a mentor would be a much better idea than a social skills group
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It's all politicians, mental health and math people in our circles
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I have been thinking of a college age girl
If the goal (or a main goal) of the mentorship is the development of DD's social skills, some may say that a person in an established career (therefore with proven, demonstrated skills in successfully building relationships and working with others) may be a more qualified socials skills coach than a college age student?
You did not mention whether this would be a paid mentorship; While I'm familiar with college-age babysitters, tutors, and nannies, it seems the child often has the upper hand in these relationships and may frequently threaten to fire the college student when the college student gives advice, sets limits, etc., which the child may not like.
If you are determined to have a college-age mentor to assist in the development of your DD's social skills, you may wish to make a well-thought-out list (possibly with the help of the psych) as to the skills you wish to have directly taught, role-modeled, etc... as it appears from your posts that your child may be one who does not pick up on interpersonal skills by casual observation in daily life situations (as some would say: does not learn "by osmosis").
Also consider whether you want the social skills development to follow a certain approach, such as
social thinking, perspective taking, theory of mind, etc.
In my observation and experience, children who do best with a mentor may be those who are positive, respectful, open to new ideas, forge healthy relationships, are flexible, and strongly internally motivated... who see bumps in the road as something routine, to be expected, and to learn from, therefore do not catastrophize or "fall to pieces", but take things in stride. In a word: undaunted.
Probably the only thing in this list that applies to DD is "internally motivated". I can understand the polite factor - but why "undaunted"?
In a nutshell, mentees who are
undaunted may tend to be successful because this entails qualities such as being dedicated to making things work, building a positive and healthy relationship, learning from the mentor, remaining realistic, taking responsibility for one's own communication/actions/responses/reactions... rather than catastrophizing or "falling to pieces" when encountering any of life's little disappointments... turning on the mentor or blaming the mentor.
Put another way, the mentor/mentee relationship must work for both people... both parties would benefit. A mentee who may be negative, emotionally needy, easily discouraged, or chronically disappointed may be a poor risk for any mentor to take on. For example, such a mentee may drain the mentor's energy, detract from their own goals, damage their reputation, etc.
Linking to a blog hop by Gifted Homeschoolers Forum (GHF):
Gifted Children and the Role of Mentors.