Disclaimer: I am not a grammatician (if there even is such a word). I usually rely on my instincts, and sometimes a sentence just dosen’t sound “right”.
Anyway, inspired by gitfiddle’s GQ thread, and TJVM’s post therein, I checked out what level of English language proficiency is needed for US citizenship.
Both of the following sentences are quoted directly from CIS’ Sample Sentences for Written English Testing.
So, are these sentences grammatically correct, and if not, why?
Gracias.
Perfectly correct English sentences.
I suppose this one’s technically not correct since it breaks the supposed rule about not ending a sentence with a preposition. This rule would lead to the more correct (and colloquially rather absurd) version:
It is a good job with which to start.
No, no, NO! There is NO reason not to end an English sentence with a preposition. The very idea that this might be the case is an old canard invented by stuffy people who decided that since you can’t end a Latin sentence with a preposition, you shouldn’t end an English sentence with one, either. This is ridiculous, since English is not a Latin-based language.
Case in point: Child asks dad to get a book from downstairs for a bedtime story. Dad brings up a book about Australia, which is not the book the kid wants. Child asks, “What did you bring that book I didn’t want to be read to about down under up for?” Ends in six prepositions.
This is the sort of thing up with which we will not put. 
Well, it’s an interesting example, but not a great case in point. Given that it’s almost incomprehensible, it actually is making the opposite case from the one you intended. I don’t like people going all fascist about sentence endings, but I would argue that ending a sentence with a preposition or six can sometimes confuse the meaning.
I agree that both sentences are fine grammatically. The second sounds a little odd to my ear, but only because it strikes me as an odd way to express the idea. Probably if I hung around a dfferent set of people or read a different sort of books it wouldn’t stand out at all. Or perhaps I’ve just looked at it too long.
“Down Under” isn’t a preposition (nor two prepositions), it’s a noun. Way I’ve heard the sentence usually is “Why did you bring that book I don’t want to be read to out of up for?”
But, yeah, anyway - there’s nothing incorrect about ending sentences with “prepositions” (scare quotes to indicate that in many of the cases people complain about, they’re not actually prepositions at all, but parts of phrasal verbs.)
Anyway, the second sentence is at very least stilted and poorly-written.
You mean “We are very smart to learn this”?
It parses perfectly naturally to me. I can’t figure out what the objection with this sentence could be.
Amateur. Father, who is habitually henpecked, embarks on a lame explanation that does not impress the child, who sighs and says “Will you get your excuse for what you brought that book I don’t like to be read to out of about Down Under up for over with?”.
I think it sounds strange to many native English speakers (well, at least me and Excalibre) not because of the strict syntax, but because it doesn’t really express a complete thought. A slight shift in tense would make a clear thought, however, so it comes across just as odd to native speakers, rather than as complete nonsense.
In other words, it’s not clear whether the sentence is saying
“We’re smart [because we made the good choice] to have learned this.” ; “We would be smart to [make the good choice to] learn this [in the future].” ; or “Learning this shows that we’re smart.[past or future]”
So syntactically it may be fine, but it’s not a very good demonstration sentence.
Well, of course I would never use a preposition to end a sentence up with, because it might be difficult to make sense out of, and, after all, what would I want to use a preposition to finish a sentence that you cannot make any sense out of up with for?
From It was a Dark & Stormy Night: The Final Conflict
I think if the sentences sound a little odd, it’s because they’d normally contain contractions. “It’s a good job to start with.” “We’re very smart to learn this.” Both of those sound more natural to me. But there’s nothing ungrammatical about the original examples.
I agree with Quercus, in that the oddity of “We are very smart to learn this.” has more to do with tense than anything else.
It feels as though there are two implied, yet undefined, opposing tenses fighting against each other in the same sentence. Though grammtically correct, it sounds…off.
“We are very smart to learn this” doesn’t communicate a clear idea to this native English speaker. What is common is a construction like “it was very smart of you to do that.” But the way the example is worded, I don’t know what it’s supposed to mean, and I’ve never come across anyone using a sentence like it.
Excalibre made a point above about phrasal verbs which was apparently missed by many. In English, we often take an intransitive verb (one that doesn’t take an object, such as “look”) and effectively make it into a transitive verb by adding a preposition (such as “look at”). This combination can be thought of as an intransitive verb followed by a preposition (and then the preposition’s object), which is the old style of viewing it, or a more modern way is to think of “look at” as a whole, as a transitive verb, and these are called “phrasal verbs.” The nice thing about this idea is that it’s more intuitive, closer to what the speaker means. My understanding is that most sentences that get ended with prepositions are, in this view, ended by part of the phrasal verb, and that it’s uncommon to end a sentence with a preposition that’s not part of a phrasal verb. I hope this makes sense - IANAG.
I believe the word you are looking for is grammarian.
And when I wish to avoid ending a sentence with a preposition (without sounding stilted), I simply append "motherf*cker to the end of it. I find that tends to satisfy the needs of any insufferable pedants within earshot.
At least someone got that joke.
I like it. You are a true [del]grammatician[/del] grammarian.
This looks like a pretty typical German sentence to me. 
Re: “We are very smart to learn this.”
I have seen sentences very like this. Probably in educational or moralistic books written for children with a bit of a smug and condescending air.