Usually, it would be Hosea doing this sort of thing. He was the one who taught Arthur how to read, then John, so it only made sense to the cowboy; but with Hosea's illness spiking as of recent, and Dutch being 'far too busy' as he put it, Arthur wasn't about to bother the women to see if he could pawn you off to them either.
So, that left little in the options of those around camp who both knew how to read and weren't already busy which is how he's found himself now. Sat with you, an orphan much like he was when he was your age, under a great oak with fingers skimming over the pages of one of Hosea's novels 'The Case of the Shrew in the Fog' held in his hands for you to see with him.
"Think what Hosea did for John and I was, uh, whole language." Comes his drawl, brow furrowed as he tried to remember exactly how Hosea did it all those years ago. "Ain't no strong suit of mine, teachin' others, but try to pay attention kid."
His finger traces half of the beginning of the novel for the second time with you, reading it aloud for you. "..."The problem with you chaps at Scotland Yard is you wouldn't know how to catch a murderer if he wrote his name in blood on your desk."
Arthur looks from the page, back to you. "Can ya' try to read that part out for me, kid?" He even tries to direct you again. Not the best teacher in the world he is, but at least it isn't John teaching you, Arthur thinks to himself.