By Katherine Mangan

Waco, Tex.

When Edward B. Burger presents a math challenge to his class at Baylor University, he paces the aisles and pairs students together. "I want to hear chattering," he says. Before long, students are laughing and shouting out answers. He dashes to the chalkboard to scribble them down, creating long rows of numbers topped with running stick figures.

Mr. Burger, 46, who is visiting from Williams College, keeps up a rapid-fire banter with his students, whom he calls by name.

He is here this semester as a recipient of Baylor's annual Robert Foster Cherry Award for Great Teaching, which came with $215,000 in cash and $35,000 for Williams's math department.

The 12-member committee that culled more than 100 nominations from around the country was impressed with his string of teaching awards, his multimedia textbooks and videos for secondary schools, and his televised analysis of the math behind the 2010 Winter Olympics.

Mr. Burger was younger than the students he's teaching at Baylor when he discovered how much fun teaching math could be. Armed with a lesson plan and a conviction that he could cut through his classmates' collective fog, he asked his high-school teacher if she'd step aside and let him teach two classes.

"She agreed, and at the age of 17, I stood up in front of a precalculus class of about 40 students who looked at me like I was the biggest nerd in the world," says Mr. Burger.

He began teaching night classes at Austin Community College at age 22, while he was working on his doctorate at the University of Texas at Austin. "What I was trying to do was to take really complex, intricate, abstract ideas of mathematics and make them come to life for these students," he says. He began encouraging students to be creative and take risks, and even bases a portion of their grades on "the quality of their failure."

He judges that quality, he says, "by the size of the risk they've taken and the amount of insight they have generated from their mistakes."

In 1990 he received a tenure-track position at Williams, where he is also a professor of social responsibility and personal ethics. The most important issue, he says, is what students will retain from his class 10 years later. "If we are in the business of transforming lives and can't give a good answer to that question," he says, "we're failing."

To demonstrate the concept of infinity to a class of mostly liberal-arts students at Baylor, he sketches a trough that he describes as containing an infinite number of Ping-Pong balls, which are falling into a barrel, 10 at a time, as a hypothetical student reaches in and plucks balls out at shorter and shorter intervals.

"Soon you'll be working faster than the speed of sound, than the speed of light. You black out, regain consciousness, approach the barrel, look inside. My question to you is, 'What's inside? What is in the barrel?'"

The students pair up at their desks and compare guesses. "It has to be infinity," one says. His partner responds, "He's trying to trick us. ... Maybe the answer's zero." Mr. Burger writes these and other guesses, which he draws out of more-hesitant students, on the board. He tells the class to come back on Tuesday for the answer.

Adam Telatovich, a sophomore math major, says some of his favorite lessons in Mr. Burger's number-theory class follow that pattern. "He starts out with a big picture, describing these really far-out problems, and says this is what we're going to work up to. Then he builds up suspense and leaves the punch line for the next class. When the class is over, we're disappointed."

Lance L. Littlejohn, chairman of the department of mathematics at Baylor, describes Mr. Burger as "a teaching phenomenon": well organized, articulate, and engaging.

At Williams, when his students arrive for the first day of class, they sometimes tell him that they've already had him in a course. That's because he wrote an online, multimedia math textbook used in many classrooms nationwide. California just started a pilot program in which middle-school students are given iPads to read his textbook and watch his lecture series.

Mr. Burger, who once planned to go to law school, discourages students from zeroing in too early on a career. "The whole point of higher education is to mess things up and challenge basic assumptions about how you look at the world and fit into it," he says. "If you don't allow your education to challenge those assumptions, there's no point in it."

He advises students to choose their careers by finding things they would do on their own for fun. "On good days," he says, "I almost feel it's criminal to accept money for what I do."

This fall he's stimulating discussion about good teaching across the Baylor campus by helping to organize weekly lunch discussions for faculty members. He will also speak this week to a regional meeting of K-12 math teachers and plans to visit local public schools to meet with math teachers and students. "He's wonderful in the college classroom," says Heidi J. Hornik, a professor of art history and chair of the Cherry award committee, "but he also reaches deep down into the academic system to make math exciting for everyone."

By the way, the answer to the question about the number of Ping-Pong balls in the barrel: zero.