Inside the buzzing classroom of Old Marshall School, Jack O'Connell, state superintendent of public instruction, looked over Adrienne Wyman's shoulder, scanning a fraction worksheet.
"What's the common denominator on that guy?" he asked a hesitating Wyman. She buried her left hand in her hair.

Wyman was getting a lesson from a man who since January has been the state's highest elected education official. It was his last night class of the six-week summer session, during which O'Connell has helped a half-dozen students prepare for the General Education Degree exam, the equivalent to a high school diploma.

He taught once a week this year after teaching twice a week last year.

"I get to stay connected to the classroom, and I thoroughly enjoy the teaching environment," he said.

As a statewide elected official, O'Connell is mandated to travel with a protective officer. A California Highway Patrol officer in a gray suit lurked in the hallways of the midtown school.

Another student, observing O'Connell's suit, briefcase and ramrod posture, thought he was in the FBI. So the student asked about his day job.

"I told him I am the state superintendent of public instruction," O'Connell said. "He just glossed over it -- 'OK, what about this algebra problem?' "

Wyman, who is hoping to trade her career as a hairstylist to become a nurse, said she suspected O'Connell was a politician.

"After he was describing the Legislature, it made it really exciting to be here in the capital," she said. "He's a great teacher. He's a natural."

O'Connell recounts some humbling moments with a smile and an attendance roster in his hand. He had to give his fingerprints to qualify to teach, and he has to keep accurate attendance rolls like any other teacher.

The toughest part about teaching again, he said, was adjusting after a window air conditioner broke. "And the paperwork," he said, waving his attendance sheets, "needs to be streamlined."

O'Connell was the first person in his family to graduate from college. After he earned a teaching credential at California State University, Long Beach, in 1975, he taught high school and adult night school in Southern California. It had been more than 20 years since he last taught when he arrived at the Old Marshall School last summer.

His political career included a stint on the Santa Barbara County school board, three terms in the Assembly and two in the Senate. In November, he was elected to take the place of Delaine Eastin, who had filled the office for eight years.

In the Legislature, he championed educational issues, including higher teachers' salaries, reduced classroom size and a 55 percent majority rule on votes over school funding. The 55 percent rule, which replaced the two-thirds majority, bolstered schools with millions of dollars in bond funding.

O'Connell spent Monday delivering a morning speech in Orange County and lunching with officials in San Francisco before teaching the night class.

On the previous Monday, he led a social science discussion, but he leaves politics out of the class.

Stepping back into the world of elected office, O'Connell said he opposes the upcoming vote to recall Gov. Gray Davis. As a high school government teacher, he said, he taught students that the recall was reserved for malfeasance in office, not philosophical differences.

Mary Prather, Old Marshall School principal, invited O'Connell to the school, as she has with other political leaders. She said she holds back on lobbying him about needs in the school's specialties -- adult education and English as a second language. But she welcomes his first-hand attention.

"We're affecting the lives of individuals," she said. "Some of these people are working hard, but they can't advance without a degree."

Next summer, O'Connell said, he plans to teach again -- "if my principal lets me," he said, grinning at Prather.

"We'll see how his evaluation comes out," she said, laughing.