No. The constitution deals with citizens. Whether we define as citizens Free White Males Over 21 Who Own Land, or whether we define it slightly more broadly, we still only apply it to citizens. If we want to define citizens so broadly that it includes children, then we can, but as far as I can tell, given that you have to be 21 to buy a handgun or practice medicine, 18 to vote or join the army, it is clear that we do not give the same rights and responsibilities to children as we do to adults. (This assumes school uniforms refers to school uniforms for minors, not for college students.)
Child-hater
Do you support the UN Treaty on the Rights of a Child or whatever? >P