If you're in a state that isn't regressive, teach your kids to jaywalk. It changes your view from focusing on the traffic signals to what the cars are actually doing. I don't think I go a single day without seeing a car flagrantly run a red light. There are no more rules and kids need to understand that.
Seconded. On bicycle, I learned the Idaho stop techniques - treating stop signs as yield signs, and treating red lights as stop signs.
The most important thing I got out of this experience is that traffic signs and lights are suggestions. A red light usually means stop, but sometimes it is safe to go. A green light usually means go, but sometimes I must stop to avoid getting T-boned or cut off.
The only absolute rules of traffic are observation and physics. I predict other road users' behaviors and avert dangers, regardless of what the traffic signs/signals say or even if they're absent. For example, I slow down or stop near blind corners, even if there is no stop sign - and there have been times when vehicles popped out. I always look left and right even when I have the right of way, even when crossing a green light, because time and time again this trust has been broken.
At my university, the drivers are very used to stopping to let students cross, but a lot of people don't seem to look around or even lift their eyes from their phones. If I tried doing that, I'd be really nervous that I would be the one where a driver unfortunately doesn't stop in time. I really don't get those people.
I don't think GP is suggesting that you step out in front of cars and hope for the best, but rather that you cross in places other than those which have been deemed for crossing. In theory, walking a half mile to a crosswalk, waiting 30 seconds, crossing when okayed by the light, and walking a half mile back should be "safer". But just walking across the road when safe requires an understanding of how traffic works and how to judge safety.
It might be Baader-Meinhoff phenomonon, but In the past two days I've seen multiple pickup trucks hopping the curb in places that I find shocking, so I'm becoming more inclined toward taking safety into ones own hands. The system clearly isn't working.