Do a Google search on portfolio grading and you'll get a lot links to Centers for Writing. I suppose that is the teaching area where this sort of assessment is most prominent. One wonders why. Part of this must be a lingering belief elsewhere that one can measure "learning" via static measurements, i.e., exams, as long as one does a pre-test and a post-test implementation. (For example, that's the basis of one of the studies mentioned here, where this measure of learning is correlated with student course evaluations.) There is, however, a lot of trouble with implementing this sort of thing, namely that students typically don't have reason to take the pre-tests seriously. Further, the methods are rarely if ever used to inform the students of their own learning. When the post-test grade is returned to the student, it typically isn't accompanied with the pre-test grade, let alone a breakdown by topic so students can see where they improved and where they didn't.
(My first semester of grad school in the first or second day of class Robert Eisner, who taught the core macroecon course where we read the General Theory and started on Money, Interest, and Prices and did a bunch of other interesting and challenging stuff as well, administered an old final exam he gave for his undergraduate introduction to macro course. Not having been an econ major as an undergrad, I thought I was at a distinct disadvantage compared to my classmates. I scored in the mid 20's on that exam and was kind of humiliated by the experience. That put me in the lower half of the class or so I gathered by comparing notes with my classmates, but I was not an outlier. Whether the purpose of that exam was to deflate our egos or to establish a baseline, I don't know. I, for one, worked extremely hard that quarter to make up for my deficiencies. So maybe it was appropriate for some students. But it set up an adversarial tone between the faculty and the students that I believe can be quite discouraging, making the learning feel like a cutthroat competition when that does not seem to be necessary to me. I thought my class extremely non-intellectual and I attributed a good chunk of that to the tone that was set.)
It may also be that many instructors simply want to to measure, for lack of a better word, mastery and are less interested in measuring growth in understanding. Most likely, however, many instructors haven't thought this through. They simply embrace the practice that they themselves were exposed to, without questioning whether the practice is consistent with other goals they have for the teaching. If one did think it through, however, I believe there are several conclusions that would be reached by a broad array of those teaching, not just the writing instructors.
First, students becoming aware of their own learning is helpful, both to engage the students and to make them cognizant of their own deficiencies that require improvement, pointing them where to focus their efforts (or acknowledging those deficiency areas that will remain unlearned). Second, novices aren't as proficient as those with more experience. If you grade the novice as if he or she is proficient, that can be discouraging. Feedback that facilitates improvement but is otherwise evaluation-free is preferable. The evaluation can happen later after a body of work has been accumulated giving evidence that the student has "moved down the learning curve." Third, if a system of assessment is put into place that essentially ignores the student learning needs, that can breed cynicism or worse. (See the compelling essay by Peter Gray on this point.) This, in a nutshell, is the argument for portfolio assessment, a better if still imperfect approach.
Now let me bring in the LMS, since I've not yet mentioned it. It would be a delightful thing if instructors got new ideas about their teaching via their own reflection or from ongoing conversations with their peers, where professional practice dictates a somewhat experimental approach to the instruction, in the spirit of Donald Schon, where the instructors viewed themselves as learners about the art of teaching. However, it is my experience that often such communities of practice are lacking. An instructor operating more or less on his own stops innovating, so the teaching ends up being very traditional, sometimes very stale. Therefore it would be very good if alternative approaches were embedded in other channels the instructor might confront, the LMS gives one prominent such example.
This becomes a vexing question for the learning technologist - to be out ahead of the instructors who are supported or to be right there with them. And we've experienced some of both, so that ePortfolio systems developed separately from the LMS, although most campuses can't afford to run separate systems and the grade book would ultimately remain an LMS function. (The vendors seemingly figured this out and ePortfolio became much more focused as a resume tool.) One wonders then if portfolio grading for within-course learning can survive and do so in an LMS-only environment.
I'm not sure of the answer to that, but I am pretty sure of where we are at present. An instructor can do portfolio grading using the LMS grade book in a somewhat passive way, to display those grades that are given to the students writing. But the work flow part - whether the students turned in the writing pieces on time, whether the instructor has given back comments, how those comments are communicated, etc., is not tracked through the grade book and must be invented by other means. This means the technology will not serve to diffuse the method. It will instead reinforce the traditional way.
Part of the argument for going outside of the LMS and indeed to make student work publicly available is to introduce some performance incentive rather than grade incentive into encouraging students to put in their best effort. But there is another part, to encourage instructor invention. We need that other part now.
A fantasy I have that probably will never happen is to make the Writing Center folks in charge of teaching and learning for the Campus as whole, backed up by real budget authority to make changes. The problem is, these folks scare the bejesus out of many others in the administration, because they wouldn't just make changes around the edges. So it won't happen. But it is an intriguing thought. And I believe portfolio grading would be a big part of what they'd recommend.