After reading this post by Alexis, I have decide to change some things in my DMing methods. I am going to ditch the screen once and for all. I have been convinced for a long time now that running without the screen is better. I have talked about it and even tried it a couple times, but I was never committed to it. I always went back to it, at least for D&D, because of all the charts on the screen; they can prove to be so useful. If I really need them so badly I can print out a cheat sheet an store all the info I need immediately in a binder or folder.
I am also going to change my approach to teaching the game to new players. I have been used to a rotating cast of new or relatively new players changing every week due to my running for the tabletop club at CSUN. I would just tell the player what die to roll and then tell them what happened, I would not tell them why they were rolling or what their chance of success was or any basic principles of the game. And this worked because there were very few players who showed up every week and people enjoyed themselves and didn't have to worry about reading and memorizing a 300 page tome. In all my time at CSUN there was only one player who showed any interest in the actual rules and the book, though he had played 3.5 and 5e before, so that may have prompted him. I sent him a PDF of the Cyclopedia, but I don't think he actually went through it thoroughly.
To change this apathy in the rules I am going to actually try to teach the rules through play and maybe even give them some of the DM responsibilities such tracking npc hp. When I ask the players to roll I will tell them their chance of success and why they are making such a roll. Why are they making an ability check instead of a saving throw? why use wrestling rating instead of an ability check? why a to hit roll instead of an ability check, why does an ability adjustment apply here and not there? Simply put I will tell them what type of roll they are making, chances of success, bonuses or penalties, and the why of it all.
Also I am going to make a stronger effort to engage them in the fiction of the world; explain the possible motivations of npcs and why things happen the way they do. A goal here is to encourage cooperative play. All the players should work together toward a goal of their own choosing, not something I have dangled in front of them and they feel obligated to follow because "that's how you play D&D." I will try to encourage them when they suspect danger where there is none or they are foolhardy when they should be cautious. If there is some danger the players should be warned of it before it appears so they always have a choice, and have complete control of their characters' agency.