It's from the Southern Harmony. William Walker had the published the first edition published in @1835. Click here for the music. Walker put his name on the tune. He would put his name on tunes he wrote himself or arranged from the oral tradition. If you get the 6/4 tunes like this one going at the right tempo, you can sometimes hear the original dance tune behind it. It was not unusual to use a secular tune for religious texts, but I'd also guess the school version is the modified one. A secular song as inspiration for a religious one was generally not of a religious nature at all. For parallel religious/secular songs see The Old Oaken Bucket (DT) and The Family Bible

I'll try to work the out later, but just looking at the middle line, where the melody is, I'd say it's what people have taken to calling modal. It's notated as A minor, but the melody has no 3rd & the 6th is used just once as a passing note. This makes it nicely pentatonic & neither major or minor. These can often sound strange & mysterious. The harmonies are minor. I did just try the treble, it uses just 5 notes. 1-5 of the minor scale. I like it.

A collection I have at home might have this tune & some additional notes. I'll check.