The plane’s ground speed in a crosswind? Ms. Cascio’s students will explain that it is greater than it would be in calm air, and with a few deft sketches of vectors and triangles, they will tell you by how much.

Image THINK Faye Cascio and a class at the Academy of Science in Virginia. Credit... Photographs by Brendan Smialowski for The New York Times

The students can articulate their reasoning because, for one thing, they have no choice. One recent morning, Ms. Cascio asked several students in succession to explain the logic of their answer to the same question — and, “Uh, yeah, I agree with Yasamin and Josh” just wouldn’t do.

“It’s called dipsticking,” Ms. Cascio said. “It’s really important to make sure the kids are picking this information up, and so I ask, Is this clear to you? Do you really understand it? and I won’t go on until I get a positive, satisfying answer.”

A bigger reason the students seemed to wear the material comfortably emerged when they pulled from the classroom closet genuine items of clothing: white lab coats. The Academy of Science is built on the principle of what its director, George Wolfe, calls inquiry-based learning. “I want them to learn to think like scientists,” he said, “rather than regurgitate facts.” From the moment they enter the program, students do experiments, lots of experiments. Not canned experiments, either, of the sort found in the average “science is fun!” book that spell out every step. Here, the students must design experiments themselves, which means they must learn essential lessons like how to ask questions in an answerable way, what’s your error bar, and, will you please just give me some data already.

Their natty new lab jackets shrugged into place, the students in Ms. Cascio’s physics class set out to demonstrate by experiment, in four four-person teams, the Newtonian verity that force equals mass times acceleration. One team proved hyperefficient, and within moments was catapulting ever more heavily weighted wheeled mini-carts along the tabletop and timing each run. Another team got bogged down debating whether their experimental design would work better with one long string or three short ones, until finally their teacher trilled, “Stop obsessing — let’s go!” A boy yearned for a pulley. Too bad, none available.

A mildly manic half-hour later, the data from the four teams were in and projected on an overhead slide for all to see. Calculators clicked as the young white coats computed the percentage of error in their collected findings, and, whoa, it was only 6.6 percent. “That’s phenomenal!” Ms. Cascio crowed. Think about all the things that could have thrown your experiments off course, she told the class — the low-tech equipment, friction from strings rubbing on stacked textbooks. “But even with that, look at how fabulous the results are,” she said. “You set up a great lab, and you should be proud.” It’s one thing to read about Isaac Newton and apples falling from a tree. It’s another to test his laws of motion and see how right they can be.

Ms. Cascio, 57, is a law of motion herself, a stylish dynamo whose voice retains the comforting vibrato of her natal Jersey City. As an undergraduate at Douglass College of Rutgers University, she studied molecular biology and planned to become a doctor, but while living in Greece she began teaching and fell in love with the profession, eventually earning master’s degrees in biology and education. With her decades of experience and a string of national teaching laurels, Ms. Cascio could easily have settled into rote mode, but instead she decided to join the fledgling Academy of Science, where, she admits, the pace can be grueling. “It takes a lot more time to teach inquiry than by plug and chug, by getting up in front of a class and lecturing by the book,” she said.