Why is it bad to treat "Considering the hour" as a participial phrase?

All things considered, I'm on your side on this one, Faldage.

But, seriously, how does it advance the argument by even mentioning parts of speech [if that's what they are] such as "prepositions" or "participles"? Those terms may have some meaning for the initiated, but the initiated are already initiated.

We need to get to the uninitiated -- the one's who are being left behind. Surely, every educator can agree about that.

Let's approach this from a different angle -- the angle of "Common Sense Writing".

Let's ask students without any comprehension of terms like "prepositions" or "participles", and certainly no affection for them, to judge particular examples by their sound.

I would call this part of the lesson "sound judgment".

Let's use your own examples, Faldage.

1. "Considering the hour, [we should wrap this up]", and

2. "Into the house, I saw a cat"

My guess is that most kids in Grade 6 [or above] would tell you Example #1 sounds OK, and Example #2 doesn't make any sense -- even if they can't tell the difference between a dangling participle and a dangling fishing pole.

Any kid who says OK to Example #1 and "Huh?" to Example #2, would get a pass in "Sound Judgment", and that's that.

Any kid who thinks Example #2 makes sense, certainly needs help, but teaching them the meaning of "prepositions" and "participles" is like putting a kid who failed Grade 6 into Grade 10 to straighten them out.

Anyone who has a taste for this type of esoterica, should write learned essays about it to the profession. But are children under the age of consent fitting subjects for this sort of thing?