Rva-diggin, you say:
"
I've been wanting to hunt some school grounds behind my house but can't find out if I will break any laws or not"
If you wonder if there's any "
laws" that address your intended activity, where they live, then all you need to do is this: Go to your city's (or county if in the case of county owned property) website. Afterall, practically every city and county seat has a website nowadays, right? On there, there is usually a menu option for codes, laws, or city ordinances, or the park section has their park rules, and so forth, right? Simply see there if there's any prohibitions against metal detecting on city land (parks, schools, etc...). Do a key-word search, for instance, with variations of "metal detector(s)" etc... If it is silent on the issue, then I'll be durned, I guess there's no laws

And if there's no website to find this, then for sure the city hall or county offices will have their charter, law-book, etc... out on the front desk, for public viewing, since it's public domain info. Just leaf through it. If it's silent on the issue, well then so be it
Next, you give the ARPA text link. This is a
federal level land law, and therefore has nothing to do with
county of
city level land laws. Ie.: just because the federal runs their parks in a certain way, does not mean county and city parks are bound by that.
The only exception to this would be if a county or state SPECIFICALLY incoorporated it into their own rules, by specific
written inclusion into their wording. Sometimes, yes: cities and counties borrow from each other's wordings, decades (or centuries) earlier, and simply quote, word for word, from neighboring cities, counties, or their state, or the fed's wordings on a particular topic. So in that case, if they said ".... as per ARPA...", then sure, it would apply. But if not, then the fed. parks can have different rules than podunk city or county parks can have. In the same way that parks have different "rules" all the time, right? Ie.: one allows alcahol, while another doesn't. One allows overnight camping, while another closes at sunset. And so forth.
A final thought on this: If you were to ask some city or county person (instead of the preferred method of looking it up for yourself, as I outline above), and they were to cite ARPA as their reason for saying "no": Just be aware that
THEY TOO might be mistaken about the different layers of laws, and simply assume that since their county is a part of the larger state, which is a part of the larger fed, that therefore they must be bound by the higher fed. rules. That's why it's better to look it up for yourself. Because there are many many examples that float on forums, of people asking, and getting a "no", when no real prohibitions exist. Simply someone saying "no" and simply morph something else to apply to apply to your "pressing question", when odds are, no one would ever have cared or noticed you.