I had to make a blog post about the Atlantic article, The Math Revolution. The article describes math training programs which have excited ambitious teenagers (from the United States) to compete in international math competitions–and win. “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.” Here are some of the major points I got from it:

- Here are some of the curriculums listed: “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.”
- Online resources: Art of Problem Solving, Proof School, Brilliant.org
- Brick and mortar resources: Russian School of Mathematics
- Math Kangaroo is a math competition for as young as 1st grade.
- Games to play: “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.”
- How the Russian School of Mathematics started: “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.’ ””
- The approach of the Russian school: “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.”
- More on how it works:”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*.” - How the teachers are often working professionals: “In my experience, a common emotion in the NYU math circles, at the Russian School, in the chat rooms of the Art of Problem Solving and similar Web sites, 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.”
- How it develops friendships “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
- How the students think of their future: “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.”
- Early learning is vital: “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.”