I taught my two daughters to drive, along with driver’s ed. The things I emphasized after the basic car control were:
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Parking lots are dangerous! Seriously, people and cars are moving in all sorts of directions and you need to be watching for them everywhere. The speeds are low, so the consequences are usually minor fender-benders, but I’m sure there are more accidents in parking lots than anywhere else.
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Look way down the road. Think about what’s going on 1/4 mile or so ahead. You get many fewer surprises that way. Expect people to do dumb stuff and be ready for it.
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Keep driving the car! I always get annoyed by the phrase “the driver lost control.” What that almost always means is the driver gave up control. Maybe you are sliding and really can’t do anything, but you should keep trying because you can almost always have some effect on the car’s motion, and if not you can at least know that you tried everything you could.