Rules of Logicology

 A real, sane school would have a logical times table.

 Once you understand how multiplication works through the 1s and 2s, you don't bother to individually work it out. You just memorize a big table.

 Likewise integration. What's the integral of cosecant? Once you CAN  work it out for yourself, there's no point in doing so. Let someone else do it and look up their answer.

 Likewise, logic is very simple. It's modus ponens and modus tollens. The +1 and -1. However, you don't want to be laboriously proving a multiplication table and the quadratic formula and the integral of Euler series starting from counting each and every time. Much as there are lists of fallacies, there should be lists of common logical isomorphisms.

 E.g. there's a bunch of distinct subtypes of proof by contradiction.

 Logic is in fact geometric. Why isn't there an algebra and geometry and logic class?

 E.g. there's the free_will/determinism shape where the response called for is identical regardless of what your priors are. Convergent logic.