And the center-right government of President Sebastián Piñera once more looked powerless to curtail the anger in the streets.

The country, seen as a model of progress since dictator Augusto Pinochet’s iron grip slipped 21 years ago, continues to be buffeted by the most serious and sustained protests in a generation of democracy. That has raised an uncomfortable question: Why do so many Chileans — tens of thousands in the streets, millions more who say they support the protesters — believe that their country has failed to address widespread needs, beginning with an education system that even the government acknowledges has flaws.

At the center of the discontent has been the Piñera administration, in office less than a year and a half, and its seeming inability to placate the protesters.

“There are consequences for the government, which has demonstrated a low capacity for governance, of preparation or of perhaps not comprehending what’s happening in Chile,” said Sergio Bitar, a former education minister. “That means an important weakening.”

The ostensible reason for the protests is a drive, years in the making, to overturn Chile’s complex, multi-tier university and secondary school systems, which have a high level of private participation and lag in educating the working class and poor.

Since May, that has resulted in a most unusual uprising in this country of 17 million — classes canceled in dozens of high schools nationwide, with students commandeering campuses and joining thousands of university youths on the streets of Santiago and other cities.

In some cases, groups of students as young as 14 have sought the advice of lawyers as they have negotiated with school administrators. The police have stood back as students, carrying blankets and snacks packed by their parents, have taken over high school classrooms, staying overnight for weeks on end. The protests have included attention-grabbing stunts — such as 30-minute “kiss-ins” and choreographed dancing to the music of Lady Gaga.

It is an eye-catching way to win attention for serious demands.

“We are waiting for a response from the government,” said Valentina Cerda, 18, a high school senior who, with a group of friends, has seized part of one school. “If not, we could be at this until the end of the year.”

A year ago, as the government grappled with an earthquake and then the rescue of 33 trapped miners, Piñera’s popularity topped 60 percent. Today, it has dropped to 26 percent, and a majority of Chileans said in a recent poll that they oppose the “for-profit” education system in place since the middle of Pinochet’s 17-year rule.

Mario Waissbluth, a university professor and head of a group called Education 2020, said the protests are symptoms of a broader restlessness about an economic system that has not delivered prosperity to all Chileans, even as it recorded high growth rates.

“What the government offers is the same as the ’80s model, a little of this, a little of that, with a little more money,” Waissbluth said. “If the government does not negotiate the basic educational model, we will have a country in conflict until the end of his presidency.”

Many analysts say that is an exaggeration. Indeed, some who have closely studied educational issues said the government’s recent offers may lead to talks.

“I don’t think the students can keep up their movement on the streets,” said Harald Beyer of the Center for Public Studies.

The government’s proposals have included removing the education minister, directing $4 billion toward an education fund, increasing scholarships and drastically lowering what officials have considered onerously high interest rates for student loans. The government will not do away with private institutions, as many students demand, but has offered a constitutional amendment guaranteeing a quality education.

“We have listened, we have heard and, I want to stress, we are closer than it has appeared,” Felipe Bulnes, the new education minister, said in a nationally televised speech Wednesday, referring to the possibility of a negotiated solution.

In many ways, the dispute is rooted in ideology — on one side, a market-friendly government, and on the other, youthful leaders who believe the inequities in society signal the need for another economic model.

Both offer data to buttress their case. The government notes that Chile will grow 6 percent this year, unemployment is low, inflation is in check. The students say Chile remains a country with vast income inequality. (U.N. data show that is true but indicate the gap is less than in the past.)

“We are seen as an example to be followed,” Camila Vallejo, president of the University of Chile Student Federation, said in an interview. “But we have a 30-year system whose time is up.”

On the streets and in the schools, many simply talk about the burden of paying tuition and loans, or dealing with an education system that falls short in the country’s poorest districts.

Sebastian Sandoval, 18 and in high school, suggested that the government shift funding from the military and other areas to education.

“Many people believe that education can be improved in Chile,” he said. “Chile has the resources to do it.”