So I'm running a D&D 3.5 game right now with 4 friends, soon to be 5. I was talking with one of them after a session asking what they thought I could do to improve the campaign and they recommended that I find ways to engage the players so that they're thinking about the game away from the table. As I see it, this could have several advantages, if I get my players pondering what happened in the campaign when the campaign isn't happening, I believe it will do a great deal to increase immersion, as nothing is better for getting players to engage with a campaign then to have them thinking a great deal about it.
As things stand, while my players love the sessions, they spend so little time thinking about the campaign out of session that they often forget their character's stats and have trouble staying in character or recognizing that I'm talking to them when I mention their character's name. I'm really hoping that, by thinking about the campaign more, they'll be more absorbed in their characters and that will increase the quality of the roleplay.
So far, I've thought about running parallel plot lines to increase intrigue (e.g. is this dead nobleman part of the Nightmask's plot to take over the city or part of the machinations of the local wizard guild to accrue power in the city... or both? Which should we pursue first?). I think the kind of engagement I'm hoping to inspire is the kind of way I engage with Game of Thrones for instance - where I can't help but think about who is Azor Ahai or what 'x' character will be up to next.
Are there some common techniques used by DMs for engagning players between games? Looking for a experienced based answer.