It works that way here, too (late drop offs) except for that its when its RAINING (at least half if not 2/3s of the time.
Ditto, its because parents don't want their kids out in the weather. Matters not that xyz could take care if "it" (warmer clothes, rain gear, etc.). Some parents just ARE NOT going to do xyz (because they can't or because they choose not to).
Our school closed the parking lot.
So there aren't kids in it. Ever.
Instead, parents drop kids off at the curb. So there are no kids crossing and its a MUCH larger space (rings the whole school).
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I think your idea sounds reasonable, HOWEVER it will only take care of SOME of the problem AND creates budget problems (if kids are indoors, they need people to supervise), AND creates definition problems (I consider 'cold' to be between 32&60. I'm more 'warm' in 31 to -20 than 30's. So if the policy changes to 'below freezing'... Some parents will get upset / want it changed to 40's others to 50's others adamant its not cold until negative numbers, etc. So there will be lots of 'dialogue' (arguing).
Which is probably what the school is looking at. Because it won't fix the problem (just alleviate SOME), but create more... Its not worth it to them.
I don't know what your schools layout is, but our school's solution MAY work:
Dear Students & Families,
Because of the ongoing problems in the parking lot, the parking lot will now be closed 30 min before and after drop off & pickup times. Parents may continue to drop off at the curb, but may no longer drop off in the parking lot.