David Santos paces back and forth before the blackboard, introducing mathematical formulas as if he were showing off prize-winning thoroughbreds. He points out the finer features of Vandermonde's Convolution and other showpieces of numbers theory.
On this hot July morning, he faces a room of math-hungry teen-agers who are devoting seven hours a day to this subject at the Center for Talented Youth Program at Johns Hopkins University.
"Numbers theory is the only branch of mathematics where you can name more than five problems that haven't been solved for over 100 years. It's a fairly classical and difficult area of math," says the 27-year-old professor. "I see it as an intellectual construction, like art, as something to be admired. In numbers theory, we are interested in problems such as, 'Is every even integer the sum of two primes?' "
Dr. Santos and his class are working in a summer educational program in which students ages 12 to 16 study such subjects as math, science, creative writing and art history with accomplished teachers just itching to work with such dedicated children. Each of two summer sessions this year offered 17 courses for 260 students taught by 36 teachers.
Many of the instructors, recruited from around the country, live in nearby dorms and eat in the same cafeteria with the students during the three-week program. They spend seven hours a day passing on knowledge and, sometimes, advice.
"It's quite rewarding to work with these talented students," says Dr. Santos, a Puerto Rican mathematician and assistant professor at the University of North Texas. "Not only are they interested in solving problems, but they're also interested in posing problems."
The university established the Center for Talented Youth Program in 1979. Each summer, the center runs a dozen residential and commuter programs on campuses around the country. Students take accelerated courses in such subjects as psychology, etymology, geology, biology, writing, logic and genealogy. A semester's worth of college-level material is often covered in each three-week session.
Because the courses depend upon students' abilities in verbal and mathematical reasoning, the program chooses its participants by their scores on the 11th-grade Scholastic Assessment Test.
"They're basically all very positive children," says microbiology professor Jeff Morse. "Not all of them are here at their own wish -- some parents see this as a way to a fancy school -- but once they are here, they will spend three weeks tackling a semester-long college course done in an appropriate fashion for high school students."
Mr. Morse, who has taught science at the center for the past eight summers, represents the high standards for instructors: He illustrates a lesson about the basics of biological energy with a Sony Walkman, and he's a master at presenting vivid examples of how abstract principles affect his students' lives.
He says the intensity of this program brings him closer to students in three weeks than do his yearlong courses at William Penn Charter School, an independent high school in Philadelphia. "I get letters every year from former CTY students telling me they're graduating from Yale and going on to this or that research project," he says. "I also get other kinds of letters, like the seven-page letter from one boy lamenting the distance between himself and some of his CTY friends."
Many teachers in this program respond to the center's ads in various national magazines. Many more apply because they've heard praise from others.
'This joyful thing'
Take 33-year-old Julia Miller, a doctoral candidate and teaching assistant at SUNY Buffalo who is instructing "thirteen 13-year-olds!" on how to write essays.
"I came because I believe I have something to give kids who are on the edge of their lives, who are realizing that the things they believed as children don't fit what they see. Writing is important to helping sort out the process of the gap between childhood dreams and adolescent realities. I wanted to be present to try to change and enlarge their vision.
"What I didn't expect was what I was going to get: the students' exuberance and passion. They don't know what writer's block is yet or how to criticize themselves so fiercely that they will block. They love their own work. And I am reminded that writing can be this joyful thing."
For Kirsten Rinkelberg, a doctoral candidate and teacher in 20th-century art at the University of North Carolina, teaching talented middle-school students means being in a room "where people are paying attention, where none of them are hung over or asleep or ignoring me." Her history of art course teaches students to look critically at images rather than memorize dates and styles.
Mathematician Jeff Grell, who is getting his Ph.D. at Johns Hopkins, hopes eventually to start a program like this back home in Trinidad. He instructs a class with some of the youngest students, all working through algebra II and geometry at their own pace with the help of tutors. The center's system of education adjusts its curriculum to match individual students' levels of learning.
Not kid stuff
"You can more or less give these students a free hand," says Mr. Grell. "They can go to the book on their own, although you must guide and monitor their progress."
He gazes in admiration at the 14 youngsters sitting quietly at their desks, poring over textbooks while many of their pals back home are swimming, doing kid stuff.
"I don't think I had seven hours of schoolwork a day until I reached university level," he says.
"Most of these students cope well, which is surprising, because they don't come from that sort of educational background. Some of them are accustomed to breezing through school.
"Most seem to rise to this challenge. What provides the $l motivation is that they are truly interested in the material. They like what they're doing."
It's a scene, replicated many times across campus, that recalls teachers' own memories of the pleasures of learning.
"For me, mathematics was the only academic subject I enjoyed," Mr. Grell says. "I can still spend a whole night happily working on math."