Vern Williams was reviewing a math quiz with seventh-graders at Longfellow Intermediate School in McLean. Before him, students in fluorescent surfer shorts and high-top sneakers listened intently.

"When planes go to airports, they don't go plop like this," Williams said, drawing a vertical line on the blackboard to explain why the class should not have drawn a right angle to calculate the plane's descent in a word problem.

"I don't like planes," Williams said, smiling shyly. "And I certainly wouldn't like them if they went like that." The students snickered.

In his reserved way, Williams has touched the hearts and minds of students at Longfellow, where he has taught for nine years.

For his contributions to education, Williams has been named Teacher of the Year by the Fairfax County school system and has joined other regional winners to receive The Washington Post's Agnes Meyer Outstanding Teacher Award.

"I teach basically because it's fun," said Williams, whose Subaru wagon sports a vanity tag that reads "PI 3 14" and whose desk bears a sign that advises "If you can do better, please do it!"

Williams's love for math came early, he said, when "great" teachers turned him on to the subject while he was a student at Paul Junior High School in the District.

"I'm a traditional, pretty much old-fashioned teacher and I love learning because of it," said Williams. "I kept thinking, if going to school is this good, maybe I should go to school until I retire."

At Longfellow, Williams teaches gifted seventh- and eighth-graders who study everything from sequences and series to algebra and geometry. In working with advanced students, Williams said the key is "letting them know that their intelligence doesn't threaten you.

"Don't look at them like 'who do you think you are,' " Williams said. "If they disagree with you, once they know they can do that, they know they can share their ideas."

Williams prefers not to disclose his age, saying, "It's kind of a game I play with the kids.

"You can do all the math you want and you won't figure out how old I am," he chided them last week, after overhearing a group of his eighth-grade students guessing about his age.

He graduated from the University of Maryland in 1972 and taught previously at Hayfield Secondary and Glasgow Intermediate schools in Fairfax County. He was nominated for the award by Marcy Paskowitz, whose son, James, is a student.

"We've had many good teachers in the school system but we've never had any that have shown what he has," Paskowitz said. "I'd personally like to capture and bottle what he does so that every teacher could use it. A more caring person can't be found."

Seventh-grader Jennifer Burris used to hate math, but under Williams's direction, she has grown to love the subject. "If you need help, he's always there to help you," Jennifer said after math class last week. "He's made it fun. It's just not plain math to me."

Parents, students and administrators alike describe Williams as a modest man, a confidant of students, and a tough but fair teacher. They point to his willingness to go that extra step, by calling parents to discuss their child's progress or by coming early or staying late to tutor.

Under his direction, Longfellow math teams have won several awards, including first place in the competitive Virginia Math League, for almost a decade.

"There's a great demand to be in his classes," said Assistant Principal Vincent Lynch, who added that Williams's classes embody "critical thinking at its best. We have people up in the high schools telling us that his students are among the best prepared for further math courses."

"If you just give them something new, those kids will eat up knowledge," Williams said. "You can almost see it on their faces, and that's what I try to do."