Final answer:
The constitutional protection that best applies to college students demonstrating peacefully against tuition increases is the First Amendment, guaranteeing the right to peaceably assemble and petition the government.
Step-by-step explanation:
Students at a public university demonstrating against an increase in the cost of college tuition are protected by the First Amendment to the United States Constitution, which guarantees freedoms concerning religion, expression, assembly, and the right to petition. It specifically includes the right of the people to peaceably assemble, and to petition their government for a redress of grievances. Therefore, a peaceful protest addressing the escalation of tuition falls precisely under these protections.
The relevant protection in this scenario is the First Amendment, which protects the students' right to organize a peaceful demonstration. The Tinker v. Des Moines case, where the Supreme Court upheld the right to wear armbands in protest on public school grounds, further confirms that peaceful protest is a protected form of speech in educational settings. As long as the protest remains peaceful and does not disrupt the educational process or violate other laws (such as property destruction), the students are within their constitutional rights to demonstrate.