The teachers' union says Neil M. Gorsuch has a record on students with disabilities that raises questions about whether he would stand up for such students.
The justices returned the case on transgender rights in schools to a lower court in light of Trump administration's withdrawal of Obama-era guidance on gender identity.
School groups, as well as several former U.S. secretaries of education, are on opposite sides of the major U.S. Supreme Court case on transgender student rights.
The court's clerk admonished lawyers whose friend-of-the-court briefs refer to the transgender male student in the case as "her" on their covers rather than "him."
A Virginia school board and the ACLU urge the justices to decide if Title IX requires schools to permit transgender students to use restrooms corresponding to their gender identity.
In an argument that touched on school websites, the justices consider a North Carolina law barring those on a sex-offender registry from accessing commercial social media sites.
The high court asked lawyers for the Gloucester County, Va., school board and Gavin Grimm to file letters by next week on how the case set for argument should proceed.
The Trump administration sends a letter to the justices informing them of its withdrawal of guidance on transgender students in schools issued under President Barack Obama.
The justices gave a unanimous, but for now partial, victory to the family that sued a Michigan district after the district barred a service dog for a child with cerebral palsy.
With the Senate Judiciary Committee set to consider Judge Neil M. Gorsuch for the U.S. Supreme Court on March 20, the Alliance for Justice issues a report critical of the nominee.