[XorNot]

The point I was driving at is we still end up with people who don't understand basic algebraic manipulations. So the issue isn't "you never did math", the issue is we're failing to get people to understand it.

The converse side of the idea - which I'm presently experiencing - is to definitionally heavy and try and show the proofs for all sorts of things. From my personal experience, this is equally as bad - I have real difficulty following proofs, where applying the results of said proofs is straightforward - easier to memorize, and apply, and slowly from that work backwards to figure out what the ramifications are elsewhere. But that's a process which takes years - I have 1 semester so in a practical sense memorization is the key.