The Socratic method is a solution to the teacher training problem

It encourages teachers to instruct students in how to think, not what to think

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The best instructor I ever had gave everyone an A—but you had to earn it. It was a philosophy class and the assessments were open-ended questions about assigned readings. The instructor posed a set of questions to the entire class. We submitted our responses, then, based on our responses, he posed a new set of questions, individualized for each student. He did this a third and final time. If he thought we still did not grasp the content, we had to meet with him for one-on-one instruction. 

I never worked so hard as I did in that class—I even attended an optional, instructor-led study session to hash out the complicated ideas with the instructor and fellow students. In a typical graded course, you do the work assigned, receive a grade, then move on to the next task—often, mastery of the content is not required. But this class encouraged students to think deeply about the ideas and concepts taught and prove that they understood them—you could not turn in good-enough work, take a letter grade, then move on.

The instructor clearly did not like assigning grades to student work. He assumed that students were enrolled in his class to learn the material and concepts covered, and what each student got out of the class was up to them. But alas, that is not how school, neither K-12 nor university, works. To avoid having to tell students that they were either right or wrong in their thinking, he used a variation of the Socratic method. In the instructor's response to student work, he would point out areas where he thought arguments needed further development or where the prepositions were not lining up to create an argument, but he would never mark an answer as incorrect. Instead, he would ask questions.

Similarly, Socrates, according to Plato, does not tell his dialogue partners that they are wrong, per se. Instead, he teases out their arguments through questioning, which may lead them to realize where there are errors in their arguments or proclamations. Socrates would not tell others what to think, or even what he thinks, and this was a great irritation to some of his dialogue partners, and it is a great irritation to many people who read Plato's dialogues. But from the perspective of an instructor, the Socratic method is the means through which you teach your students how to think, not what to think. Certainly, in a math class, for example, there are correct and incorrect answers to problems. But even so, asking questions is a better teaching method to help students understand how they have arrived at their solutions to problems than simply saying "yes, you are correct," and how to address errors they have made rather then simply saying, "no, you are wrong." Essentially, the process matters just as much, perhaps even more, than the answer. Arriving at a correct answer is certainly important, but understanding and mastering the process provides students with the skills and knowledge required to solve future problems and innovate.

With that said, the Socratic method should be taught in all schools of education as part of a liberal education. Not only will students who take classes with teachers trained in the Socratic method learn how to think, rather than what to think, training teachers in this approach, with the assumption that they will implement it, would preempt accusations of indoctrination on the part of the teacher. 

Take the Platonic dialogue, Euthyphro, for example. Socrates has a dialogue with Euthyphro in hopes of learning what is piety and what it means to be pious. He utilizes his typical method to seek the truth: questioning. Through his questioning, Socrates encourages Euthyphro to define his terms clearly by providing definitions, not examples, so that the terms can be applied to multiple scenarios.

"Bear in mind then that I did not bid you tell me one or two of the many pious actions but that form itself that makes all pious actions pious[.]" "Tell me [...] what this form itself is, so that I may look upon it and, using it as a model, say that any action of yours or another's that is of that kind is pious, and if it is not that it is not."

But Socrates does provides examples not related to the topic at hand to ensure that he and his dialogue partner mutually understand the terms they are using. 

 "We have [...] stated that the gods are in a state of discord, that they are at odds with each other, Euthyphro, and that they are at enmity with each other." "What are the subjects of difference that cause hatred and anger? Let us look at it this way. If you and I were to differ about numbers as to which is greater, would this difference make us enemies and angry with each other, or would we proceed to count and soon resolve our difference about this?"

And he requests proof to back up claims being made.

"[T]ell me, too, that I may become wiser, what proof you have that all gods consider that man to have been killed unjustly who became a murderer while in your service, was bound by the master of his victim, and died in his bonds before the one who bound him found out from the seers what was to be done with him, and that it is right for a son to denounce and to prosecute his father on behalf of such a man. Come, try to show me a clear sign that all the gods definitely believe this action to be right."

Finally, Socrates ensures that he and his dialogue partner thoroughly examine statements and arguments being made by each other rather than simply accepting them at face value.

Euthyphro: "I would certainly say that the pious is what all the gods love, and the opposite, what all the gods hate, is the impious."

Socrates: "Then let us again examine whether that is a sound statement, or do we let it pass, and if one of us, or someone else, merely says that something is so, do we accept that it is so? Or should we examine what the speaker means?"

Euthyphro: "We must examine it, but I certainly think that this is now a fine statement."

Socrates: "We shall soon better know whether it is."

Through the Socratic method, students will learn: how to clarify terms when reading and speaking with others, and how to articulate the terms they use; how to identify central arguments being made in written works and by speakers, and how to present arguments themselves; and, most importantly, how to seek the truth.