Head-first and Once more unto the breach, dear friends, once more1
I find myself straddling several points here. As a good and faithful servant of SE, I looked to Meta Stack Exchange for some guidance. Well, for a bit anyway. My largest concern was the part about the goal of getting answers for one, or for many, users. Partially from the OP's question and partly from an answer. I believe that the focus on that point leads to implicit guidance on many other points.
In several posts, across multiple sites and within the chatrooms, I've encountered the idea that the goal of SE, in general, is to be a repository of knowledge, curated by the users, for all of the Web to access. To quote from our site's tour page, "With your help, we're working together to build a library of detailed answers to every question about Computer Science education." Now, with only 8+ months in Beta, it's hard to imagine that we can even begin to answer every question about Computer Science education, but that is the goal, nonetheless.
Frequently I have seen it said that an answer that only works for one user, has no value to anyone else. The so-called "too localized" questions. I just knew there had to be a canonical answer on Meta SE about such questions. To my surprise I found the opposite. I've never heard of user Jaydles before, and I'm not 100% certain that the profile can be trusted, but it lays claim to "VP & GM of Stack Overflow." Maybe not a perfect spokesperson for the question, but reasonably close. For full-disclosure, there is a bit of debate between him and Jeff Atwood, who seems to be a rather authoritative voice on SE as well. In any case, the upshot of Jaydles answer is that a question that ends up helping tens of thousands of people is good, "[b]ut helping 100 people is pretty good, too, and helping 1 is better than 0". He adds, in large bold type, "Questions should NOT be closed simply because they only help one, or too few people, but patterns of questions that threaten the greater good should eventually be made off-limits."
Of course, Stack Overflow has been around a lot longer than we have, and there is no reason we cannot learn from their lessons, and avoid some problems they have figured out how to avoid. We also are not Stack Overflow, and have a different user expectation, and some of what didn't work there might work here, and some of what did work there might not do so well here. We will have to find, and strike, our own balance between helping users and building the site. Any good question is likely to help more than one person anyway. As the user base grows, currently only 4,089 users with 152 at 200+ rep, we might have to further limit questions using some criteria or another. I doubt that required context is it, however.
Considering that our stated objective is to answer every question about Computer Science education, we must allow every question. We cannot have the answer to a question not asked. Even with that in mind, we still should have some kind of limits. We cannot, for example, have the answers to questions such as "What is the best programming language to present to Masters Candidates in the Class of 2024?" Prognosticators we are not. Other questions, most notably lists, AKA "shopping questions", just don't fit well on most SE sites. (We are slightly more tolerant than some sites, and reviewing this post might be helpful in that regard.) Still, that leaves a lot of questions that just cannot be answered with good answers and that are not worth keeping around for the ages. Finding, and closing, those questions, after we figure out what they are, will be a "process" the site follows as long as it exists. What merits closure is likely to continuously evolve as our site marches through time as well.
The sample question given by the OP is probably not a good choice for presenting the OP's case either. It seems to be thought out, researched, and coherent. It provides enough context to present the problem succinctly without getting into the gray area of being a one-person answer. The subject does not need context relative to "things like subject matter, age group, teaching style, etc." In fact, the potential issue is relevant to all CS education as given, even though presented in a programming context. As such answers can be helpful to the asker, and to future readers.
Additionally, a question might receive answers from different contexts, as happens most of the time on other sites network-wide. All those questions may very well be equally "correct" within their context, or as a whole. As an example, this question on Stack Overflow received 4 answers in 13 minutes. According to the voting, all are "correct" and remain in the top 5 after the 7+ years the question has been there. That OP selected one as his choice of "best" answer, not the same as "the single correct" answer. From personal experience I can say that the top rated, and/or accepted answer is not always the one that solves my problem. Three examples where my vote went to a "lessor" answer recently have dealt with
bin in the
PATH environment variable, working with GPG keys, and installing the bootloader. The popup "hints" for the voting do not say "This answer is correct" and "This answer is incorrect", they say "This answer is useful" and "This answer is not useful." So far having such a collection of correct answers, with various degrees of overall usefulness to other users has not broken the voting system of SO, and I doubt it will break the voting of CSE either.
In summary, I oppose the proposed rule to require questions to include explicit context generally. A question that needs it can have comments added, or be put on hold, but only if the question needs it, the same as any other defect in the question would call for a hold.
What are my thoughts on this?
What constitutes appropriate context?
As much as is needed, and only as much as is needed, to make the question clear. Maybe a lot, maybe none at all.
Is closing too extreme?
Since SE calls it "On Hold" for the first five days, it is not too extreme when it is warranted. It is too extreme if the question can stand, as is, even if more context might be helpful.
Can I suggest a more specific rule?
Yes. A rule of "non-thumb." A rule of thumb seldom works in the majority of cases for the long term. Such rules help make spontaneous decisions when limited facts are available and a decision must be made soon. Otherwise the thumb accounts for only 20% of the digits on your hand (typically) and has an average success rate nearly the same. (For blocking the sun when you need the greatest field of vision, however, the rule of thumb is perfect.)
Basically, every question deserves to be judged on its merits, not on the merits of previous questions, even when "similar."
1) William Shakespeare, Henry V, Act III, Scene I