The student movement that began at the University of California at Berkeley in 1964

The university of Berkeley is a very prestige college in California

The student movement that began at the University of California at Berkeley in 1964 was the Free Speech Movement.

Explanation:

The Free Speech Movement (FSM) was a student protest that was launched in 1964 at the University of California at Berkeley in response to the university executive's restrictions on student political groups. Its informal leaders were students Mario Savio, Hal Draper, Brian Turner, Steve Weissman, Art Goldberg, Bettina Aptheke and Jackie Goldberg. This type of event was completely new for the time. Students protested the university administration's ban on political activities on campus.

The Free Speech Movement called for recognition of students' freedom of expression and academic freedom.