Imagine a rope that runs completely around the Earth’s equator. You cut it and tie in another piece of rope that is 710 inches long, increasing the total length of the rope by a bit under 60 feet.

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?

A. Bacteria. B. A ladybug. C. A dog. D. Einstein. E. A giraffe. F. The space shuttle.

This is a question (slightly edited) from the math and science site Expii.com. In “The Math Revolution” in the March issue of the Atlantic magazine, Peg Tyre cites it as an example of “a new pedological ecosystem” that’s contributing to a heartening rise in math abilities shown by many American students. Common in Russia and other former Soviet states, she says, this approach involves clustering students by ability in small groups and giving them problems that could be solved in a variety of ways. The idea is that math is not learned by teaching kids rules and asking these students to apply them, but by asking them to look at the real world and apply broader reasoning skills.

Tyre writes that American kids are a lot better than they used to be at math — she begins with U.S. teenagers’ victory over usual powerhouses China, Russia and South Korea at the 56th International Mathematical Olympiad last summer — but that most of the gains have come as the result of private initiatives outside the U.S. educational system.

Tyre writes about the Russian School of Mathematics, with 17,500 students this year in after-school and weekend math academies in 31 locations around the United States; the Bridge to Enter Advanced Mathematics, or BEAM, a nonprofit based in New York; and an assortment of math circles and other programs. The challenge, Tyre says, is to incorporate this kind of learning back into the school systems — possibly via that familiar and sometimes controversial institution, the gifted-and-talented program.

It’s all interesting and, for a change, rather optimistic.

BEAM offers an encouraging example of better math programs for lower-income students. A seventh-grader in the South Bronx, bored with regular school math, was delighted when presented with this unconventional problem because there was no obvious formula for solving it: “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?”

The answer is four. And the answer to the first problem is Einstein.

But how do you arrive at those answers? Tyre doesn’t say. You figure it out.