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Richard Rusczyk’s Worldwide Math Camp

By Ingfei Chen

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 AoPS Academy

History & philosophy.

Art of Problem Solving textbooks have been used by outstanding students since 1993. The AoPS website launched in 2003, and its online community now has over one million users. Many of the winners of each year's International Math Olympiad use the AoPS site as a primary training resource. The AoPS Online school has over 20,000 enrollments annually in courses specifically designed for high-performing math students. Most of the winners of major American national math competitions are AoPS alumni, and thousands of our alumni enroll in top universities each year.

With AoPS Academy, Art of Problem Solving brings its curriculum and pedagogical techniques to the classroom, offering advanced math, science, and language arts courses for grades 1-12.

AoPS Academy is accredited by the Western Association of Schools and Colleges.

Focus on Challenging Problems

A generation ago, there were many intellectual careers that required repeatedly solving routine problems. Most of those jobs are performed by computers now. Successful people in the next generation will need to develop new skills throughout their careers as their older skills become obsolete. Therefore, we go well beyond the basics in our classes, providing students a deep and rigorous curriculum while training students how to tackle difficult problems that are not replicas of problems they've already seen. This teaches students how to learn, so they'll be ready for the challenges of top-tier colleges and internationally competitive careers.

Active Learning

Students best learn how to solve hard problems by tackling the problems themselves, not by watching passively as others do the work. In our classrooms, students solve each problem, with instructors asking motivating questions as guidance. Only after the students have solved a problem does the instructor provide direct commentary that reinforces key insights.

Outstanding Peer Group

AoPS Academy draws strong students from many schools, giving AoPS students an outstanding peer group with whom they can learn, form friendships, and draw inspiration. Each year, the AoPS network has many students earn admission to highly selective colleges like MIT, Harvard, and Stanford. Their work in AoPS classes helps prepare them for the competitive, challenging environment they'll find in these schools.

Communication Skills

Collaborative efforts have become crucial in most professional environments, so AoPS is expanding to language arts instruction through AoPS Academy. We extend this emphasis on communication to our math and science classes, in which students learn how to express their advanced mathematical ideas and scientific understanding clearly and rigorously.

Meet Some AoPS Alumni

USAMO Winners

For the past decade and a half, most of the winners of the USA Mathematical Olympiad have been AoPS students. The twelve 2019 USA Mathematical Olympiad winners shown above collectively took over 110 classes at the Art of Problem Solving Online School. The students on the the United States teams that won the International Mathematical Olympiad in 2015, 2016, and 2018 also collectively took over 110 classes with us. Photo is courtesy of the Mathematical Association of America, distributed under a CC license .

Melody Guan

Melody earned the prestigious International Physics Olympiad Bronze medal, International Chemistry Olympiad Silver medal, and the International Biology Olympiad Gold medal, all while representing Canada. She is also a two-time winner of the Math Prize for Girls Olympiad Bronze medal and was invited to the Canadian International Math Olympiad Training Camp in 2012. Melody graduated from Harvard University in 2016 with a B.A. in Honors Chemistry and Physics as well as an M.A. in Statistics. She maintained an overall GPA of 4.0 while pursuing both degrees. While at Harvard, Melody pursued opportunities as a Proprietary Trading Intern for D.E. Shaw & Co. and as a member of the Douglas Melton Laboratory developing assays to quantify insulin production by stem-cells. Following graduation, Melody joined the Google Brain research team as a deep learning resident.

Luke Robitaille

Luke has been studying math with AoPS since 2012. He came in second in National MATHCOUNTS in 2016 before winning in 2017 and 2018. He has also taken the USAMO five times and the USAJMO once, won the 2018 Harvard-MIT Math Tournament (HMMT), the 2018 American Regions Math League, and took home a silver medal at the 2019 Romanian Master of Mathematics competition. Luke has been invited to the Math Olympiad Program three times and was also a 2017 Spirit of Ramanujan Math Talent Initiative Winner. He likes eating pizza and says that one of the best things about math competitions is that "elegant math is fun to do."

Celine Liang

Celine was a USA Mathematical Olympiad winner in 2015 and was a team member of the United States team that won the Romanian Masters in Mathematics competition in 2016. She has attended the Math Olympiad Summer Program twice, won first place at the Math Prize for Girls in 2014, and won the Wendy Ravech Akamai Mathematics Scholar Award in 2015. She was a gold medalist in the USA Physics Olympiad in 2014 and 2015, and was invited to the Summer Program in Applied Rationality and Cognition (SPARC) at Berkeley. Celine was also a top-10 finisher in National MATHCOUNTS and was a member of the first place California team in 2011. She has taught at a variety of programs for younger students, and participates in the DACA competitive swim team, tennis, violin, and piano.

Espen Slettnes

Espen has taken 22 different AoPS Online courses, as well as attending classes at the Berkeley Math Circle, where he is now an instructor. He is currently interested in graph theory and has published research through the MIT PRIMES/AoPS Crowdmath project, as well as winning Project of the Year at the 2018 California Science and Engineering Festival for his college-level work in mathematics. He is both a 2018 World Science Scholar and a winner of the 2017 Spirit of Ramanujan Math Talent Initiative. Espen also took the 2018 USAJMO and won a bronze medal at the USA Physics Olympiad (USAPhO). In his spare time, he enjoys talking about math with other enthusiasts and playing board games, especially Risk.

Maria Monks Gillespie

Dr. Maria Monks Gillespie got her start in mathematics through competitions and programs such as AoPS. A two-time MOSP qualifier, she studied mathematics at MIT, where she wrote six undergraduate research papers and was awarded the Alice T. Schafer Prize and the Morgan Prize for her work. She was a recipient of the Churchill, NSF, and Hertz graduate fellowships, and recently completed her Ph.D. at the University of California, Berkeley. She is now an NSF postdoctoral fellow at the University of California, Davis. Dr. Gillespie has taught in the AoPS Online School, as well as MOSP, IDEA MATH, Girls' Angle, and the Duluth REU over the last eight years. Most recently, she and her family founded Prove it! Math Academy , a two-week summer program for high school students designed to bridge the gap between computational and proof-based mathematics.

Evan discovered Art of Problem Solving in middle school, after hearing about Alcumus. In 2014, he earned the second-highest score in the USA Mathematical Olympiad (USAMO)—the same year that he won a gold medal on the Taiwanese team at the International Mathematical Olympiad (IMO). Evan can be found learning and teaching math all over the place: on the AoPS Community, at MIT (where he earned his BS in math, and where he is now in the PhD program), and at the Mathematical Olympiad Summer Program (MOP), where he has been a grader and is now the Assistant academic director. In his spare time, Evan enjoys playing games and blogging .

Elissa Redmiles

Elissa is currently working on her Ph.D. in computer science at the University of Maryland, where her research interests include subjects such as cybersecurity, survey methodology, and machine learning. She has been awarded the prestigious Graduate Research Fellowship from the National Science Foundation, the National Defense Science and Engineering Graduate Fellowship from the Department of Defense, and the Facebook Fellowship. Elissa has presented her research at conferences held by The Institute of Electrical and Electronics Engineers, The Association for Computing Machinery, and The USENIX Association. She has written for Scientific American and The Conversation, and her work has been covered by the Maryland Cybersecurity Center as well as TechRepublic.

Arjun Ramani

Arjun has participated in math research and math competitions and values the opportunities he's had to explore topics he loves with like-minded peers. In high school, he won third place at the 2017 Regeneron Science Talent Search for his research in network theory. He has also taken the USAMO and USAJMO, won prizes at the Intel International Science and Engineering Festival (IISEF), and was awarded a 2017 Davidson Fellowship for his research. Of all the kinds of math problems in the world, Arjun most enjoys probability—especially problems whose “solutions contradict your initial intuitions.” He is currently taking courses in math, computer science, and economics at Stanford.

Blythe Davis

Blythe grew up exploring logic puzzles and games with her family. She read the Art of Problem Solving in fifth or sixth grade and took AoPS Online classes through middle and high school. Blythe's wide-ranging curiosity led her to conduct award-winning environmental research near where she grew up. She is now majoring in math at Duke University. Although she used to like that there was just one answer to most of the math problems she encountered, she now loves the complexity of research math and is delighted by how much she has yet to learn. In her free time, Blythe loves writing, reading, and paying attention to patterns, interactions, and relationships of all kinds.

Alfredo Alef Pineda Reyes

Alfredo represented Mexico at the 2017 International Mathematical Olympiad, earning a silver medal. He also received the highest silver medal score at the 2017 Iberoamerican Mathematical Olympiad, as well as back-to-back bronze medals at the 2016 and 2017 Asia Pacific Mathematics Olympiad. In the Summer of 2017, Alfredo was invited to the first ever European Summer Program on Rationality (ESPR), an immersive summer workshop for mathematically talented students from around the globe. When not competing in the international math competition circuit, Alfredo enjoys reading and swimming. He hopes to attend MIT where he’d like to study pure mathematics.

Girishvar Venkat

Girish encountered Art of Problem Solving for the first time in seventh grade, when he joined his middle school’s MATHCOUNTS team. In high school, besides doing graduate-level math research through MIT’s PRIMES program, Girish also earned a perfect score on the 2013 USA Mathematical Talent Search (USAMTS), attended the Mathematical Olympiad Summer Program (MOP) in 2014, and achieved honors on the USAMO, USACO, and other science and math competitions. He earned a BS in computer science and mathematics from MIT and is currently a quantitative trader at New York’s Seven Eight Capital. Girish’s advice to younger students who like math is not to get discouraged: “every time I failed, I learned a very valuable lesson.”

Davie Rolnick

Davie was a USA Mathematical Olympiad winner in 2008, and credits much of his early math education to AoPS. He also attended the highly-selective Research Science Institute (RSI) summer program for high school students. He graduated from MIT in 2012 with a double major in mathematics and music, after which he became an instructor in the AoPS Online School. He spent a year in Berlin studying under a Fulbright grant, and then returned to MIT to pursue a Ph.D. in discrete math. When he's not doing math or singing, Davie plays word games, hikes, and studies moths (which are, after all, not dissimilar to maths).

Francisco Proskauer

Francisco represented Puerto Rico twice at National MATHCOUNTS. During high school, Francisco was a member of the Puerto Rico team at the Central American Math Olympiad and Iberoamerican Mathematical Olympiad, winning medals twice at each event. In 2015 and 2016, he earned bronze medals at the International Mathematical Olympiad. He also participated in the first summer of the EuroSPARC (now ESPR) program. He was a frequent contributor to the AoPS Online Community, spending most of his time solving problems and posting problems from competitions, and now works for AoPS as a teaching assistant and grader. Outside of math, Francisco enjoys singing in his a capella group, fantasy sports, and listening to hip-hop. He is currently in his sophomore year at MIT studying computer science.

Derek took his first AoPS class, Introduction to Counting & Probability, when he was eight. He earned a perfect score on the 2017 AMC 8 and in 2018 was one of fewer than 250 students invited to take the USA Junior Mathematical Olympiad (USAJMO). He is also a winner of the Spirit of Ramanujan Talent Initiative, a global math outreach program that connects promising students with opportunities for advancement. In his spare time, Derek likes hanging out with friends, solving and creating puzzles, and building modular origami models. When he grows up, Derek dreams of becoming a chemist so that he can keep solving interesting problems.

Juan Carlos Ortiz Rhoton

Juan represented Mexico at the International Mathematical Olympiad four times, earning one gold and two silver medals. He also earned a gold medal at the Asian-Pacific Mathematical Olympiad, and a gold medal with a perfect score at the Iberoamerican Mathematical Olympiad. He attended the prestigious Summer Program in Applied Rationality and Cognition (SPARC) at Berkeley, and is currently studying mathematics at MIT.

Meet Our Curriculum Designers

Richard Rusczyk

Art of Problem Solving was founded by Richard Rusczyk 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 received the World Federation of National Mathematics Competitions Paul Erdös Award in 2014. 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.

David Patrick

Dave joined AoPS in 2004. He is the author of Art of Problem Solving's Introduction to Counting & Probability, Intermediate Counting & Probability, and Calculus textbooks, and co-author of Prealgebra. Dave earned the sole perfect score on the American High School Mathematics Examination (AHSME) in 1988 and was a USA Mathematical Olympiad winner that year. He attended the Research Science Institute (RSI) in 1987, and the Math Olympiad Summer Program in 1988, where he first met fellow student Richard Rusczyk. He also finished in the top 10 on the Putnam exam in 1991. Dave graduated from Carnegie Mellon in 1992 with a BS in Mathematics/Computer Science and an MS in Mathematics. He went on to earn his Ph.D. in mathematics from MIT in 1997. He was an acting Assistant Professor at the University of Washington from 1997 to 2001. Dave is originally from Western New York and is an alumnus of the SUNY Buffalo Gifted Math Program.

Jason Batterson

Jason joined AoPS in 2010 to lead development of the Beast Academy series. Before joining AoPS, he taught mathematics and coached the math team at Ligon Middle School. Ligon won state MATHCOUNTS titles in 2008 and 2009, where Jason taught a future International Math Olympiad gold medalist. In addition to teaching and coaching at Ligon, Jason coached the math team at Fred Carnage Middle School for the 2009-2010 school year. Ligon and Carnage placed 1st and 2nd respectively in the state MATHCOUNTS competition in 2010, with 6 of the state's top 10 competitors coached by Jason. While teaching, Jason wrote and published Competition Math for Middle School. He enjoys puzzles, running, skiing, and playing in the pool with his kids Parker and Ada.

Courses Overview

During the school year classes meet weekly, bringing together small groups of high-performing students to work with outstanding instructors. Our summer courses keep students sharp for the upcoming school year.

The AoPS Academy curriculum is carefully designed to prepare students for the rigors of advanced university classes and highly competitive careers. We stress both the fundamentals and extending those fundamentals to advanced applications in all of our math, science, and language arts classes. Students develop a deep understanding of new concepts, and learn how to use them in complex situations.

AoPS Academy instructors are chosen based both on proven domain expertise as well as their pedagogical skills. Many of our instructors have advanced degrees, and our curriculum is designed by experts in their fields.

Mathematics Courses

Our math curriculum is centered on students solving problems. Rather than spoon-feed students material for them to echo, we guide them through the experience of developing new mathematical ideas. Our focus on rigor provides a thorough understanding of the fundamentals, while our approach to creative problem-solving trains students to handle novel mathematical and scientific situations. Graduates of our math program will be well-prepared to continue their math-related studies at outstanding universities, and be equipped for a rapidly-shifting professional landscape. Each class session includes:

• Extensions of past topics : Students solve challenging problems based on the previous week’s material, both to review recent topics and to hone their problem-solving abilities.
• Introduction of new fundamentals : Students explore a series of problems to add new strategies and tools to their toolboxes.
• Challenging problems : Students reinforce their understanding of their new tools by applying them to more difficult problems, some of which are drawn from major national and international contests.
• Collaborative problem-solving : Occasionally groups of students work together on particularly challenging problems, with successful groups presenting their solutions to the class.

AoPS Academy classes aren't confined to the classroom. Our classes employ many of the online resources that have been cornerstones of the AoPS online school for over a decade. Our Academic Year math courses include the following support material outside the classroom:

• Weekly homework : Students have a weekly homework set including problems with a wide range of difficulty. Students receive instant feedback on the accuracy of their work, and have access to detailed solutions after finishing each problem.
• Weekly reminder emails : Students and parents receive weekly emails detailing the students' progress and upcoming due dates.
• Thorough reporting : Students and parents can view detailed reports regarding students' performance.
• Class outlines : Students can access class outlines online. Outlines are linked to reading material, so students can review past classes, prepare for future classes, and catch up when they miss classes.
• AoPS textbooks : All students receive AoPS textbooks and have assigned reading each week in support of the weekly lesson.

Science Courses

Our first physics class is for students who have a good understanding of Algebra 1 and want to learn more about the world around them. Our growing science program is designed to teach students to ask questions about the physical world and to design experimental frameworks to answer those questions. We use a hands-on approach to teach scientific thinking and prepare students for future study of many types of science.

Language Arts Courses

Our core language arts classes in grades 2-12 teach students both the craft and art of effective communication. Instruction focuses on multiple components of writing, building from the fundamentals to give students a deep appreciation of language. Graduates of our language arts program will be fluent writers and excellent critical readers. They'll develop these skills by starting from words, progressing to sentences, and then organizing these sentences into well-constructed paragraphs, essays, and stories.

Class sessions include instruction in three broad areas:

• Vocabulary : Expressing oneself and understanding intricate writing starts with a mastery of the basic building blocks of language: words. Our study of vocabulary extends far beyond simply memorizing definitions. We emphasize the stems, origins, and other tools to help students develop a rich palette from which they can choose the right word at the right time.
• Grammar : Our students learn grammar by studying passages from classic literature and other primary sources, through which they learn how to comprehend complex passages. They then learn how to apply this understanding to their own writing to produce well-structured, effective prose.
• Writing : All of our core language arts instruction targets students' writing skills. Our students write, analyze, edit, and then write some more. Rewriting is at the heart of excellent writing, so many of our writing assignments are spread over several weeks, with students revisiting and refining their own work based on instructor feedback and in-class discussion of their work.

Summer Courses

Summer learning loss is a well-documented educational concern, with students regularly losing proficiency in math and reading during their idle summer months. AoPS Academy offers summer classes in math and language arts to keep students sharp and get them prepared for the upcoming school year. Our math and language arts summer programs include a variety of two-week camps featuring activity-based learning designed to pique students’ curiosity and keep them engaged.

Our summer Math Beasts camps extend topics that students learned in the past year and allow students to explore new areas of math. Each camp features Problem Solving and Mathematical Exploration:

• Problem Solving : In Problem Solving, students review a key topic from the previous year and then explore that topic further, pushing their understanding well beyond grade level. Students engage with Problem Solving through math-related games and puzzles, challenging activities that call for group collaboration, and intriguing problems that encourage students to think in novel ways as they apply new skills.
• Mathematical Exploration : Through our Mathematical Explorations, students encounter new topics that are typically not introduced until much later in their schooling, and mathematical strategies they can apply throughout their education. This year, our camps will take on a variety of topics including spatial reasoning, pattern recognition, working backwards, invariance, graph theory, and cryptography.

Our Middle School Math Contests and High School Math Contests camps are excellent fits for students seeking to prepare for contests like MATHCOUNTS and the American Mathematics Competitions–or for students who simply want an extra challenge over the summer. In these camps, students are introduced to important new topics while reviewing and applying concepts they have already encountered to advanced problems. Students also participate in practice individual and team competitions, gaining both mathematical skills and test-taking experience that will prepare them for key events in the upcoming school year.

Our first science camp, Waves and Sound for Grades 5-6 , is a great choice for students who are curious about how the world works. Using scientific problem-solving methods, students will study the types and properties of waves, how sound waves interact with human hearing, and a surprising number of other wave phenomena in the natural world.

Our writing camps provide a venue for students to hone their writing and critical thinking skills over the summer. In Creative Writing for Grades 3-4 , students learn the craft of fiction while composing their own short stories and poems alongside their classmates. Classes feature a mix of interactive writing activities and engaging lessons in the elements of storytelling and poetry. Our Academic Essay Writing for Grades 8-10 camp introduces students to the craft of essay writing at a college level. In addition to teaching students how to plan and write an academic essay, the camp explores the purpose behind such essays, examining their role both in academic settings and in the real world. By thinking critically about academic writing as an intellectual pursuit, students become not just better writers but deeper thinkers.

Our reading and performance camps help students develop critical reading and thinking skills while polishing their presentation skills. Readers Theater for Grades 4-5 guides students through a challenging novel while training students to write, rehearse, and perform their own plays. Students in Mock Trial: Persuasive Speaking for Grades 7-8 explore a Newbery Honor Book by acclaimed children's author Avi, and then prepare for a mock civil case based on events in the book. Through their preparations, they learn the arts of clear and concise writing, argumentation, and public speaking.

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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.

So much to learn.

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

https://artofproblemsolving.com/

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https://www.facebook.com/artofproblemsolving

Length - 01:07:08

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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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Art of Problem Solving (AoPS) Prealgebra F Fourth Printing Used Edition

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• ISBN-10 1934124214
• ISBN-13 978-1934124215
• Edition F Fourth Printing Used
• Publisher AoPS Incorporated
• Publication date August 9, 2011
• Language English
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• Publisher ‏ : ‎ AoPS Incorporated; F Fourth Printing Used edition (August 9, 2011)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 608 pages
• ISBN-10 ‏ : ‎ 1934124214
• ISBN-13 ‏ : ‎ 978-1934124215
• Item Weight ‏ : ‎ 2.95 pounds
• Dimensions ‏ : ‎ 10.38 x 8.38 x 0.5 inches
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About the authors

David patrick.

David Patrick has been an author and curriculum developer at Art of Problem Solving since 2004. He is the author of Art of Problem Solving's Introduction to Counting & Probability, Intermediate Counting & Probability, and Calculus textbooks, and co-author of AoPS's new Prealgebra textbook. He is also an instructor in AoPS's widely-acclaimed online school for high performing middle and high school students.

Dave earned the sole perfect score on the American High School Mathematics Examination (AHSME) in 1988 and was a USA Mathematical Olympiad winner that year. He attended the Research Science Institute (RSI) in 1987, and the Math Olympiad Summer Program in 1988, where he first met fellow student Richard Rusczyk. He also finished in the top 10 on the Putnam exam in 1991. Dave graduated from Carnegie Mellon in 1992 with a BS in Mathematics/Computer Science and an MS in Mathematics. He went on to earn his Ph.D. in mathematics from MIT in 1997. He was an acting Assistant Professor at the University of Washington from 1997 to 2001. Dave is originally from Western New York and is an alumnus of the SUNY Buffalo Gifted Math Program.

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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About the Art of Problem Solving Initiative

Founded in 2004, the Art of Problem Solving Initiative, Inc. was created by people who love math and love teaching to help students access the study of advanced mathematics.

The Initiative began by running the USA Mathematical Talent Search , a nationwide math contest sponsored by the National Security Agency which continues to run to this day. In each round, this contest gives students a full month to work on five challenging proof-based problems. Students then get individual feedback on their work, including comments on their mathematical reasoning and on their proof-writing skills. By taking away the usual time pressures seen in many math contests, students have the opportunity to go more deeply and to explore.

For many years, the Initiative also ran the Local Programs Initiative which provided fiscal sponsorship to math circles and clubs across the country.

Now, the main project of the Initiative is Bridge to Enter Advanced Mathematics (BEAM) , a project to help underserved students find a realistic pathway towards becoming scientists, mathematicians, engineers, and programmers. During the summer after 7th grade, students are invited to participate in a free three-week residential program on a college campus where they gain the academic and social/emotional preparation to succeed in future programs for advanced study. They then receive academic advising throughout 8th grade and high school to help them and their families find the best opportunities for their educations.

The Art of Problem Solving Initiative receives support from Art of Problem Solving (AoPS) , which develops resources for high-performing middle and high school students including the largest online community of avid math students in the English-speaking world. The AoPS online school has trained many winners of major national mathematics competitions, including several gold medalists at the International Math Olympiad, Davidson Fellows, and winners of the Intel and Siemens Talent Search competitions.

The Art of Problem Solving Initiative is a 501(c)(3) charitable organization. It continues to be led by expert mathematicians and educators to this day. Please consider joining our contributors by donating to support advanced math education.

Financial Information

The Art of Problem Solving Initiative, Inc. makes its financial statements available for public inspection in the interest of greater transparency. Please see below to learn more about the organization.

• Tax return (Form 990)
• Audited financial statements
• Tax return (Form 990) (Note that due to a change in fiscal year these cover a shortened period.)

About About Beast Academy BA

Why we created beast academy ba beast academy ba.

Beast Academy was created by the Art of Problem Solving team that has trained tens of thousands of outstanding middle and high school math students since 1993. As we prepared these students for the rigors of top-tier universities and internationally-competitive careers, we often wondered why there aren't more students who enter middle school loving math the way AoPS students do.

Beast Academy is our attempt to solve this problem by presenting mathematics as the beautiful, creative discipline it is. We do so with challenging problems, engaging explanations, and a focus on the hows and whys of mathematics. It's the curriculum we wish we'd had when we were aspiring math beasts ourselves.

A Brief History of Beast Academy

In 2009, Art of Problem Solving founder Richard Rusczyk and future Beast Academy author and creator Jason Batterson met at the national MATHCOUNTS championships in Orlando. Jason was located in North Carolina at the time, teaching and coaching math teams as well as drafting his first book, Competition Math for Middle School. Richard was looking for someone to lead the creation of an Art of Problem Solving curriculum for younger students. The two hit it off, but it would take another year before Jason could switch coasts and begin work on the new elementary curriculum for AoPS.

The idea of a comic-style curriculum came from a desire to model conversations about math in a way that students could enjoy and relate to. The little monsters at Beast Academy model attitudes and approaches that we want to see in classrooms, including making mistakes and learning from them. The format also gives us the chance to provide lots of visual explanations that help students understand the concepts we are teaching.

Comics are a lot of fun, but don't think that a fun curriculum can't also be rigorous. Beast Academy was written to help students understand math concepts deeply and apply them to solve challenging problems.

Neither Richard nor Jason was any good at drawing, which made it tough to start creating a comic series. They knew they needed a talented artist and were very lucky to find Erich Owen, who has led the creation of all the art for the series. Those familiar with the series can guess which of these early sketches eventually became our beloved purple furball, Grogg.

Plans were set for a series of Guide and Practice books . Shannon Rogers joined AoPS in 2011 to help author the Practice books, and the first four books (Beast Academy 3A and 3B Guide and Practice) were published in 2012. The books were well received and well reviewed; we knew we were creating something special. The remaining books for levels 3, 4, and 5 were published over the next five years, with Kyle Guillet, Chris Page, and world puzzle champion Palmer Mebane contributing their talents to the series, and artist Greta Selman adding color to the Beast Academy world in the Guide books. A set of 'prequel' books for Level 2 followed and were completed in February of 2019. Finally, Level 1 was completed in 2022.

To date, over 1,000,000 Beast Academy books have been sold. We are currently working on completing Puzzle books for each Beast Academy level.

We always intended to bring Beast Academy to the digital world, and in 2015 we began our ambitious plans for Beast Academy Online. We needed a strong team of software developers to build a robust learning system that spanned all levels of Beast Academy and a team of talented curriculum developers to design and implement the curriculum online. The software development team was initially led by Anika Huhn, followed by Corinne Madsen. Anakaren Santana led the curriculum team and continues to oversee the writing and revision of lessons in BA Online. To date, Anakaren and her team have designed and written more than 1000 lessons that include more than 20,000 problems.

In August of 2018, we launched the original version of Beast Academy Online!

2016 marked the opening of the very first AoPS Academy learning center in Morrisville, NC. Now, students across the nation use Beast Academy in after-school learning centers. In 2019, we launched a new suite of tools for schools that brought Beast Academy Online to thousands of students in public, private, and charter schools. We hope to continue expanding into even more schools so that eager students everywhere can play math with our little monsters.

We've spent a lot of time creating the math curriculum we all wish we had when we were kids, and there are lots of big improvements on their way for Beast Academy Online. We're developing materials that allow parents and teachers to deliver Beast Academy to students, monitor their progress, and find the right tools to help them succeed.

We've also started developing Beast Academy science books. Students will soon be able to explore how the world works and what it's made of with the four little monsters of Beast Academy and a whole new group of professors.

To keep an eye on what we're up to, join our mailing list or become a fan of Beast Academy on Facebook . There's lots more to come!

The AoPSWiki is a wiki, or a publicly editable resource, that is dedicated to students of problem solving. It is administered and hosted by the Art of Problem Solving . It is run with the software MediaWiki , which was originally only to be used to create Wikipedia.

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