BEAM recruits low-income middle schoolers in New York City and prepares them for high-level math in high school and college. Photo: Erin Patrice O’Brien, *Atlantic*

“Online and in the country’s rich coastal cities and tech meccas . . . accelerated students are learning” more complex math than ever before, writes Peg Tyre in *The Atlantic*. A “new pedagogical ecosystem” — math enrichment camps, after-school and weekend classes, “math circles” and online sites — is growing rapidly.

“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,” she writes. Richard Rusczyk, a former Math Olympian who founded the site, is opening two brick-and-mortar centers to teach advanced math and plans an online program for elementary students.

The Proof School, a small independent secondary school in San Francisco, also teaches “amped-up math” — often to the children of high-tech parents.

STEM parents hope 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,” writes Tyre.

U.S. elementary teachers often are uncomfortable with math says, Inessa Rifkin, a co-founder of the Russian School of Mathematics, which enrolls 17,500 students in after-school and weekend math academies in 31 U.S.

locations. She thinks kids start to go astray in second or third grade.

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.

“Students quickly learn their math facts and formulas,” then use that to explore the world, writes Tyre.

From the 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.

Einstein is the right answer. But the point is get students to “execute the cognitive bench press: investigating, conjecturing, predicting, analyzing, and finally verifying their own mathematical strategy,” writes Tyre.

Bridge to Enter Advanced Mathematics (BEAM), a New York City nonprofit, looks for joyful problem solvers in low-income middle schools. They’re offered “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.”

Tyre implies that conceptual understanding and “problem solving” can be learned without foundational skills, responds Barry Garelick, author of *Confessions of a 21st Century Math Teacher.*

She compares a regular ninth-grade algebra class to a lecture “on the basics of musical notation” versus a middle-school problem-solving students singing “an aria from Tosca.”

Singing an aria from Tosca requires “years and years of training in basic vocal skills,” writes Garelick. “Musicality is built up from mastery of the basics.” Similarly, students learn to solve complex math problems by learning how to solve basic problems, then harder problems and so on.

Here’s a profile of the Los Angeles math teacher whose student earned a perfect score in AP Calculus — and whose students all pass the AP exam.

Teachers “should always think of the next level,” said Anthony Yom, who was born in Korea. “Where are they going in the next level, what are they learning in the next class? Then, you can do some backward planning, and that will help you do a good job at explaining things.”

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