I have never heard of anything like that, and I have taken a number of ed classes and learned about a number of different progressive pedagogical and assessment methods. There is either more to this than we are hearing, or Hawaiian schools are run by people who don't know a thing about education.
As to not having a time frame for homework, that could or could not be a problem. Sometimes teachers don't check homework. In that case, the students who do it learn the material, and those who don't, don't. I have no problem with that, especially in the later grades. It helps students to take responsibility for their own learning. Nine times out of ten in college, homework is not checked. The accountability comes when you are tested on the material. If you did the homework all along, you are in good shape for the exam; if you didn't, you have to cram it all in at the end and won't do as well. There is accountability, it just comes at test time, rather than homework time, and I think that is a better system for older students. At work, your boss isn't going to check your work at every point, most of the time; they will simply want to see the end product. So, developing the motivation to complete a project without having a teacher holding your hand the entire time can be a good thing, as long as the teacher makes himself or herself available to any student needing help.
But, the idea of a teacher saying "Maybe" to whether or not an answer is right is insane. No good teacher would say that, unless they honestly weren't sure and were going to check and get back to the student. But, as a teacher, you can asks questions that have a right or wrong answer, and you can ask questions that don't. If you ask questions that have a right or wrong answer, then they are either right or wrong. If you ask questions that don't have a right or wrong answer, then they are neither right nor wrong. In no case would a competant teacher ask a question to which the answer of whether or not it was correct is "maybe." (Unless, of course, they honestly didn't know and had to check. Believe me, it is far less embarassing to tell a student "I don't know, but I'll find out and tell you next class" when they ask about something--like the kind of weird, intricate grammar questions my students sometime ask--than to make up an answer and have the student go and look it up and tell you you were wrong. After that, you have NO credibility to that student.)
I have never heard of any teacher doing that, nor have I ever seen that recommend as a pedagogical practice, in even the most radical of pedagogies. There are ways to tell a student they are wrong without making them feel bad. If you ask a student what the capital of Michigan is, and they say Detroit, you don't have to give them a curt "No" or a "Come on, you should know by now the capital is Lansing." You can say something like, "I can see why you might think that, since Detroit is the largest city in Michigan, but it isn't the capital. Can anyone help _______ with what the capital of Michigan is?" As a teacher, it can be really helpful to figure out not just if a student is right or wrong, but why they are wrong, when they are wrong. In this case, you can assume that the student thought that Detroit was the capital of Michigan because it is Michigan's largest city, and that does make sense, even if it is wrong. If you can try to get into your students' heads and figure out why they have the wrong answers they do (because wrong answers sometimes come out of nowhere, but not usually), then you can address and correct their wrong prior assumptions (such as "Detroit must be the capital of Michigan because it is the largest city there") which makes it more likely that they will retain the correct information. You don't cut down their self-esteem by making them feel like only an idiot would think Detroit is the capital of Michigan, but neither do you let them go on thinking that it is.
And, then there are questions that don't have right or wrong answers. When I teach college writing, it is very rare that I ask a question that has a right or wrong answer; usually, that only happens when I'm covering grammar, and that's generally a small part of the class. Most of the time, though, my students' essays are not "right" or "wrong" but "better" or "worse." If I ask them to write an essay explicating a poem, there are answers that might be wrong, but there are also many answers that can be right. The real question is whether they can support their interpretation with evidence, not whether they are "right" or "wrong." Same thing when they write about other things. In the last class I taught we did a unit on social issues, and their assignment was to write an essay in which they examined a contemporary social issue, explored several different arguments on either side of the issue, and then presented their own take on the issue. Several students wrote about gay marriage. A couple supported it, a few were unsure, and one was against it. Neither stance was "right" or "wrong"; it was all a matter of how well they supported their arguments. They all did a good job of it and I think I ended up giving all of them As or Bs. But, obviously, the answer to if they were right wasn't "maybe," it was "that's not a relevant question."
So, again, I have never heard of this, and I cannot imagine it is common practice in Hawaiian schools--and I KNOW it isn't common practice in mainland schools--to tell students "maybe" in regards to a right or wrong answer. And, unless the class is using a portfolio system where the work is graded at the end of the term, I can't imagine most teachers simply don't care when work is handed in. I have taught classes where I've allowed students to come up with their own plan of work (I tell them they need to produce 25-30 pages of writing by the end of the term, that half the pages must be handed in by midterm, and that they must write at least two papers and at least one paper over 7 pages, for example, and then they figure out how they want to negotiate that--they can write two 13-page papers, or four 7-page papers, or one 7-page paper and 6 3-page papers, or whatever combination they would like), but that is to make them more accountable for their own learning, not less. I don't do it all the time, though, because it is hard for me to be constantly grading papers, which is what usually happens. In an ideal world, though, I would probably always do that. But, again, it's different from having no due dates, and I cannot imagine a teacher having a class with no due dates.
So if the teacher is doing this, I'd look at either a new teacher or a new school, because there is just no way this is a common practice. As a teacher, it really bothers me to think that there are teachers out there telling students "maybe" regarding whether an answer is right or wrong, because that is never an appropriate answer.
