I was recently told a true story by a former student, one many horn teachers have heard.
He inherited several young private students from another teacher. This teacher was a brass player but not a horn player. One of them he was told going in could only play three or four notes even though he had taken a number of private lessons already. In the first lesson, sure enough, the student could only play three or four notes. He had been rented a single B-flat horn; the former teacher had him using fingerings for single F horn. The problem is obvious; of course he could only play three or four notes! In one lesson my student had the young hornist playing a full octave of range with the right fingerings.
There are many lessons for us from this. One would hope that the topic of single F and single B-flat horns would be discussed clearly in a methods class, but that is not always the case. And anyway, there are many brass players that do not have a music education background teaching young hornists. The horn is confusing to teach for non-hornists. In my new book, Introducing the Horn, I cover the topic of single F and single B-flat horns pretty thoroughly, and in my main site I have some good basic information on both instruments (with photos) in Getting Started on the Horn.