Now I can't be certain that what I'm about to say applies to your advisor, but it does apply to many interactions. I've learned that with any advisor (given that you have adequately prepared yourself for your meetings) always err or the side of "appearing stupid" to trying to "interpret vague directions". Science is all about clarifying confusion, and asking "dumb questions". In fact, some of the best research has it's origin from scientist questioning something that "didn't quite make sense" to them. Most likely the questions you ask aren't dumb, and even if they are, hiding the misunderstanding will only lead it to be revealed at a later time. Even worse, something might seem vague or confusing because the advisor is wrong or hadn't thought out all the details. Never set out do something your advisor told you, when you don't understand, that usually leads to problems down the road. Instead ask for clarification, even if you think it will tarnish your reputation a bit. If he appears fussy now, oh well, you still need to learn. If you think he is the one who is wrong or vague, asking (politely) specific questions is the best non confrontational way of approaching the situation, so you two can discuss the issue and mutually come to a consensus (which might be a consensus to disagree - for now - and come back to it later). If he is a good advisor he will respect someone asking him questions.
I know you said "If I ask for clarification, I often get chastised because he sees nothing wrong with the bad directions he gave me." What exactly does he say? I can often think I am being chastised by someone who doesn't intend on that being the case. Without more detail than this, I'd like to give your advisor the benefit of the doubt. It's possible that he really is frustrated, but that may not be the case here.
Note that many advisors can appear agitated when they aren't in the slightest bit upset or annoyed. This can occur for a bunch of reasons, but two common ones are (1) the advisee is projecting his own feelings of inadequacy onto the advisor and assuming the advisor thinks bad things of the advisee, when he actually doesn't, (2) he makes scowling or upsetting facial expressions when he is confused or thinking hard (this may have nothing to do with you).
I suspect (1) is especially at play here. Graduate students (and sometimes even professors!) frequently suffer from an impostor syndrome (me included), and the description of your advisor relationship could go along these lines.
If your advisor focusses on fostering independence, his students are going to fail a bunch of times; he (hopefully) knows this and views it as a good thing (and I agree independence is a very good thing to foster!). Your advisor most likely knows that asking a "good research question" and coming up with procedures and algorithms on your own, with only vague tips, is very difficult. He has likely had many students fumble around for years with nothing to show for it until one day, with their hard work it eventually pays off. You will come to your advisor with "strange" ideas; that comes with the territory of being this kind of advisor. The key for you is to not let your frustration lead into thoughts about what your advisor thinks of you. I often spin stories in my head about how my advisor thinks about things I do. These thoughts are unhelpful, and while it's easier said than done you should try your hardest from going down this path. Beyond working hard, what your advisor thinks of you is out of your control. Ask him the stupid questions, the people who ask stupid questions are often the people who get ahead in life.
When I was in undergrad I asked professors, grad students, and peers all types of questions. I thought, what do I have to lose, I'm just an undergrad. When I got to graduate school, I all of a sudden shut the "question asking off" out of intimidation and now realize that this was a major mistake which hindered my success during my earlier years of graduate school.