They don’t have any. I’ve noticed this in CT’s opinions in Morse, Brown v. EMA, and Safford v. Redding. This article sums it up nicely.

Morse v. Frederick
In a concurrence in a 2007 decision restricting the school speech rights of students, Justice Thomas said he would go further than the court’s majority and overrule the landmark decision in Tinker v. Des Moines Independent Community School District.

 [I]n the earliest public schools, teachers taught, and students listened. Teachers commanded, and students obeyed. … In the name of the First Amendment, Tinkerhas undermined the traditional authority of teachers to maintain order in publicschools. 

 

Safford Unified School District v.Redding
Justice Thomas dissented from a 2009 decision that a strip search by school officials of a 13-year-old student violated the Fourth Amendment’s guarantee against unreasonable searches and seizures.

 [T]he most constitutionally sound approach to the question of applying the Fourth Amendment in local public schools would in fact be the complete restoration of the common-law doctrine of in loco parentis. … So empowered [in the early years of U.S. public schooling], schoolteachers and administrators had almost complete discretion to establish and enforce the rules they believed were necessary to maintain control over theirclassrooms. 

 

Brown v. Entertainment Merchants Association
In a dissent from a decision this year striking down California’s attempt to regulate the sale of violent video games to minors, Justice Thomas wrote at length about the originalist understanding of the rights of children, both in school and in society at large.

 The historical evidence shows that the founding generation believed parents had absolute authority over their minor children and expected parents to use that authority to direct the proper development of their children. It would be absurd to suggest that such a society understood ‘the freedom of speech’ to include a right to speak to minors [or a corresponding right of minors to access speech] without going through the minors’ parents. 

 

Zelman v. Simmons-Harris
In a concurrence in a 2002 decision upholding a state-funded voucher program allowing poor children in Cleveland to attend private schools, including religious schools, Justice Thomas said that urban school systems were failing minority students.

 Frederick Douglass once said that ‘education means emancipation. It means light and liberty. It means the uplifting of the soul of man into the glorious light of truth, the light by which men can only be made free.’ Today many of our inner-city public schools deny emancipation to urban minority students. … [P]ublicly funded private school choice … programs address the root of the problem with failing urban public schools that disproportionately affect minority students.