-The sentence or phrase is bracketed in the question. My answer is bracketed as well.

1.Were I a polemicist, I might say what I was after is a pragmatic pedagogy, one grounded in "the arts of complicity, duplicity, and compromise," the very same arts [that are deployed, with such enervating effect, by the host of social, bureaucratic and corporate institutions that govern all our lives.]


[relative clause] YES, modifying “very same arts”

prepositional phrase

non-restrictive relative clause

reduced relative clause

2.Between the poles of these two representations of schooling as either radically liberating and empowering or ceaselessly oppressive and [instrumentalist], one finds a vast, unexplored territory--the fraught, compromised world where all of our classes are actually convened.


[adjective] YES

verb

adverb

noun

3. Were I a polemicist, I might say what I was after is a pragmatic pedagogy, one grounded in "the arts of complicity, duplicity, and compromise," the very same arts that are deployed,[ with such enervating effect], by the host of social, bureaucratic and corporate institutions that govern all our lives.

dependent clause

noun phrase

[prepositional phrase] YES, a PP functioning as a result adjunct modifying “deployed”.

verb phrase

4.[Were I a polemicist], I might say what I was after is a pragmatic pedagogy, one grounded in "the arts of complicity, duplicity, and compromise," the very same arts that are deployed, with such enervating effect, by the host of social, bureaucratic and corporate institutions that govern all our lives.


[dependent clause] YES, a conditional adjunct.

verb phrase

independent clause

noun phrase

5.And, of course, as teachers we too are subject to the demands of the classroom drama, which requires that we meet the ambient expectations [about what it means to teach and to be an authority on one's subject]. Thus, we are quick to cover our own ignorance, talk over our own confusion, hide our own doubts about the rewards of learning because, if we act otherwise, we would risk rending education's public transcript by exposing the highly credentialed person at the front of the room as nothing more than a fraud.

noun phrase

prepositional phrase It is a PP introduced by the prep “about” which has the subordinate interrogative clause (embedded question) as complement.

verb phrase

[dependent clause] NO

6.And, of course, as teachers we too are subject to the demands of the classroom drama, which requires that we meet the ambient expectations about what it means to teach and to be an authority on one's subject. Thus, we are quick to cover our own ignorance, [[talk over our own confusion]], hide our own doubts about the rewards of learning because, if we act otherwise, we would risk rending education's public transcript by exposing the highly credentialed person at the front of the room as nothing more than a fraud.

verb phrase YES, the second of three coordinated VPs functioning as complement of “quick”.

independent clause

[dependent clause] NO

action verb

7.And, of course, as teachers we too are subject to the demands of the classroom drama, which requires that we meet the ambient expectations about what it means to teach and to be an authority on one's subject. Thus, we are quick to cover our own ignorance, talk over our own confusion, hide our own doubts about the rewards of learning because,[ if we act otherwise], we would risk rending education's public transcript by exposing the highly credentialed person at the front of the room as nothing more than a fraud.

independent clause

[dependent clause] For those who take “if” as a subordinator it’s a dependent clause. For those who take “if” as a preposition, it’s a preposition phrase. In both cases it’s a conditional adjunct.

noun phrase

verb phrase

8.And, of course, as teachers we too are subject to the demands of the classroom drama, which requires that we meet the ambient expectations about what it means to teach and to be an authority on one's subject. Thus, we are quick to cover our own ignorance, talk over our own confusion, hide our own doubts about the rewards of learning because, if we act otherwise, we would risk rending education's public transcript [by exposing the highly credentialed person at the front of the room as nothing more than a fraud.]


restrictive relative clause

verb phrase

noun phrase

[prepositional phrase] YES, functioning as a means adjunct.

9.Between the poles of these two representations of schooling as either radically liberating and empowering or ceaselessly oppressive and instrumentalist, one finds a vast, unexplored territory--[the fraught, compromised world where all of our classes are actually convened].


noun phrase YES: a supplementary appositive noun phrase referring to “unexplored territory”.

[independent clause] NO

dependent clause

prepositional phrase

10.Between [the poles of these two representations of schooling] as either radically liberating and empowering or ceaselessly oppressive and instrumentalist, one finds a vast, unexplored territory--the fraught, compromised world where all of our classes are actually convened.

noun phrase YES, an NP as complement to the prep “between”.

adjectival phrase

[prepositional phrase] NO
verb phrase

11.Were I a polemicist, I [might say] what I was after is a pragmatic pedagogy, one grounded in "the arts of complicity, duplicity, and compromise," the very same arts that are deployed, with such enervating effect, by the host of social, bureaucratic and corporate institutions that govern all our lives.


independent clause

verb phrase YES, “might say” is part of the larger VP consisting of the whole string from “might” to “lives”.

noun phrase

[auxiliary verb] NO

12.And, of course, as teachers we too are subject to the demands of the classroom drama, which requires that we meet the ambient expectations about what it means to teach and to be an authority on one's subject. Thus, we are quick to cover our own ignorance, talk over our own confusion, hide our own doubts about the rewards of learning because, if we act otherwise, we [would risk] rending education's public transcript by exposing the highly credentialed person at the front of the room as nothing more than a fraud.


prepositional phrase

[verb phrase] YES, part of the larger VP from “would” to “fraud”.

action verb

noun phrase

13.

And, of course, as teachers we too are subject to the demands of the classroom drama, which requires that we meet the ambient expectations about what it means to teach and to be an authority on one's subject. Thus, we are quick to cover our own ignorance, talk over our own confusion, hide our own doubts about the rewards of learning because, if we act otherwise, [we would risk rending education's public transcript by exposing the highly credentialed person at the front of the room as nothing more than a fraud.]


[independent clause] YES

verb phrase

dependent clause

noun phrase

14.Between the poles of these two representations of schooling as either radically liberating and empowering or ceaselessly oppressive and instrumentalist, one finds a vast, unexplored territory--the fraught, compromised world where all of our classes [are actually convened.]


prepositional phrase

noun phrase

[adverbial phrase] NO

verb phrase YES

15.And, of course, as teachers we too are subject to the demands of the classroom drama, which requires that we meet the ambient expectations about what it means to teach and to be an authority on one's subject. Thus, we are quick to cover [our own ignorance], talk over our own confusion, hide our own doubts about the rewards of learning because, if we act otherwise, we would risk rending education's public transcript by exposing the highly credentialed person at the front of the room as nothing more than a fraud.


noun phrase YES, as direct object of the verb “cover”.

determiner

[adjectival phrase] NO

noun

16.And, of course, as teachers we too are subject to the demands of the classroom drama, [which requires that we meet the ambient expectations about what it means to teach and to be an authority on one's subject]. Thus, we are quick to cover our own ignorance, talk over our own confusion, hide our own doubts about the rewards of learning because, if we act otherwise, we would risk rending education's public transcript by exposing the highly credentialed person at the front of the room as nothing more than a fraud.


noun phrase

[restrictive relative clause] NO

dependent clause

non-restrictive relative clauseYES, note the comma which indicates it’s non-restrictive.