I don't know what state you're in, but here in CA, I have found the back-country 1-room school houses to be basically poor places to hunt (in so far as coins go, anyhow).
You've got to figure that back before the age of autos (say, prior to the mid-teens or whatever), whenever 5 or 7 neighbors had 15 or 20 kids between them all, they'd erect a 1-room school house. And these could be a little as 4 or 5 miles apart, dotting country roads all throughout back-countries. They could be short-lived little affairs lasting as little as a year or two, or maybe 10 or 15 yrs, or whatever. They faded away in the age of automobiles, as the little schools gave way to the bigger consilidated schools, or bussing them to town, etc... So very few of these schools tend to have lasted later than about 1920 (unless of course, they were the consolidation point of mulitple other smaller ones).
And the demographics of kids in the 1800s, and through the teens, was to have zero (read, "zero") coins to carry around, to begin with kids. There was simply no need. I've hit SOOOO many of these, that I know for a fact are virgin, yet tend to find no coins. I'll get buttons, suspender clips, pencil tops, harmonica reeds, rivots, etc... showing me the site is virgin, yet nothing of value. Or if I DO get a coin, an interesting pattern developes: Let's say the school existed from 1888 to 1918. Oddly, the only coin to surface will usually tend to be a teens wheatie, for instance. I think to myself "bingo, a seated or IH is sure to pop up next". But try as I may, it'll be the only coin. I've seen this repeated again and again.
I used to laugh at the oldtimers who grew up before, and during the depression, who would say "we never had any money to carry when we were kids". I used to think that was just cutsie sayings, platitudes, poor memories, etc... But the more and more I hunted 1-room school houses, the more I realized there was a truth to it.
I've seen this same demographics played out at urban schools too: For anyone who's hunted since the 1970s, back when urban schools were still fairly virgin, they'll see this demographics played out too: If a school, for example, were built in the teens or '20s, the coin-spread is never evenly spread throughout the decades. The vast majority of coin finds were and are always from the 1940s/50s losses. Ie.: a lot of post-war silver losses (mercs, roosies, etc.. and if the mercs were teens, they were more worn evidencing longer circulation). We used to reason that the reason for this, was the older silver, from the earlier days of the school, must simply be deeper than our old TRs could reach. But occasionally when we would find a crisp (early loss) early dated wheatie or V-nickel or whatever, we would notice that depth was not the issue. And later, when deep-seeking machines allowed us to punch deeper, there was never a "magical layer" of the "next 100 silvers", that was simply older than the strata we'd already farmed out. So why isn't the decade of the teens and '20s having just as many coins (assuming student populations were relative)? Because of the demographics of wealth at the time. The post-war generation was very affluent, compared to the depression and earlier. It became nothing for kids in the 1950s to have coins in their pocket, especially with the introduction with school lunch programs, milk-money, etc....
About the only time country school yards will have coins (beyond flukes) is if the school were also used for adult purposes. Like some of the doubled as grange halls, community rooms, churches on Sundays, dances, etc....
JMHO