Emily Z. Gardiner is sitting in a tiny plastic chair that is so low to the ground she is practically squatting. Her knees barely fit under the round table in the storage room where she tutors youngsters from Timber Lane Elementary School on the fine points of reading and arithmetic.

Today, Gardiner has second graders Chris O'Connor and D.J. Dbrouski reciting the multiples of four.

"Four, eight, 12, 16, 24," said Chris.

"Now dear, what comes after 16? Twenty, right?" gently corrected Gardiner.

The youngster smiled sheepishly and began the sequence again.

Gardiner, who has volunteered her teaching skills to the Falls Church school four days a week since October, has brought more than her infinite patience and her kind nature to the small number of youngsters she tutors.

"She brings her training, her expertise, her level of concern and real caring," said Cos Renzi, principal at Timber Lane. "She helps the kids see their own goals."

Gardiner, who politely but sternly refuses to reveal her age, has taught reading and mathematics for more than 25 years at The Kingsbury Center in Washington, a private, nonprofit school for youngsters and adults with learning disabilities. She says that nothing in the world gives her greater pleasure than helping a child learn to read.

"One very rarely in my position as a tutor can teach a child to read . . . . You're mostly filling in the gaps" from the regular classroom, Gardiner said. "But sometimes you get a child to tutor who doesn't really know how to read at all . . . and it's like opening a new life to them."

Gardiner, who says she is a direct descendent of William Floyd, one of the signers of the Declaration of Independence, and whose American roots date to 1698, started her career as a tutor in the 1950s when her husband Arthur was transferred to Pakistan on assignment for the U.S. Foreign Service. After Pakistan, the couple lived in Vietnam and Japan before they returned to Fairfax County in 1965.

"As a Foreign Service wife I couldn't have a job . . . . I've done volunteer work all my life," she said. "I'm sort of a jack-of-all-trades, master of none."

But to the children with whom Gardiner shares her secrets of memorizing multiplication tables and pronouncing odd-looking words such as "whole," the native New Yorker holds the key that turns learning into something fun.

"When I first came [to see Gardiner], I was really embarrassed because I didn't know anything," said D.J., 8. "But she made it a a lot easier for me to do math."

Suzanne A. Zunzer, director of The Kingsbury Center, said that what makes Gardiner so adroit at teaching young pupils is her uncanny insight into a child's emotional, as well as academic, well being. Zunzer, who has worked with Gardiner for 19 years, said Gardiner looks beyond the books and numbers to understand a child's learning weaknesses.

"She helps the youngsters become joyful, able and coping children . . . and is willing to go the step beyond to find what works with a child," Zunzer said. "She helps the [pupil] become a joyful, able coping child."

Fairfax County school officials said that in the 1984-85 school year, 51,535 volunteers donated a total of 1,138,756 hours to various education programs in the area. Officials said that if these volunteers -- tutors, chaperones and library aides, among others -- were paid the $5.79-per-hour rate for a beginning teacher's aide, it would cost the school system an additional $6.5 million a year.

Gardiner does not plan to retire from her teaching duties soon. "The tutoring is wonderful for me," said Gardiner, her soft blue eyes glistening with enthusiasm. "I can feel tired when I go to teach and then [start the lesson] and feel marvelous," she said. "Children have an enormous desire to learn, and all you have to do is open the door."

When Gardiner is not tutoring at Timber Lane or The Kingsbury Center, making games and puzzles for her students at home or shopping for new learning tools and ideas, she is puttering in the flower garden at her McLean residence or attending civic group meetings all over the area.

"She is full of warmth, wisdom and kindness," said Zunzer of The Kingsbury Center. "She is very perceptive and has spent her entire life giving herself to living things."