Gunfighter,
The 10th amendment says this:
"The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people."
One of the powers delegated to the US in Article I is this:
"The Congress shall have power to lay and collect taxes, duties, imposts and excises, to pay the debts and provide for the common defense and general welfare of the United States; but all duties, imposts and excises shall be uniform throughout the United States;"
Notice that Congress can tax to "provide for the ... general welfare." Already in the 1830s, Joseph Story in his commentaries on the Constitution exhaustively analyzed and rejected the argument that this only entails the ability to spend on things that are elsewhere authorized, and even then the arguments were not original. (In brief, if that were true, then the "Necessary and proper" clause would already cover it, so the "general welfare" clause would be completely redundant, and we shouldn't interpret a clause to be redundant if we can help it).
So the tenth amendment doesn't apply, because the power to spend, in most cases, IS delegated to Congress. That includes things like spending on schools.
It might or might not be a good idea, but it's not unconstitutional.