I should do that with my husband! I need some new tech.

I keep my phone in my purse...if I get a notification (email/text), I'll glance at it and act on it only if it's important. If it's a phone call, I'll only answer if it's my mom (who only calls if it's something important) or my husband. Every one else goes to voice mail.

Using a different ring tone for important contacts takes care of the need to even glance at the phone.

But doesn't really help if it's on vibrate. And you'll probably still need to interact with the phone to at least turn of the ringer if its not somebody you want to answer, lest you annoy everyone around you by letting it continue to ring.