Molly - here's some thinking:
I do think it's silly to assume that mothers then (or fathers either) NEVER swatted their children. Never smacked them on the bottom to get them going? Why do you label it "American-style"? Even Greek schoolmasters in the Golden Age used a good swat to keep discipline! Spanking of children has been prevalent throughout history (Augustine is a good example) and is not a recent "American-style" thing.
Besides, the "style" of the punishment is NOT the issue here. The issue is, is corporal punishment encouraged? Yes it is. You just can't get away from that, although you may try :) And if a beating with a rod was condoned (which is rather tough!), then lesser forms would certainly be allowed.
Yes, I'm aware that many ancient peoples had a different view of the afterlife (esp. the Greeks), although I think David shows in the Psalms that he certainly understood it, as a man who understood God's own heart. He did not see merely a place of dead people. He referred to a pit, and removal from God's presence. No one is saying that spankings alone are going to keep someone out of eternal perdition. But even the OT Jews would see this as "corporal punishment keeps a child away from death." It helps children avoid dangerous options. Death comes from sin. Punishment helps to avoid sin. It is a deterrent, and the change in behavior steers the child toward righteousness. Isn't that rather plain?
As an aside, Jerome's Latin translation in 400 AD translates "sheol" as "inferno."
And I must say that when God put his words into men's mouths even thousands of years ago, he still had all his children in mind. He designed his word to be clear, and to be eternally helpful. The concepts given are not only culturally applicable 3000 years ago. God wrote his eternal word to be accessible to us without being scholars of ancient culture.
My hubby is checking the Latin, Greek and Hebrew. He's my resident language scholar. All the words used in the verse in question, which are translated "child" repeatedly in English translations, literally mean "boy" (Latin) or "child" (Greek) or "boy" (Hebrew). This last, from the Hebrew, can be translated as "babe, boy, child, lad, servant, young man" in English. The term applies to anyone from infancy to adolescence. And the Jews really wouldn't have seen a teenager as, well, a teenager. (Now that IS an American invention!) A boy became a man at 12. So a boy would be 11 or under. My husband used his Hebrew Bible, an online Strong's Concordance, and his Hebrew lexicon (Davidson) - which defines the word as a "male infant." One other verse that uses the same word is Ex. 2:6 (baby Moses in the basket); it's also translated as "son" and "youth" in OT passages.