Janet,
   These are wonderful questions. Much of what I would say Bill covers, so
I'll add a few sidenotes. I have struggled through the same questions
and feel a little more settled in my thinking.
   I think it's so much more important to describe the structure than it
is to put it in the "right" category. So looking closely at these
non-finite structures and saying they usually are missing a subject
(not always) and aren't grounded with finite verbs is probably the most
important thing. My students seem OK with saying we'll call them
clauses, but traditional grammar calls them phrases. I end up doing
somewhat the same thing with "gerund" as a term. I don't like it, but
it's out there, and it helps to at least point out what the word refers
to for the people who use it.
   I start out with "the elements of the simple clause", so I cover
postnominal modification with prepositional phrases first and say there
are other word groups in that slot that we'll cover later. That seems
to work for me. I sometimes postpone restrictive and non-restrictive
modification until later as well. Appositional phrases also fit in that
slot, but I don't bring them in right away.
   I think you mistakenly ask about "Joe" as indirect object in your cake
sentence. My guess is you meant "me". I like the multi-functional
analysis of functional gramamr for that one. From that view, the
transitivity system helps us represent the world. The clause gives us
processes and participants and circumstances andestablishes participant
roles. We also have systems in place for construing that event in
different ways. In passives, for example, the direct or indirect object
gets shifted into the grammatical subject slot without changing their
real world roles. ("The cake was baked by Joe. I was baked the cake by
Joe." In both these cases, Joe is obviously still doing the baking.)
This can also give us a way to put different information in the usual
given slot and in the clause ending slot we usually use for new
information. "Who was the cake for?" "The cake was baked for me." 
"What did Joe bake you?"  "Joe baked me a cake."  "Who baked the cake? 
"The cake was baked by Joe."  Students seem to enjoy putting a clause
through its various permutations and then reflecting on how that
"construes" the process. We can also say something like "Joe baked all
night", or "Joe baked with great care", not because we have stopped
understanding that "baking" means you bake something and are probably
doing that for some sort of beneficiary, but because those elements are
not always in focus. Even categories like "transitive" and
"intransitive" and "di-transitive" and "complex transitive" can be used
to talk about the verb itself as well as about the structure of a
particular clause. Is "Joe baked all night" intransitive? I think
that's easier to understand if you realize the process hasn't changed,
but certain aspects of it are simply not in focus for the statement.
   I have found that most state tests for students have no real knowledge
content to them. Even the phrasing of the standards is something like
"Can puncutate sentences," never anything like "can identify a
participle phrase" or "Can differentiate compound sentences from
compound predicates." Even the SAT simply asks students to pick a
version that seems more effective or more correct. It never asks for
terminology. Language, at least for students, is treated like a
behavior.
   Are there teacher tests in your state?

Craig

 How would you analyze this:  Once upon a time, there was a prince named
> Joe.
>
>
>
> Do you analyze a prince named Joe as a noun phrase with a participle
> phrase modifying the noun head, or as a participle clause?  I've always
> called these non-finite constructions reduced clauses or participle
> clauses, but I have run into a problem.  In my grammar class for
> pre-service teachers, I start with noun phrases.  When I teach noun
> modification, I want to teach students about post-modification, but they
> really don't know anything about finite and non-finite verbs yet, nor do
> they know much about clauses.  So this semester, I decided I would just
> call them participle phrases which modify nouns.  But then I was in
> trouble when we got to clauses because I wanted to call then reduced or
> non-finite clauses.  By that time, the students knew enough to say "Hey
> wait a minute!  Didn't you just tell us those were phrases?"  At least I
> know they were listening in October.
>
>
>
> Also, do you call 'Joe' a retained object complement, or is there a
> better way to label this?
>
>
>
> How about this:  Joe baked a cake for me.  Can I just go ahead and call
> 'Joe' an indirect object? It means exactly the same this as Joe baked me
> a cake.
>
>
>
> This is an on-going problem for me, because, even though I try to teach
> them a pretty straight forward descriptive-structural-functional view of
> syntax (Quirk et al is my bible), with a little discussion of
> prescriptivism thrown in so they'll know what to expect when they get
> into the schools, I find that frequently there is more than one way to
> analyze a given structure.  This disturbs my students.  They want to
> know the 'right' way, and it better be the way that it is gong to show
> up on the subject area test they have to take.  Do you think there is
> any consensus on the 'best' grammar approach to teach pre-service
> teachers?  This is not a trivial issue, since they have high-stakes
> tests (for themselves and their students) principals and parents in
> their futures.
>
>
>
> Comments?
>
>
>
> Janet Castilleja
>
>
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