Like most of the Rev. Jesse Jackson's crowds, this one was on its feet the other day, gladly and loudly reciting his oath:

"I am somebody. I am somebody. Respect me. Protect me. Never neglect me. My mind is a pearl. I can learn anything in the world. I am somebody."

It has happened before. But the crowd this time was a joint session of the Texas legislature, and the magnetic Jackson, preaching a rather conservative gospel of self discipline, good education and racial harmony, brought down the house. And the senate.

As he rode away, Jackson elbowed a visitor and whispered his own disbelief: "The... Texas... state... legislature!"

Just the night before, in New Orleans, he had similarly roused a crowd of 65,000 students, teachers, parents and others, overwhelmingly black, in the Superdome as he inaugurated his "Push-for-Excellence" (Push-Excel) school program in two high schools in that city. He exacted from students raised-hand promises of harder study and greater discipline and from their parents an oath to better supervise their children's schooling.

Largely untested, its long-range impact unknown as yet, Push-Excel is nonetheless reaching across America into a growing number of troubled and in some cases desperate schools. These school grounds have become battle grounds, as Jackson puts it.

Increasing amounts of money are being put into local schools for Push-Excel. The federal government has given $425,000 already to Jackson and contemplates $3 million more over the next three years. In some quarters there is a fear that if this approach doesn't help the schools after years of unsuccessful innovations, then maybe nothing will.

Much of Jackson's success lies in the common appeal of his message to blacks and whites, liberals and conservatives: through hard work, self discipline and equal educational opportunity, blacks can get ahead; then jobs and paychecks will replace welfare and crime.

He denounces dope, pornography, teen-age sex and a general national pursuit of pleasure as barriers to achievement.

To blacks he preaches racial pride, to whites equal opportunity.

It is not so much a school program as a set of values. It meshes with a growing national conservatism in politics and individual behavior as well as a return to basics in the schools.

"We feel like it's a movement," says Marie Langie, director of Push-Excel in New Orleans.

"We're going into this with our eyes open," said Louisiana school superintendent Kelly Nix of Push-Excel's untested impact and of past educational innovations now being discarded.

The broad appeal of Push-Excel was illustrated in Louisiana. Nix was elected state superintendent in 1976 after calling for a return to teaching basic skills (two years of high school English have since been added). Then the legislature's black caucus asked Nix, a conservative white, to support Push-Excel programs in the state.

He did, the governor did, and the legislature voted $300,000.

"We needed something to motivate the lower socio-economic groups," Nix said. Eventually, six schools in the state, with black, Cajun and poor white students, will have such programs.

"We hope to see results," Nix said the other night at the Superdome, with partial results visible in the crowded stands around him. "But we may never know. If this doesn't work, there really is not a great deal left. But I think it will work."

In Los Angeles, Push-Excel has been accompanied by reductions in absenteeism, tardiness, vandalism and assaults on teachers.

The program itself is a blend of packaging, payroll and personality.

The wrapping is signed pledges by teachers, parents and students to do more and to do better, for students to turn off the television and the radio and the telephone in favor of homework, and for parents to get to know their children's teachers and to take a more active role in school affairs.

Money pays a teacher's aide to hold group counseling sessions with students, to raise each one's belief in his or her abilities. A fulltime paid community liaison worker helps parents keep their part of the bargain, because Push-Excel, though offered in schools, is basically a voluntary effort.

But the personality is all Jackson's. The 37-year-old civil rights minister can show up in an open-necked two-piece bush-cut suit in New Orleans one night and in a three-piece gray Givenchy here the next day -- and get identical responses from different audiences.

For three years he has been spreading the word of Push-Excel, the educational effort of his Chicago-based People United to Save Humanity. Push-Excel is at work in perhaps 12 to 15 communities.

One of this state's most formidable lobbying groups, the Texas Automobile Dealers Association, provided plane and pilot to fly Jackson from New Orleans.

Al Edwards, a black freshman state representative from Houston, arranged for Jackson's visit here to promote educational programs and budgets now facing the legislature but not a specific Push-Excel program yet.

While Jackson's movement is aimed at education, it is also a civil rights movement. Students, he says, should be given a diploma in one hand and a voter's registration card in the other. "That is the way," he tells his audiences, "to stop being 'them' or 'those students' in the eyes of politicians and to become 'my distinguished constituents.'"

And so in Austin, Republican Gov. William P. Clements canceled a trip to hear Jackson's speech. In New Orleans, U.S. Rep. David Treen, a Republican candidate for governor, attended a luncheon with 1,200 Jackson followers.

"No side of town has a monopoly on genius," Jackson told his mostly black audience in New Orleans. To that he added in Austin: "No side of town has a monopoly on dope, no side of town has a monopoly on family breakups."

Part of the difficulty in assessing the impact of Push-Excel lies in the broad nature of Jackson's challenge. "We are now trying to shift the winds," Jackson said in an interview, "to shift prevailing attitudes, to shift prevailing values."

"Hands that picked cotton in 1960," he told the Superdome, "will pick presidents in 1980." Evidence of the possibly changing winds was the 6-year-old girl who introduced Jackson and brought 65,000 people to a standing cheer: "I am somebody," she recited. "I can learn anything. I can achieve."