My high school was heavily focused on Latin and ancient Greek. We spent the first two years grokking grammar and semantics. Then, in liceo (the last 3 years) we would study history by translating and studying poems, speeches, plays...
Teacher and students used to discuss for hours about the meaning and context of this or that sentence. It was a wonderful way to understand our ancestors' mindset. Dead languages are the best tools for a deeper appreciation of history.
German has specific prepositions I recognize as equivalent to each main Greek preposition as defined in that chart, except maybe the distinction between εις and εν, which German would handle by a noun case distinction (ancient Greek εις την θαλασσαν → German ins Meer (accusative, < "in das"), ancient Greek εν τῃ θαλασσῃ → German im Meer (ablative, < "in dem"). German breaks up some meanings differently -- "among" is unter (shared with "beneath" rather than "between") -- but anyway there are other languages with a pretty nice set of prepositions!
Picking up latin as an italian seems far simpler (and probably more useful) than as an english, as you can guess large part of the lexicon and you will be exposed to "volgare" (transitional latin-italian) when studying early italian literature.
But would studying Old English be of any use for italians? I am not sure.
The United States is largely monolingual in English for a thousand miles, and the language ideology here causes immigrants to want their children to shift to English monolingualism as quickly as possible. And thus bad Latin is more useful than bad German.
I've visited Mexico with my Spanish-speaking wife (semi-natively) and while the locals loved to hear her speak their language, we communicated mostly in English if we wanted to be easily understood.
The struggle is real for Americans, or for native English speakers as a whole. For Americans, there is no other language spoken for thousands of miles like you mentioned (Mexico and Quebec (to a limited extent)), and even then, most of the people we interact with on vacation will speak English.
I put serious effort into maintain my German, and she puts serious effort into maintaining her Spanish. But we rarely have the chance to actually use it, even if we're in a country that speaks the language. English has won.
I have been learning Chinese in China for about 7 months, and have a functional command of most conversations because I never ever use English during those conversations. English will always win if you keep biking with the training wheels on.
When I lived in Cambodia for an even longer time I didnt learn nearly as much Khmer because I was constantly speaking in English, even though I diligently listened to Khmer conversations and researched the language. Like programming, language learning is much slower as a spectator sport.
In my travels, I've yet to run into someone who I really need to talk to who only speaks their native (non-English) language.
And feel free to drop me a mail and have a call if you want. :)
There's this common argument that prescribes utility to studying Latin via the value you gain by understanding biological, legal, and religious terminology.
I think that the net utility that you gain through this mechanism is approximately zero. Or rather, the net utility over other, more direct methods of acquiring this knowledge is zero. I think you could gain the requisite understanding of Latin to gain 99% of this utility in a few weeks of study, and that if understanding these roots is so important it should be material in our English classes, not in a long-term study of the Latin language itself.
Besides the "it helps you to know roots" argument, the study of a language gains utility largely in being able to speak the language, make do when traveling to places where the language is spoken, or consume the literature and media in the language. Moreover, the utility you gain from the language increases exponentially - a year of (half-assed, high-school-level) study is pretty useless, but after a few years of it, especially with higher (college-level?) standards, it's immensely useful because it opens you up to whole new worlds.
I think the best argument for teaching languages in high school is that this exponential growth starts earlier and is more likely to ever happen (especially for people who don't go to college or don't study languages there) if we start earlier.
Granted, there's utility gained from appreciating the culture of the language even as you learn the beginnings of it in high school, but I think that's dwarfed by the long-term potential for useful bilingualism and having the ability to more more easily experience new cultures.
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also, anecdotally, my bad Latin has given me essentially 0 utility in my entire life since high school. Perhaps I got a few novelty realizations here and there, like identifying that "tractor" came from "trahere" and "et" means "and" in "et cetera", but those are trivial. Maybe my experience was unusual and others gained more from it. Also, admittedly, I can't really quantify or remember whether it improved my SAT scores or whatnot, but my overall assessment is that my Latin study was negligible.
Arguably, you could say that about many bodies of knowledge as much as Latin. The question is really: What percentage of people take that mandatory one year minimum of high school language and really build it into something valuable? I think it's pretty low. And,
bad German < bad Latin < good Latin < good German
U.S. school systems generally are simply unwilling to invest the resources needed to get kids really bilingual.
I do think that if all language programs are bad at a school then bad-Spanish would still have a higher utility than bad-Latin.
I actually got to do lots of creative problem solving somehow, but I understand how many did not. Coding is where that really took off but I did math contests and stuff when I was younger.
I took Latin in high school and felt that I wasted four years I could have spent learning (rudimentary) Spanish, or at least something that had any cultural relevance at all. You have to find a way to make kids care about it as well as justifying its utility.
I see Latin and Greek education as historical relics, akin to how we used to emphasizing testing students' ability to construct shapes with compasses and straightedges, or their ability to memorize bible verses.