Recess Temperatures

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Our school recently informed the elementary teachers that students are not allowed outside for recess when it is below 40 degrees. I'm trying to find some info or statistics as to safe temperatures, or even recommendations as to specific temps and windchills. As a high school teacher who teaches these elementary kids in the summer, I'm trying to imagine a day with them cooped up inside like this. No wonder my friends in the elementary school are complaining. These kids need to run, even if only for 10 minutes!

I have found policies from different schools. One school in Texas has a cutoff of 55, and then some in the north, such as in Minnesota lets them out at 0.

Our superintendent likes cold hard facts, statistics and charts, and instead of grumbling to each other, I think the teachers just need to present their case to the Super. (Don't get me wrong, I think this guy is the best thing to happen to us, and I know he would listen). Seems every school has it's own policy, but if I could get some statistics from national studies, doctors, etc., I'd appreciate it! I'm not having any luck.