Yikes! Article I, Section 8 is a list of what they are allowed to do. Schools aren't here.
Since you haven't ever read the Constitution, here is the list:
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;To borrow on the credit of the United States;
To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes;
To establish a uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;
To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;
To provide for the Punishment of counterfeiting the Securities and current Coin of the United States;
To establish Post Offices and Post Roads;
To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;
To constitute Tribunals inferior to the supreme Court;
To define and punish Piracies and Felonies committed on the high Seas, and Offenses against the Law of Nations;
To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water;
To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years;
To provide and maintain a Navy;
To make Rules for the Government and Regulation of the land and naval Forces;
To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress;
To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the Erection of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings; And
To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.
This is what the 10th amendment means when it states: "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"
The powers not delegated - meaning, Article I Section 8, also meaning, there is no constitutional requirement for there to be "prohibitions". That's propaganda promoted by progressives. Everything is prohibited unless specifically granted. That's the plain language.
This is simple stuff here.
See my post #63, where I excerpted the Georgia Constitution. Check your own state's constitution.
Then from your excerpt from the US Constitution:
To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution.
From paragraph #1 in your enumeration we see
The Congress shall have Power To ... provide for the common Defense and general Welfare of the United States.
An educated public can certainly be intrinsic to the "general welfare" of the Nation. Jefferson dwells on this at length; and, his arguments make sense. It must have made sense to a lot of Congresscritters in the interum.