My classical voice teacher emphasizes an exercise where I am to sing through a sequence of vowels while maintaining the same open jaw position. The idea is that a singer should be able to produce vowels with the tongue and lips alone, never needing to adjust the jaw and only moving it when consonants come into play. In particular, I am to sing "eee" or [i] with a slack jaw, the idea being that only a high tongue, not a closed jaw is necessary to produce that sound. At the same time, my teacher has suggested that I study IPA to gain a better understanding of vowels, and I see that IPA identifies vowels according to jaw position (close, mid, open) as opposed to tongue height. My question is whether phoneticians consider jaw position to be an essential element of vowel production, or would phoneticians generally accept that all vowels can be produced with an open jaw as long as the tongue and lips are positioned properly? When studying IPA, is it safe to mentally translate jaw positions (close, mid, open) into corresponding tongue heights (high, mid, low) or would something essential be lost in doing that?
I should start by mentioning that I studied voice for many years, as well as linguistics (I was a double major in music and linguistics in college). What your voice teacher is trying to get you to do is quite standard in vocal pedagogy.
The short answer to your question is--yes, it is safe to translate close, mid, and open to the corresponding tongue heights.
@jlawler and @TKR both make valid points. As TKR notes, you can produce some semblance of an [i] with a slack jaw and a high tongue. As jlawler notes, it won't sound like a prototypical [i] for most languages (English, for example). But that's actually OK for singing.
jlawler's mention of ventriloquism is quite apropos; ventriloquists learn to seamlessly substitute certain sounds for some of the phones that are impossible to produce without moving their lips from a neutral position--for example substituting a dental [d̪] for the labial [b] (see jlawler's answer to a question about ventriloquism). The reason that the speech is still intelligible to the audience is that the general relationships among the sounds is largely preserved--"back" consonants are still "back" and "front" consonants are still "frontish". And vowels still contrast in tongue height and backness. On top of all that, ventriloquists rely on the native speaker ears of their audiences to bias them toward hearing actual words as opposed to gibberish--if the ventriloquist produces "I like ice crean" the audience's ears are going to "hear" "I like ice cream" because that makes sense.
What trained singers do is in fact a kind of ventriloquism. As long as the appropriate contrasts are in place--/i/ sounds higher than /e/, /e/ sounds higher than /ɛ/, etc., listeners' ears will be very forgiving. The demands of classical singing are very different from those of everyday conversation--singers must project to be heard in large spaces over an orchestra, they must sustain single vowel sounds for many seconds, and they must produce speech sounds over a pitch range that is quite unnatural for speech (especially in the case of females). Because of these demands, we make compromises such as the one your teacher is having you practice.
At the risk of getting too off-topic for this site, I'll just add that, in some cases, voice teachers will have students exaggerate the "ventriloquism" technique toward the beginning of their training, as it allows the students to focus more on minimizing tension and producing a consistent, beautiful sound throughout the vocal range, independent of text. As the kind of coordination required to do this becomes more second-nature for the student, it becomes easier for her to maintain it while producing slightly more "faithful" renditions of a variety of speech sounds.
In some more searching I came across a specific area of research that may shed light on this question and wanted to mention it as a complement to @musicallinguist's very helpful answer and the other comments here. Apparently there have been a number of studies of how speakers produce vowels when the jaw is held open artificially using a "bite block." Many of the studies reference the following paper:
Lindblom, B. & Sundberg, J. (1971). Neurophysiological representation of speech sounds. 15th World Congress of Logopedics and Phoniatrics, Buenos Aires.
What follows is a quote from Ohala, J. J. & Eukel, B. W. 1987. Explaining the intrinsic pitch of vowels.
Lindblom and Sundberg (1971) showed that speakers can produce acoustically normal vowels when speaking with the jaw in abnormal fixed positions if they produced compensatory tongue gestures. For example, by increasing the elevation of the tongue they can produce good [i, u] vowels with their jaws propped open by bite blocks.
As another example, the abstract of a 1980 paper by Wright and Riordan titled Articulatory compensation in the production of vowels with bite blocks begins with this sentence: "Studies of vowels produced using bite blocks have shown that speakers compensate for unusual degrees of jaw opening thereby preserving acoustic vowel targets." See http://scitation.aip.org/content/asa/journal/jasa/68/S1/10.1121/1.2004669 and search for other Acoustical Society papers mentioning "bite block."