Utah has a daunting challenge: To maintain a respected education system even though the state has the nation's largest percentage of school-age children for its population and spends the fewest dollars per student for their schooling.

"Why, in the face of these challenges, can this state do well. . . ? It's because of a wonderful support system . . . and the PTA stands at the very center of that," James R. Moss, the state's superintendent of public instruction, told 2,000 parents and educators gathered Saturday night for the opening session of the 92nd annual National PTA Convention."You represent a force for good in public life that we deeply need," he told the group, which has more than 6.4 million members in its 26,300 local chapters nationwide.

"On behalf of the 400,000 young students in this state, I welcome you here," said Moss, who, with Gov. Norm Bangerter, greeted the PTA leaders gathered in the Salt Palace for the four-day convention.

The National PTA is in Salt Lake City to address issues ranging from AIDS education to children's self-esteem. Convention delegates will choose from nearly 50 workshops and training sessions during the session.

While stressing the benefits of PTA assistance in hard economic times, Moss credited Bangerter for the political will to stand behind a $160 million tax increase in 1987, "much of which went to support education."

"We're not a rich state," Moss said. But "I'm proud to report that Utah education is doing well," he said, pointing to higher-than-average ACT scores, strong advanced-placement programs and "high graduation rates."

Bangerter welcomed the PTA "because some of America's most important education leaders are here with us today." The organization, he said, is one of the major tools available today to address "the critical needs we have in this nation."

The governor identified difficulties in the area of education faced by the state, which has seen a 32 percent increase in the number of school-age children in the past 10 years. Most other states, Bangerter said, are seeing an enrollment decline.

The conference, with a theme of "Building Tomorrow Today," will also focus on serving the needs of minority families and developing school-linked health clinics, conference officials said.

The PTA has developed a number of nationwide programs, including the AIDS Education Project designed to assist parents in talking to their children about the fatal disease, the officials said.

U.S. Surgeon General C. Everett Koop will discuss AIDS education at the conference, and Dan Zucchi, publisher of Redbook magazine, will discuss child safety issues to be covered in an upcoming issue of the magazine.

Also, Olympic Gold Medal figure skater Peggy Fleming, the PTA's honorary membership chairman, will speak on parental involvement, and syndicated columnist Jack Anderson will appear as well.