It's that time again!
Ending sentences in a preposition. Ah, of course you know this one, good reader! That's incorrect!
All right, can you tell me why?
...Right. The best explanation I have ever heard is one for the clarity of the sentence in question. This being clear, obviously a sentence changed around to avoid putting a preposition at the end when this makes it more difficult to understand is something up with which one should not put.*
The explanation that I believe is that some scholars thought that Latin was superior to language because...because it is! It's older, and it's the scholarly language!
But English has Germanic roots. Trying to make it look like Latin is going to end up being silly, confusing, or both.
The point of language is, and always has been, communication. The idea of knowing proper grammar is that this allows one to use it. There are instances where grammatical inaccuracies are meaningless, and therefore we can assume them to mean the closest correct thing. There are places where they mean something else, and what a reader/listener should be able to assume is that the statement being made is the one the writer/speaker intends.
On these grounds, I would say that clarity should be valued above accuracy. This does not mean accuracy is valueless. Accuracy feeds into clarity. If both the person communicating and the person understanding agree on what is correct, it will make communication and clarity much easier.
On these grounds, I would say that both
"What did you step on?"
"On what did you step?"
Are perfectly fine. The former might be slightly easier to understand, but both should be understandable to a fluent English speaker.
Unnecessary prepositions are improper regardless of their placement. For instance:
"I fell off of my bike,"
can simply be
"I fell of my bike."
Even though the preposition is in the middle of the sentence, that preposition is still sloppy, because it is an additional syllable that gives no additional information. The one exception to this would be when and author is establishing an accent. Then it is still wrong, just not sloppy. It adds information.
Incidentally, there is one type of sentence where the preposition at the end burns me. Dad, if you're reading this, you're going to wince.
"On what did you step on?"
Just...gah. The person is trying to correct the sentence--because there is no accent I know of that would start the sentence with, "On what," like that, I will assume this--and then goes on to make the 'mistake' that person was trying to avoid.
Beginning, end, middle, just don't sandwich.
* I am perfectly aware that the original quote could have been rendered, "I will not put up with that sort of pedantry." But this raises the question of why that is any more correct than, "That is the sort of pedantry I will not put up with," in the first place.