> If you speak math problems to your child you are… wait for it… teaching them arithmetic. That’s what teaching is.

Exposure to something and being taught something are usually recognized as being quite different, but it is clear now that you just want to play a game of semantics, so we can put and end to that.

> I doubt a kid would even pick up language if you never spoke to them directly, and instead they just heard bits in passing between adults.

Kids not being able pick up on language by listening to a recording of adults speaking about some random thing is supported by the research so there is likely some validity to the latter half of your claim, with some assumptions about what you mean about "heard in passing", but the research also strongly suggests that kids can pick up on language if those adults are surrounded by additional context. For example, if adults in the same room were talking about a visible object in front of them then the research suggests that the child would be able to pick up the language even when not directly spoken to.

Why do you doubt the research?