For the full video go to: http://www.psychotherapy.net/video/counseling-psychotherapy-theories
Examples of the major psychotherapy theories all in one video! John and Rita Sommers-Flanagan present eleven of the best-known approaches to counseling and psychotherapy side-by-side, with real therapy sessions and extensive commentary covering theory, strategy, and effective techniques.
PsychotherapyNet
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So really it's just basic conversational technique whereby the listener simply repeats the Speaker's words. I wish I could figure out why everyone finds this to be so effective. Maybe they are just having trouble thinking introspectively and this helps them.
I personally tend to think that, therapy should be geared toward philosophical alignments and balance. You hear the person's philosophy, you understand it. Then you gently challenge imbalances in their philosophy, toward the ends to where they may be capable of rationalizing philosophy on their own.