SANTIAGO (Guardian) -- The nascent government of Chilean President Michelle Bachelet is facing its first major challenge with riots, strikes and a countrywide boycott by more than a million students.

A national strike called by the Coordinating Assembly of Grade School Students paralyzed the Chilean education system on Monday.

Teenagers occupied schools, barricading the entrances with desks, while riots raged for 10 hours in Santiago as police used tear gas and water cannon on marching students. Around 370 people were arrested.

The students, who raised their complaints four weeks ago, are demanding free use of public transport, lower fees for college entrance exams and a voice in government policy.

At the base of their protest is the demand for a potent upgrade of the public school system.

A full 50% of high school graduates fail the college entrance exam. In private schools, 91% of students pass the exam and have the opportunity to continue studying.

Last night, the Chilean senate was meeting in a special session to hear students' complaints.

President Bachelet, who came to power three months ago, has already offered an emergency spending bill of some $60m (£32m) in response to protesters' demands.

The offer was rejected by students, who, in addition to extra finance, are demanding a prominent voice in education policy.

Monday's strike was the largest in Chilean history. Authorities were stunned by the organization of the protest, now widely known as "the march of the penguins" - in reference to the protesters' school uniforms.

Using the internet and cell phones, the students have rewritten the rules of dissent with their ability instantly to organize marches and make collective decisions.

The organizers are very young, with an average age of 16, and their support goes all the way down to 11-year-olds, who organize forums and debate the right to a free education, turning their break into a civics lesson.

Hundreds of colleges are occupied and classes have been cancelled for the past 10 days. -----Alliances

Alliances between poor students at state schools and pupils in the private education system have erased the usual class lines that mark Chilean social protests.

"In any other country, the fact that 5,000 students are marching through the streets demanding a better education would be the object of national pride," said María Jesús Sanhueza, 16, a spokeswoman for the students. "The government should be thanking us, not beating us down."

Admiration for the students is nearly universal, with some 87% of Chileans polled saying they support the movement.

"These are not crazy revolutionaries," wrote Patricio Fernández, an influential columnist in the Clinic newspaper. "Their parents support them. Their cousins, their neighbors, their old aunts. They are bored that the wealthy schools educate those who will be boss, while their school trains them to be workers. More than combating Chilean authorities, they are convincing them."

Despite government efforts to reach a quick agreement, students are digging in.

In a sign that the movement is spreading, most universities also shut down on Monday and the teachers' union went on strike. Thousands of shop owners refused to open in solidarity.

Complaints of brutal police tactics at recent marches have heightened the tension between Carabineros de Chile, the national police force, and the public, leading to further violence.