A good supervisor realizes that in many instances student teachers perform in a certain manner because they are expected, by superiors and parents, for example, to teach that way; not, because there are good scientific grounds for their practice. For example, language teachers may be expected to use vocabulary lists for memorization and teach about verb tenses. Why? Because that is what administrators or students' parents remember from their days in school. Scientific pedagogy is not infrequently stifled by tradition.
But what is essential to being a supervisor and a good one at that? Merely the job title? I don't think anyone would be comfortable with that answer. We would not want to to leave it up to chance, nor favoritism or prejudice. On the contrary, we would expect that a person designated as a supervisor to have certain reasonable and desirable characteristics. Important among these would likely be knowledge, skills and attitudes of a certain sort. Here are some criteria of hopefully general application.
Our first criterion might be: a supervisor should be committed to improving the education of the students who are being taught by his/her supervisee. Note that "improving education" invokes values of a certain general sort, without being over specific as to exactly which ones. A usable definition of supervision should be possible without restriction to certain ideologies or philosophies.
Our second criterion is: A supervisor must have pedagogically relevant knowledge of subject matter. It is not enough for, say, a person designated as a supervisor of physics teachers to have gotten A's in physics courses herself; but rather she must posses two other capacities:
a. she must know how to represent that knowledge in ways that promote learning in those less experienced than she; and
b. she must know how to help the student teacher to represent his or her knowledge to the student.
Note how such words as "relevant knowledge" and "promoting learning" insinuate a values commitment without constraining it within specific ideological or philosophical framework. This enables supervision-defining skills and attitudes to be offered to a variety of persons without bias to a particular world view. Some knowledge, skills and attitudes can be trans-ideological, focussing on technique and means, rather than ultimate ends.
A good supervisor is, herself, a good teacher. She must be able to imagine herself ignorant and be willing to experiment with strategies to bring herself, as ignorant, to be knowledgeable. In addition, the supervisor must be willing to negotiate with her supervisee a characterization of the criticized lesson which communicates a fair and "teacherly" concern with improvement, based on educational, rather than personal reasons.
Our final criterion is that a supervisor should be professionally skeptical of the institution's ability to enhance educational outcomes: the school in which her supervisee works may engage in practices which undermine the learning of the pupils her supervisee teaches.
To be a professional is to be not entirely subjugated to one's employer; rather, it is to maintain certain standards in the face of possible institutional pressures to "sell out," i.e. to sacrifice educational goals to bureaucratic or political convenience.
The context of much teacher supervision undermines reasonable expectation of educational outcome. For example, supervisors are not infrequently given insufficient time to observe; or, they are assigned to "evaluate" teachers for punitive reasons, or in areas in which they, the supervisors, have little knowledge of subject or pedagogy.
It is not unreasonable to expect that organizational functions will normally interfere with educational ones. Pedagogical rhythms may be interrupted for the sake of the numerous supportive functions the school provides. However, it is the supervisor's duty to deflect, resist and subvert any interventions which debase the educational process.
For continued examination of this topic, see Do Schools Really Need Curriculum Supervisors? Confusing Role with Function.