One recent afternoon, he tugged at a Slinky, swung a yellow jump-rope and dunked a ruler in water -- all to keep 22 teenagers rapt.
The Navy veteran says his latest mission -- high school physics teacher in Prince William County -- is as challenging as the toughest assignments of his 30-year military career. Paulson, 60, transformed from "Captain Paulson" to "Mr. P." through a federal program that offers a stipend to military personnel who launch a career in the classroom.
Troops to Teachers, which has placed about 11,500 teachers nationwide in 15 years, is one way the Obama administration aims to draw more men and minorities into schools and fill demand in the fields of math, science and special education.
About 82 percent of the former soldiers, sailors, Marines and other veterans who sign up are men. (About a quarter of all teachers are men, according to one estimate.) Nearly 40 percent of Troops to Teachers participants are members of racial or ethnic minorities. The program has put more than 2,000 black men into classrooms.
The recruits are producing results. A recent study found that Florida students taught by Troops to Teachers participants made greater gains in reading than peers taught by teachers with similar classroom experience. In math, students in Troops to Teachers classrooms outperformed those in other classes -- even when the other teacher had more years under his belt.
"Honestly, at first, we thought a military officer dealing with today's fifth-graders and seventh-graders was not going to be very effective," said William A. Owings, an Old Dominion University education professor and one of the study's authors. "We found out that is totally untrue. We have come to believe that you're looking at life experience . . . that has a lot of crossover into good classroom skills."
When Rob LaPin, 30, left the Army to teach government at the troubled Walbrook High School in Baltimore last year, he and a fellow teacher spent lunchtime roaming the streets to find truants. LaPin was the robotics coach, student government sponsor and, much to the amusement of his friends, cheerleading coach and fashion coach.
"It engrossed me completely," said LaPin, who is working in Iraq as a government contractor but plans to return to teaching. "As a soldier in the classroom, my duty wasn't only to ensure my kids had good grades, but also to prepare them for life."
Gerrald Ash-Banks, 16, said he and his classmates in the robotics club stayed after school with LaPin almost every day. They also met on weekends. And when Ash-Banks and his mother were having trouble, LaPin sat him down for a talk. "He was like everybody in robotics' father," Ash-Banks said.
Troops to Teachers, launched in 1994 as the military was downsizing, offers up to $5,000 for courses needed to become a teacher, as well as a bonus of up to $5,000. In return, candidates agree to teach at least three years in a school district where many students live in poverty. The program receives $14.4 million a year from the Department of Education but is operated by the Department of Defense.
Rep. Tom Petri (R-Wis.), one of the program's creators, sees it as one option for Iraq and Afghanistan veterans. He is leading an effort on Capitol Hill to expand the program to bring Troops to Teachers into more schools in middle-class communities.
"It's really meant to be a broad program to help all schools," Petri said. "Kids really need to get a kind of grounding and a framework so they have some limits and can develop within them. And I think because of their experience, military people are almost uniformly able to do that."
For Paulson, it's a natural step from the microcosm of a submarine to his Woodbridge High School classroom. You've got to spot problems and fix them fast, he said.
There are hints of Paulson's background in his perfect posture. But one day last month, the man at the front of the class, in a bright blue shirt and smiley-face tie, did not seem the "super-secret mission" type.
Paulson threaded a long coil of wire onto a pole and shook the other end, demonstrating waves. He beat hollow tubes against the desk so students could hear that the shorter tube produced a higher-pitched thunk.
Each time Paulson demonstrates a physics concept, he's keenly aware of real-world applications. "I either had to repair it underwater with no lights on or had to fix it to get underway to take a VIP on a cruise," he said of his time commanding a submarine.
But what are kids most interested in? "They always want to know if I killed anybody," Paulson said. "I say when we launched a Tomahawk missile at this specific building all that was left was a crater. Yes, we did it at night, and maybe the building was evacuated. We can only hope so."
Midway through class, the students marched out into the hallway for a quick water fountain break. Paulson pulled out a yellow rope, tossed the far end to a student and started swinging.
Terrance Miller, 17, jumped in. Paulson began counting: "One one-thousand. Two one-thousand. Three one-thousand . . . "
"When Terrance was jumping two jumps per second, what was the period?" Paulson asked.
"One half," several students chimed in.
"Right," Paulson said. "It took him a half-second per jump."
As students jumped, the class calculated the frequency. Then a few students hopped in just for fun.
"I thought he was going to be kind of strict and uptight," Miller said of his teacher. "He ended up being very cool."