Argument For:

Coming into PDP, I'd never taken a rhetoric course.  We had a course in college that essentially combined composition and gen ed lit.  So during PDP, I was partially looking for someone to define rhetoric for me.  In my experience, the only thing that we covered in the orientation about that made "rhetoric" different from the composition courses I'd taken were these Greek terms. So right away I found myself thinking of these words as something that made rhetoric different from other "English classes".  I wouldn't be surprised if this attitude that I had was shared by some of my students and that would explain why they initially struggled with the terms.

In my first semester, I taught these terms as I was taught them in PDP; essentially I defined the terms and gave my students examples.  And the response I got was very similar to the one described in the response above.
 
However, I don't think that experiencing this type of reaction one time is a good enough reason to give up on teaching the terms.  Rather I think that the terms need to be taught in concert with the teaching of a method of how to use them.

I only began having success with teaching these terms when I started teaching them as tools a rhetorician can use, rather than as names for different types of arguments.  And I gave lots of examples of how different professions use tools in different professions to accomplish different effects. So for example, a doctor will use surgery to combat certain types of illnesses and medication to combat others. I tried to tell my students that when we look to analyze anything, we're looking to see the choices that were made, how they work, and why these strategies might have been chosen. And I stressed that a thorough analysis includes all of these parts.  So for example, if we were looking at the doctor's performance, we'd look to see how she utilized the tools available to her to accomplish her goal of curing patients.

I found music the most useful too to demonstrate how we can talk about the tools someone uses as a method of analysis.  Playing different versions of the same song, demonstrates how different artist wanted to express a similar message in drastically different ways. In these cases, students can talk about the decisions to use a slowed down acoustic arrangement can make when compared to an up tempo electric arrangement.  Moreover, they generally recognize that simply stating the difference between the two songs is not enough.  My goal in using this analogy is to get students to consider how an author is choosing to build  up an ethos for him/herself in one argument or appeal to pathos in another and how identifying those tools helps us understand the message behind the argument and to make decisions about its effectiveness.

This approach yielded better results for me, which indicates that when taught in a certain way, these terms can help your students perform sophisticated analyses.  So I do think the terms should be taught with an understanding that students are not learning a method of analysis.  Rather they are learning vocabulary which will aid in their analyses.

Two final quick, but not unrelated comments.  First, I think that when in the semester these terms are taught can make a big difference.  If this is something that students learn early on, I could see them thinking that learning these terms is the point of the class, but if a method is taught and then later on in the semester these terms are introduced, it may give students who were struggling to find ways to talk about argument
more of an appreciation for the terms as tools for them to use.

Second, I think that the strangeness of the terms may encourage the attitude that students have done what they were supposed to do simply by learning to define and identify them.  I imagine that if I taught the terms "largo" and "allegro" instead of talking about a slow or fast tempo in music, students would focus on the strangeness of the words rather than the use of them in analyzing the music.  So I think that the use of
these terms should be made explicit to combat this tendency.  It might also be useful to simply teach the terms as credibility, logic, and emotion.