students draw each other. Each course requires 3 to 5 hours per week of the teacher’s time, with their pay varying by course and the range of roles they fill for their courses.

RH : And what’s the price to enroll in AoPS?

RR : Many of our online resources are free, but the online school has per-course tuition. Each course runs 12 to 25 weeks, and costs 20 to 25 dollars per week. This summer we’ll launch a  subscription-based service for elementary school , which will be around 100 dollars a year, and considerably less for those purchasing the elementary school books at the same time.

RH : What do we know about how well AoPS works? What kind of evidence do you look at when assessing your impact?

RR : All of our evidence is anecdotal. Performing a randomized controlled trial would be pretty difficult for us. Probably the strongest evidence is our continued growth, particularly considering our limited focus on marketing to date. We can point to contest results, but most of our students are not coming to us for contests. As a sign of our reach among top students, we recently learned that the 2018 MIT admit class circulated a spreadsheet to share social media usernames. The spreadsheet had 5 columns for each student: Facebook, Instagram, Snapchat, Twitter, and AoPS.

RH : Now, I understand you all are in the midst of efforts to expand the population that AoPS is serving. Can you talk a little about what that involves and how it’s going?

RR : We started a non-profit organization, the AoPS Initiative, whose  Bridge to Enter Advanced Mathematics  (BEAM) program serves high-potential students in underserved communities in New York City and Los Angeles. BEAM starts with middle-school summer programs and provides support during the school year through high school. Even though BEAM has been around for 7 years, it’s still too early to tell how well we’re achieving our goal of producing more STEM professionals from underserved communities. Some of our students have earned admissions to New York’s highly selective math and science schools, which is an early indicator of progress.

Meanwhile, our company invited 40 third-graders from similar communities into our  AoPS Academy learning center in Gaithersburg, Maryland , this year through a  STEM Talent Pipeline of the Montgomery Blair High School Magnet Foundation. We’re only in the first year of this Academy program. The students on average are holding their own, and some are excelling, but it’s way too early to claim success.

RH : What was the impetus for this effort?

RR : I believe the gap between the top well-connected students and the top disconnected students has grown tremendously in the last ten to 15 years. Moreover, AoPS bears some responsibility for the growth of that gap: The connected students have leapt due to programs like ours. This realization spurred the start of BEAM. However, we have found that while BEAM’s middle-school students are just as dialed-in and excited about math as the students we work with online, they are years behind the AoPS online students in their mathematical understanding. We can close that gap somewhat when starting in middle school, but we’re looking for ways to reach the students earlier. When the Montgomery Blair High School Magnet Foundation learned of our AoPS Academy plans in their area, they asked to be our pilot program in that effort.

The AoPS Academy STEM Talent Pipeline is supported largely by AoPS with some support from the Montgomery Blair HS Magnet Foundation. The AoPS Initiative’s BEAM programs are supported by a variety individual and institutional donors. The  Jack Kent Cooke Foundation  is the largest BEAM supporter and is responsible for our expansion to Los Angeles this year.

RH : And final question: In more than two decades of doing this, what are a couple things you’ve learned along the way that surprised, frustrated, or delighted you?

RR : We’re coming to appreciate the limits of online education. As a “dot-com” guy, I’m supposed to say that online education will be revolutionary for everyone. I don’t think that’s true. It works fantastically for some students, but for many students, education is a fundamentally human problem, which will require human solutions. This is why we’ve started our  AoPS Academy  learning centers, and in coming years will explore partnerships with schools to learn how best to deploy our work in a traditional school settings. Meanwhile, for those students for whom online education shines, we are starting to partner with schools and school systems to provide avenues to allow appropriate students to take their math classes from us rather than in a traditional classroom.

— Frederick Hess

Frederick Hess is director of education policy studies at AEI and an executive editor at Education Next.

This post originally appeared on  Rick Hess Straight Up.

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Richard Rusczyk - Art of Problem Solving: Building the Next Generation of Problem Solvers - 413

Richard Rusczyk - Art of Problem Solving: Building the Next Generation of Problem Solvers. This is episode 413 of Teaching Learning Leading K12, an audio podcast. Richard Rusczyk is the founder and CEO of Art of Problem Solving (AoPS) Inc. (as well as ...

Richard Rusczyk - Art of Problem Solving: Building the Next Generation of Problem Solvers. This is episode 413 of Teaching Learning Leading K12, an audio podcast.

Richard Rusczyk is the founder and CEO of Art of Problem Solving (AoPS) Inc. (as well as the website, which serves as a mathematics forum and place to hold online classes) and a co-author of the Art of Problem Solving textbooks. 

Richard was a national MATHCOUNTS participant in 1985, and he won the USA Math Olympiad (USAMO) in 1989. He is one of the co-creators of the Mandelbrot Competition, and the director of the USA Mathematical Talent Search (USAMTS). He also founded the San Diego Math Circle. Every month, Rusczyk works on the MATHCOUNTS website to create Mathcounts Minis, where he explains problems and concepts.

Richard studied chemical engineering at Princeton University and graduated in 1993. He served on the board for ARML (American Regions Mathematics League) and managed the Western ARML site at one point.

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Connect & Learn More:

https://en.wikipedia.org/wiki/Richard_Rusczyk

https://artofproblemsolving.com/

https://www.pinterest.com/artofproblemsolving/pins/

https://twitter.com/AoPSNews

https://www.facebook.com/artofproblemsolving

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The Math Revolution

The number of American teens who excel at advanced math has surged. Why?

O n a sultry evening last July, a tall, soft-spoken 17-year-old named David Stoner and nearly 600 other math whizzes from all over the world sat huddled in small groups around wicker bistro tables, talking in low voices and obsessively refreshing the browsers on their laptops. The air in the cavernous lobby of the Lotus Hotel Pang Suan Kaew in Chiang Mai, Thailand, was humid, recalls Stoner, whose light South Carolina accent warms his carefully chosen words. The tension in the room made it seem especially heavy, like the atmosphere at a high-stakes poker tournament.

Stoner and five teammates were representing the United States in the 56th International Mathematical Olympiad. They figured they’d done pretty well over the two days of competition. God knows, they’d trained hard. Stoner, like his teammates, had endured a grueling regime for more than a year—practicing tricky problems over breakfast before school and taking on more problems late into the evening after he completed the homework for his college-level math classes. Sometimes, he sketched out proofs on the large dry-erase board his dad had installed in his bedroom. Most nights, he put himself to sleep reading books like New Problems in Euclidean Geometry and An Introduction to Diophantine Equations .

Still, it was hard to know how his team had stacked up against those from the perennial powers China, Russia, and South Korea. “I mean, the gold? Did we do well enough to get the gold?” he said. “At that moment, it was hard to say.” Suddenly, there was a shout from a team across the lobby, then a collective intake of breath as the Olympians surged closer to their laptops. As Stoner tried to absorb what he saw on his own computer screen, the noise level in the lobby grew from a buzz to a cheer. Then one of his team members gave a whoop that ended in the chant “U.S.A.! U.S.A.!,” and the smattering of applause from the other Olympians grew more robust, and finally thunderous. Beaming, one of Stoner’s teammates pulled a small American flag out of his backpack and began waving it. Stoner was grinning. For the first time in 21 years, the United States team had won first place. Speaking last fall from his dorm at Harvard, where he is now a freshman, Stoner recalled his team’s triumph with quiet satisfaction. “It was a really great moment. Really great. Especially if you love math.”

It also wasn’t an aberration. You wouldn’t see it in most classrooms, you wouldn’t know it by looking at slumping national test-score averages, but a cadre of American teenagers are reaching world-class heights in math—more of them, more regularly, than ever before. The phenomenon extends well beyond the handful of hopefuls for the Math Olympiad. The students are being produced by a new pedagogical ecosystem—almost entirely extracurricular—that has developed online and in the country’s rich coastal cities and tech meccas. In these places, accelerated students are learning more and learning faster than they were 10 years ago—tackling more-complex material than many people in the advanced-math community had thought possible. “The bench of American teens who can do world-class math,” says Po-Shen Loh, the head coach of the U.S. team, “is significantly wider and stronger than it used to be.”

The change is palpable at the most competitive colleges. At a time when calls for a kind of academic disarmament have begun echoing through affluent communities around the nation, a faction of students are moving in exactly the opposite direction. “More freshmen arrive at elite colleges with exposure to math topics well outside of what has traditionally been taught in American high schools,” says Loh. “For American students who have an appetite to learn math at a high level,” says Paul Zeitz, a mathematics professor at the University of San Francisco, “something very big is happening. It’s very dramatic and it’s happening very fast.”

In the past, a small number of high-school students might have attended rigorous and highly selective national summer math camps like Hampshire College’s Summer Studies in Mathematics, in Massachusetts, or the Ross Mathematics Program at Ohio State, both of which have been around for decades. But lately, dozens of new math-enrichment camps with names like MathPath, AwesomeMath, MathILy, Idea Math, sparc , Math Zoom, and Epsilon Camp have popped up, opening the gates more widely to kids who have aptitude and enthusiasm for math, but aren’t necessarily prodigies. In Silicon Valley and the Bay Area, math circles—some run by tiny nonprofit organizations or a single professor, and offering small groups of middle- and high-school math buffs a chance to tackle problems under the guidance of graduate students, teachers, professors, engineers, and software designers—now have long wait lists. In New York City last fall, it was easier to get a ticket to the hit musical Hamilton than to enroll your child in certain math circles. Some circles in the 350-student New York Math Circle program run out of New York University filled up in about five hours. *

Math competitions are growing in number and popularity too. The number of U.S. participants in Math Kangaroo, an international contest for first- through 12th-graders that came to American shores in 1998, grew from 2,576 in 2009 to 21,059 in 2015. More than 10,000 middle- and high-school students haunt chat rooms, buy textbooks, and take classes on the advanced-math learners’ Web site the Art of Problem Solving. This fall, the Art of Problem Solving’s founder, Richard Rusczyk, a former Math Olympian who left his job in finance 18 years ago, will open two brick-and-mortar centers in the Raleigh, North Carolina, and Rockville, Maryland, areas, with a focus on advanced math. An online program for elementary-school students will follow. Last fall, Zeitz—along with another math professor, a teacher, and a private-equity manager—opened the Proof School, a small independent secondary school in San Francisco similarly centered on amped-up math. Before the inaugural school year even began, school officials were fielding inquiries from parents wondering when a Proof School would be opening on the East Coast and whether they could get their child on a waiting list. “The appetite among families for this kind of math instruction,” Rusczyk says, “seems boundless.”

Parents of students in the accelerated-math community, many of whom make their living in stem fields, have enrolled their children in one or more of these programs to supplement or replace what they see as the shallow and often confused math instruction offered by public schools, especially during the late-elementary and middle-school years. They have reason to do so. According to the Bureau of Labor Statistics, much of the growth in our domestic economy will come from stem -related jobs, some of which are extremely well paid. College freshmen have heard that message; the number who say they want to major in a stem field is up. But attrition rates are very high: Between 2003 and 2009, 48 percent of students pursuing a bachelor’s degree in a stem field switched to another major or dropped out—many found they simply didn’t have the quantitative background they needed to succeed.

The roots of this failure can usually be traced back to second or third grade, says Inessa Rifkin, a co-founder of the Russian School of Mathematics, which this year enrolled 17,500 students in after-school and weekend math academies in 31 locations around the United States. In those grades, many education experts lament, instruction—even at the best schools—is provided by poorly trained teachers who are themselves uncomfortable with math. In 1997, Rifkin, who once worked as a mechanical engineer in the Soviet Union, saw this firsthand. Her children, who attended public school in affluent Newton, Massachusetts, were being taught to solve problems by memorizing rules and then following them like steps in a recipe, without understanding the bigger picture. “I’d look over their homework, and what I was seeing, it didn’t look like they were being taught math,” recalls Rifkin, who speaks emphatically, with a heavy Russian accent. “I’d say to my children, ‘Forget the rules! Just think!’ And they’d say, ‘That’s not how they teach it here. That’s not what the teacher wants us to do.’ ” That year, she and Irina Khavinson, a gifted math teacher she knew, founded the Russian School around her dining-room table.

Teachers at the Russian School help students achieve fluency in arithmetic, the fundamentals of algebra and geometry, and later, higher-order math. At every level, and with increasing intensity as they get older, students are required to think their way through logic problems that can be resolved only with creative use of the math they’ve learned.

One chilly December Sunday at a school in Bensonhurst, Brooklyn, seven second-graders filed past a glossy poster showing Russian School students who had recently medaled in math competitions. They settled into their seats as their teacher, Irine Rober, showed them conceptual examples of addition and subtraction by ripping paper in half and by adding weights to each side of a scale to balance it. Simple stuff. Then the students took turns coming to the blackboard to explain how they’d used addition and subtraction to solve an equation for x , which required a bit more thinking. After a brief break, Rober asked each child to come up with a narrative that explained what the expression 49+(18–3) means. The children invented stories involving fruit, the shedding and growing of teeth, and, to the amusement of all, toilet monsters.

Although the students were laughing, there was nothing superficial or perfunctory about their explanations. Rober and her class listened carefully to the logic embedded in each of the stories. When one young boy, Shawn, got tangled up in his reasoning, Rober was quick to point to the exact spot where his thinking went awry (in the enthusiastic telling of a tale about farmers, bountiful harvests, and apple-eating varmints, Shawn began by talking about what happened to the 49 apples, when the order of operations demanded that he first describe a reduction in the 18 apples). Rober gently set him straight. Later, the children told stories about 49–(18+3) and 49–(18-3) too.

Rifkin trains her teachers to expect challenging questions from students at every level, even from pupils as young as 5, so lessons toggle back and forth between the obvious and the mind-bendingly abstract. “The youngest ones, very naturally, their minds see math differently,” she told me. “It is common that they can ask simple questions and then, in the next minute, a very complicated one. But if the teacher doesn’t know enough mathematics, she will answer the simple question and shut down the other, more difficult one. We want children to ask difficult questions, to engage so it is not boring, to be able to do algebra at an early age, sure, but also to see it for what it is: a tool for critical thinking. If their teachers can’t help them do this, well—” Rifkin searched for the word that expressed her level of dismay. “It is a betrayal.”

F or a subject that has been around almost as long as civilization itself, there remains a surprising degree of contention among experts about how best to teach math. Fiery battles have been waged for decades over what gets taught, in what order, why, and how. Broadly speaking, there have been two opposing camps. On one side are those who favor conceptual knowledge—understanding how math relates to the world—over rote memorization and what they call “drill and kill.” (Some well-respected math-instruction gurus say that memorizing anything in math is counterproductive and stifles the love of learning.) On the other side are those who say memorization of multiplication tables and the like is necessary for efficient computation. They say teaching students the rules and procedures that govern math forms the bedrock of good instruction and sophisticated mathematical thinking. They bristle at the phrase drill and kill and prefer to call it simply “practice.”

The Common Core State Standards Initiative walks a narrow path through that minefield, calling for teachers to place equal importance on “mathematical understanding” and “procedural skills.” It’s too early to know what effect the initiative will have. To be sure, though, most students today aren’t learning much math: Only 40 percent of fourth-graders and 33 percent of eighth-graders are considered at least “proficient.” On an internationally administered test in 2012, just 9 percent of 15-year-olds in the United States were rated “high scorers” in math, compared with 16 percent in Canada, 17 percent in Germany, 21 percent in Switzerland, 31 percent in South Korea, and 40 percent in Singapore.

The new outside-of-school math programs like the Russian School vary in their curricula and teaching methods, but they have key elements in common. Perhaps the most salient is the emphasis on teaching students to think about math conceptually and then use that conceptual knowledge as a tool to predict, explore, and explain the world around them. There is a dearth of rote learning and not much time spent applying a list of memorized formulas. Computational speed is not a virtue. (“Cram schools,” featuring a mechanistic, test-prep approach to learning math, have become common in some immigrant communities, and plenty of tutors of affluent children use this approach as well, but it is the opposite of what’s taught in this new type of accelerated-learning program.) To keep pace with their classmates, students quickly learn their math facts and formulas, but that is more a by-product than the point.

The pedagogical strategy at the heart of the classes is loosely referred to as “problem solving,” a pedestrian term that undersells just how different this approach to math can be. The problem-solving approach has long been a staple of math education in the countries of the former Soviet Union and at elite colleges such as MIT and Cal Tech. It works like this: Instructors present small clusters of students, usually grouped by ability, with a small number of open-ended, multifaceted situations that can be solved by using different approaches.

Here’s an example from the nascent math-and-science site Expii.com:

Imagine a rope that runs completely around the Earth’s equator, flat against the ground (assume the Earth is a perfect sphere, without any mountains or valleys). You cut the rope and tie in another piece of rope that is 710 inches long, or just under 60 feet. That increases the total length of the rope by a bit more than the length of a bus, or the height of a 5-story building. Now imagine that the rope is lifted at all points simultaneously, so that it floats above the Earth at the same height all along its length. What is the largest thing that could fit underneath the rope?

The options given are bacteria, a ladybug, a dog, Einstein, a giraffe, or a space shuttle. The instructor then coaches all the students as they reason their way through. Unlike most math classes, where teachers struggle to impart knowledge to students—who must passively absorb it and then regurgitate it on a test—problem-solving classes demand that the pupils execute the cognitive bench press: investigating, conjecturing, predicting, analyzing, and finally verifying their own mathematical strategy. The point is not to accurately execute algorithms, although there is, of course, a right answer (Einstein, in the problem above). Truly thinking the problem through—creatively applying what you know about math and puzzling out possible solutions—is more important. Sitting in a regular ninth-grade algebra class versus observing a middle-school problem-solving class is like watching kids get lectured on the basics of musical notation versus hearing them sing an aria from Tosca .

In my experience, a common emotion at New York Math Circle, at the Russian School, in the chat rooms of the Art of Problem Solving and similar Web site, is authentic excitement—among the students, but also among the teachers—about the subject itself. Even in the very early grades, instructors tend to be deeply knowledgeable and passionately engaged. “Many of them are working in the fields that use math—chemistry, meteorology, and engineering—and teach part-time,” Rifkin says. They are people who themselves find the subject approachable and deeply interesting, and they are encouraged to convey that.

But excitement aside, the pedagogy is very deliberate. At the Russian School, lessons are carefully structured and each teacher’s lesson plan is reviewed and revised by a mentor. Instructors watch videos of master teachers deftly helping to clear up students’ misunderstandings of particular concepts. Teachers gather by videoconference to critique one another’s instructional technique.

Many of these programs—especially the camps, competitions, and math circles—create a unique culture and a strong sense of belonging for students who have a zest for the subject but all the awkwardness and uneven development of the typical adolescent. “When I attended my first math competition,” at age 11, “I understood for the first time that my tribe was out there,” said David Stoner, who joined a math circle a year later, and soon thereafter became a habitué of the Art of Problem Solving. Freewheeling collaboration across age, gender, and geography is a baseline value. Although the accelerated-math community has historically been largely male, girls are getting involved in increasing numbers, and making their presence felt. Kids blow off steam by playing strategy board games like Dominion and Settlers of Catan, or “bug house” chess, a high-speed, multiboard variation of the old standby. Insider humor abounds. A typical T-shirt slogan: √-1 2 3 ∑ π … and it was delicious! (Translation: “I ate some pie …”) At the Math Olympiad Summer Program, a training ground for future Olympians, one of the acts in the talent show last June involved a group of youngsters developing computer code while holding a plank pose.

The students speak about career ambitions with a rare degree of assurance. Problem-solving for fun, they know, leads to problem-solving for profit. The link can be very direct: Some of the most recognizable companies in the tech industry regularly prospect, for instance, on Brilliant.org, an advanced-math-community Web site launched in San Francisco in 2012. “Money follows math” is a common refrain.

A lthough efforts are under way on many fronts to improve math education in public schools using some of the techniques found in these enriched classes, measurable gains in learning have proved elusive.

Nearly everyone in the accelerated-math community says that the push to cultivate sophisticated math minds needs to start early and encompass plenty of thoughtful, conceptual learning experiences in elementary and middle school. The proportion of American students who can do math at a very high level could be much larger than it is today. “Will they all learn it at the same rate? No, they will not,” says Loh, the U.S. math team’s head coach. “But I assure you that with the right instruction and steady effort, many, many more American students could get there.”

Students who show an inclination toward math need additional math opportunities—and a chance to be around other math enthusiasts—in the same way that a kid adept with a soccer ball might eventually need to join a traveling team. And earlier is better than later: The subject is relentlessly sequential and hierarchical. “If you wait until high school to attempt to produce accelerated math learners,” Loh told me, “the latecomers will find themselves missing too much foundational thinking and will struggle, with only four short years before college, to catch up.” These days, it is a rare student who can move from being “good at math” in a regular public high school to finding a place in the advanced-math community.

All of which creates a formidable barrier. Most middle-class parents might research sports programs and summer camps for their 8- and 9-year-old children, but would rarely think of supplemental math unless their kid is struggling. “You have to know about these programs, live in a neighborhood that has these resources, or at least know where to look,” says Sue Khim, a co-founder of Brilliant.org. And since many of the programs are private, they are well out of reach for the poor. (A semester in a math circle can cost about $300, a year at a Russian School up to $3,000, and four weeks in a residential math program perhaps twice that.) National achievement data reflect this access gap in math instruction all too clearly. The ratio of rich math whizzes to poor ones is 3 to 1 in South Korea and 3.7 to 1 in Canada, to take two representative developed countries. In the U.S., it is 8 to 1. And while the proportion of American students scoring at advanced levels in math is rising, those gains are almost entirely limited to the children of the highly educated, and largely exclude the children of the poor. By the end of high school, the percentage of low-income advanced-math learners rounds to zero.

To Daniel Zaharopol, the founder and executive director of Bridge to Enter Advanced Mathematics ( beam ), a nonprofit organization based in New York City, the short-term solution is logical. “We know that math ability is universal and interest in math is spread pretty much equally through the population,” he says, “and we see there are almost no low-income, high-performing math students. So we know that there are many, many students who have the potential for high achievement in math but who have not had opportunity to develop their math minds, simply because they were born to the wrong parents or in the wrong zip code. We want to find them.”

In an experiment that is being closely watched by educators and members of the advanced-math community, Zaharopol, who majored in math at MIT before getting a master’s in math and teaching math, spends each spring visiting middle schools in New York City that serve low-income kids. He is prospecting for students who, with the right instruction and some support, can take their place, if not at the International Math Olympiad, then at a less selective competition, and in a math circle, and eventually at a stem program at a competitive college.

Zaharopol doesn’t look for the best all-around students to admit to his program, which provides the kind of comprehensive support that wealthy math nerds get: a three-week residential math camp the summer before eighth grade, enhanced instruction after school, help with applying to math circles, and coaching for math competitions, as well as basic advice on high-school selection and college applications. Those who get perfect grades in math are interesting to him, but only to a point. “They don’t have to like school or even like math class,” he says. Instead, he is looking for kids with a confluence of specific abilities: strong reasoning, lucid communication, stamina. A fourth, more ineffable quality is crucial: “I look for kids who take pleasure in resolving complicated problems,” Zaharopol says. “Actually doing math should bring them joy.”

Five years ago, when Zaharopol entered M.S. 343, a boxy-looking building in a rough section of the South Bronx, and sat down with a seventh-grader, Zavier Jenkins, who had a big smile and a Mohawk, nothing about the setup was auspicious. With just 13 percent of kids performing at grade level in English and 57 percent in math, M.S. 343 seemed an unlikely incubator for tomorrow’s tech mogul or medical engineer.

But in a quiet conversation, Zaharopol learned that Jenkins had what his siblings and peers considered a quirky affinity for patterns and an inclination toward numbers. Lately, Jenkins confided to Zaharopol, a certain frustration had set in. He could complete his math assignments accurately, but he was growing bored.

Zaharopol asked Jenkins to do some simple computations, which he handled with ease. Then Zaharopol threw a puzzle at Jenkins and waited to see what would happen:

You have a drawer full of socks, each one of which is red, white, or blue. You start taking socks out without looking at them. How many socks do you need to take out of the drawer to be sure you have taken out at least two socks that are the same color?

“For the first time, I was presented with a math problem that didn’t have an easy answer,” Jenkins recalls. At first, he simply multiplied two by three to get six socks. Dissatisfied, he began sifting through other strategies.

“I was very encouraged by that,” Zaharopol told me. “Many kids just assume they have the right answer.” After a few minutes, he offered to show Jenkins one way to reason through the problem. The energy in the room changed. “Not only did Zavier come up with the right answer”—four—“but he really understood it very thoroughly,” Zaharopol said. “And he seemed to take delight in the experience.” Four months later, Jenkins was living with 16 other rising eighth-graders in a dorm at the beam summer program on Bard College’s campus in upstate New York, being coached on number theory, recursion, and graph theory by math majors, math teachers, and math professors from top universities around the country. With some counseling from beam , he entered a coding program, which led to an internship at Microsoft. Now a high-school senior, he has applied to some of the top engineering schools in the country.

beam , which is five years old, has already quadrupled in size—it hosted 80 middle-school students at its summer program last year and has about 250 low-income, high-performing students in its network. But its funding remains limited. “We know there are many, many more low-income kids who we don’t reach and who simply don’t have access to these programs,” Zaharopol said.

There is already a name for the kind of initiative that might, in part, bring the benefits of beam , math circles, the Russian School, or the Art of Problem Solving to a broader array of students, including middle- and low-income ones: gifted-and-talented programs, which are publicly funded and can start in elementary school. But the history of these programs is fraught. Admission criteria vary, but they have tended to favor affluent children. Teachers can be lobbied for a recommendation; some standardized entry tests measure vocabulary and general knowledge, not creative reasoning. In some places, parents pay for their children to be tutored for the admission exam, or even privately tested to get in.

As a result, while many such programs still exist, they’ve been increasingly spurned by equity-minded school administrators and policy makers who see them as a means by which predominately affluent white and Asian parents have funneled scarce public dollars toward additional enrichment for their already enriched children. (The vaguely obnoxious label itself—“gifted and talented”—hasn’t helped matters.)

The No Child Left Behind Act, which shaped education for nearly 15 years, further contributed to the neglect of these programs. Ignoring kids who may have had aptitude or interest in accelerated learning, it demanded that states turn their attention to getting struggling learners to perform adequately—a noble goal. But as a result, for years many educators in schools in poor neighborhoods, laser-focused on the low-achieving kids, dismissed suggestions that the minds of their brightest kids were lying fallow. Some denied that their schools had any gifted children at all.

The cumulative effect of these actions, perversely, has been to push accelerated learning outside public schools—to privatize it, focusing it even more tightly on children whose parents have the money and wherewithal to take advantage. In no subject is that clearer today than in math.

The good news is that education policy may be beginning to swing back. Federal and state legislators increasingly seem to agree that all teenagers could benefit from the kind of accelerated-learning opportunities once reserved for high-aptitude kids in affluent neighborhoods, and many public high schools have been pushed to offer more Advanced Placement classes and to expand enrollment in online college courses. But for many middle- and low-income students who might have learned to love math, those opportunities come too late.

Perhaps it is a hopeful sign, then, that the newly authorized Every Student Succeeds Act, which recently replaced No Child Left Behind, asks states to recognize that such students can exist in every precinct, and to track their progress. For the first time in the nation’s history, the law also explicitly allows schools to use federal dollars to experiment with ways of screening for low-income, high-ability students in the early years and to train teachers to serve them. Universal screening in elementary school might be a good start. From 2005 to 2007, school officials in Broward County, Florida, concerned that poor kids and English-language learners were being under-referred to gifted programs, gave all second-graders, rich and poor, a nonverbal reasoning test, and the high scorers an IQ test. The criteria for “gifted” status weren’t weakened, but the number of disadvantaged children identified as having the capacity for accelerated learning rose 180 percent.

Whether individual states take up this challenge, and do so effectively, is their decision, but advocates say they are mounting a campaign to get started. Perhaps the moment is right for members of the advanced-math community, who have been so successful in developing young math minds, to step in and show more educators how it could be done.

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"What we need to work on is getting comfortable with struggle in learning."

* This article has been updated to include the name of the program run out of New York University.

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Introduction to Algebra 2nd Edition

• ISBN-10 1934124141
• ISBN-13 978-1934124147
• Edition 2nd
• Publisher AoPS Incorporated
• Publication date March 30, 2007
• Part of series Art of Problem Solving
• Language English
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• Publisher ‏ : ‎ AoPS Incorporated; 2nd edition (March 30, 2007)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 656 pages
• ISBN-10 ‏ : ‎ 1934124141
• ISBN-13 ‏ : ‎ 978-1934124147
• Item Weight ‏ : ‎ 1.95 pounds
• Dimensions ‏ : ‎ 8.75 x 1.5 x 11.25 inches
• #121 in Algebra & Trigonometry
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Richard rusczyk.

Richard Rusczyk founded Art of Problem Solving (AoPS) in 2003 to create interactive educational opportunities for avid math students. Richard is one of the co-authors of the Art of Problem Solving classic textbooks, author of Art of Problem Solving's Introduction to Algebra, Introduction to Geometry, and Precalculus textbooks, co-author of Art of Problem Solving's Intermediate Algebra and Prealgebra, one of the co-creators of the Mandelbrot Competition, and a past Director of the USA Mathematical Talent Search. He was a participant in National MATHCOUNTS, a three-time participant in the Math Olympiad Summer Program, and a USA Mathematical Olympiad winner (1989). He graduated from Princeton University in 1993, and worked as a bond trader for D.E. Shaw & Company for four years. AoPS marks Richard's return to his vocation: educating motivated students.

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Don’t Fall into the Calculus Trap

ou love math and want to learn more. But you’re in ninth grade and you’ve already taken nearly all the math classes your school offers. They were all pretty easy for you and you’re ready for a greater challenge. What now? You’ll probably go to the local community college or university and take the next class in the core college curriculum. Chances are, you’ve just stepped in the calculus trap.

The Calculus Curriculum at Your School Might Not Be For You

For an avid student with great skill in mathematics, rushing through the standard curriculum is not the best answer . That student who breezed unchallenged through algebra, geometry, and trigonometry, will breeze through calculus, too. This is not to say that high school students should not learn calculus—they should. But more importantly, the gifted, interested student should be exposed to mathematics outside the core curriculum, because the standard curriculum is not designed for the top students . This is even, if not especially, true for the core calculus curriculum found at most high schools, community colleges, and universities.

Developing a broader understanding of mathematics and problem solving forms a foundation upon which knowledge of advanced mathematical and scientific concepts can be built. Curricular classes do not prepare students for the leap from the usual one-step-and-done problems to the multi-step, multi-discipline problems they will face later on. That transition is smoothed by exposing students to complex problems in simpler areas of study, such as basic number theory or geometry, rather than giving them their first taste of complicated arguments when they’re learning a more advanced subject like group theory or the calculus of complex variables. The primary difference is that the curricular education is designed to give students many tools to apply to straightforward specific problems. Rather than learning more and more tools, avid students are better off learning how to take tools they have and applying them to complex problems . Then later, when they learn the more advanced tools of curricular education, applying them to even more complicated problems will come more easily.

Surround Yourself With Like-Minded Peers

Another danger of the calculus trap is social. Aside from the obvious perils of placing a 15-year-old in a social environment of 19-year-olds, there are other drawbacks to early acceleration. If ever you are by far the best, or the most interested, student in a classroom, then you should find another classroom . Students of like interest and ability feed off of each other. They learn from each other; they challenge and inspire each other. Going from “top student in my algebra class” to “top student in my college calculus class” is not a great improvement. Going from “top student in my algebra class” to “average student in my city’s math club” is a huge step forward in your educational prospects. The student in the math club is going to grow by great leaps, led and encouraged by other students.

In addition to this intellectual enrichment, the social enrichment of being amongst like-minded peers is invaluable. My closest friends now are doctors, bond traders, consultants, lawyers, professors, artists, and so on. Some are religious, some aren’t. Some are athletic, some aren’t. The common thread among them all is that they all enjoy using their minds. I met nearly all of them through activities or employment that selected for thinkers. In school, these activities were (and still are in most schools) extracurricular programs, not curricular ones. The top athletes don’t take PE in school, or even PE in the nearby college. They gather with other top athletes in special programs to enhance their development. The top students can do the same for their minds.

Math Students' Options Beyond Calculus

Many students get stuck in the calculus trap because they believe it’s their only option . This is a large part of why we developed our online community and teach online classes . However, we are not the only other option. Other options students have are to become involved in extracurricular programs, such as math teams. Math contests should be selected with some care: those that encourage mass memorization or just test standard curricular tools tend to exacerbate the ills of the calculus trap rather than enhance problem-solving ability. Students can also pursue independent study if they are able to find mentors. University professors are occasionally willing to fill this role to some degree. There are also many summer programs and good books for extracurricular study, and some communities have developed grassroots programs to provide opportunities for eager students. These options are usually not as easy as “enroll in the next course,” but they will be far more rewarding than settling into the calculus trap.

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Richard rusczyk, related articles, highlights from math history: charles babbage and his difference engine, the math of adele’s album releases: can a hidden pattern help predict when she’ll release next, the math of big-money lotteries: your chances of winning the powerball jackpot, more articles, how to help your advanced learners be successful this year: advice from aops founder richard rusczyk, why discrete math is important, navigating “back to school” after a pandemic, with richard rusczyk, more episodes, sapienship, with dr. jim clarke, wonder, with dr. frank keil, learning stem through fiction, with dr. pamela cosman, managing academic expectations, with charlene wang, edtech at-home, with monica burns, learned helplessness, with vida john, receive weekly podcast summaries right to your inbox, get weekly podcast summaries/takeaways.

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