1. Get a frequency list. The most common word's rank is 1, the second is 2, etc. [0]
2. Then use your favorite Spaced Repetition Software (such as anki) to learn the words in that order.
3. Define a sentence's difficulty as the maximum rank over all its words. You could refine it by adding tie-breakers but I think it doesn't matter. Then sort the sentences in order of difficulty.
[0] See https://en.wiktionary.org/wiki/Wiktionary:Frequency_lists
Clozemaster's a game to learn and practice a language in context. The objective is to fill in the missing word in a given sentence for thousands of sentences. The missing word is the most difficult word in the sentence according to a frequency list for the language, and the Fluency Fast Track feature allows you to play a sentence for each unique missing word in order of difficulty like you described.
As a Spanish learner with a strong foundation but struggling to get over the next hurdle this is just perfect. Thanks for this link!
The word "run" is a relatively high frequency word. How many different meanings for "run" does a learner need to know? Is that in isolation? With collocations? As phrasal verbs?
In many languages, the most frequently appearing words also have the most varied meanings. Interestingly, many highly vernacular languages also use relatively few words, but those words have a lot of meanings that are clearly known by the speech communities.
FWIW, some theoretical linguists consider this a non-issue. People in the field (i.e., people might die if I get this wrong) know otherwise.
While your idea sounds nice in principle, I hope you will accept the idea that reality may be slightly more complex.
* Collins Cobuild has 50+ meanings for "run" if phrasal verbs are included. Most non-native speakers are not even aware of the potential breadth of meanings it offers.
I'm a somewhat experienced language learner. I'm fully aware that words have multiple meanings but that's not as problematic as you think. A lot of distinct meanings of "run" are related, so it's not like you need to memorize every one individually. Besides, they aren't all equally important. In many cases, those different meanings are paralled in my native language (or another language I know), e.g you can translate "run" as "correr" in "he runs", "the river runs..." and "they ran the risk...". More to the point, I always study words in context. In this method the context is provided by the rest of the sentence.
The other side of the coin is that the long tail is long:
the frequency of any word in a corpus is inversely proportional to its rank in the frequency table. For large corpora, about 40% to 60% of the words are hapax legomena [words appearing exactly once], and another 10% to 15% are dis legomena[words appearing exactly twice]. Thus, in the Brown Corpus of American English, about half of the 50,000 words are hapax legomena within that corpus. https://en.wikipedia.org/wiki/Hapax_legomenon
So the chance of seeing a hapax in any given sentence is really high.
What's worse, the more rare words in a sentence are often the important content words. When I try to decipher sentences in some language I don't know much of, what I end up understanding is often something like "And then he XXXXX-ed the YYYYY just like that hahaha" (I understood 8/10 words! And I even know that word 4 is a past tense verb! But not at all the meaning).
(Not that you shouldn't study the most frequent first, that's still a good rule.)
Effectively none of the English-speaking world would bother to say "Sochi" without the olympics, but they knew the English language and had enough culture to understand from context that it is a place in Russia which hosted the 2014 winter olympics.
If you know enough of the language that you can ask "what's that?" at a non-disruptive rate in conversation (or look it up quickly in a dictionary or encyclopedia), I think that counts as good enough.
That's an important point. Knowing 80% of the words in a text doesn't mean you understand 80% of its meaning, that is, you probably wouldn't get high marks on a basic comprehension test.
I've seen some studies that indicate you need to know at least (around) 95% of the words in a text in order to understand it "enough" of it. (I don't have the links right now but could look it up at home if you're interested).