Article: School-Based Social Skills Training for Children with Autism Spectrum Disorder, by Radley and others. In Focus on Autism and Other Developmental Disabilities, 2017, 32(4).
If there is one thing I can do standing on my head, it's run a social skills group. Now that I think of it, it's probably the thing I'm most qualified to do. Well-run groups can do wonders for kids; poorly-run groups can be a huge waste of time and quite possibly have a negative impact on the child (e.g., stigmatizing). The above study indicates there is a need for a social skills training program that is effective and easy to administer, and that is what they found. The name of the program, by the way, is the Superheroes Social Skills program, and it was tested on elementary-aged kids and found to work on many levels. First of all, kids improved their social skills in a naturalistic setting (i.e., recess). Second, these improvements were maintained over time (i.e., the improvements were actual increases in skill and not the result of cramming for the Recess Test). Third, the kids who attended the training were actually rated higher on a friendship scale by their peers following the intervention (i.e., the other kids in the class noticed positive changes). And finally, teachers noted social skill improvements in these ASD kids as well.
There are a couple items in this write-up that deserve some attention. First, "social skills training" in public schools is generally terrible. This is likely the result of limited resources, limited will, and limited understanding of what it takes to run a good program. If your child has anything on their IEP about social skill development or training, ask a lot of questions about what they are doing. Ask if they are using an empirically (scientifically) supported technique (EST) or intervention. If not, ask them why not. If they don't know what you're talking about, that usually means they're not using an EST.
Second, generalization of skills (i.e., getting the ASD kids to use the skills outside the training) is a huge problem for every professional. In general, ASD individuals struggle to generalize information. Information tends to be inflexible and context-specific, so any training program that wants to be more than a complete waste of everyone's time and resource needs to address this issue. This study actually has a very good description of how to address problems with generalization that is based on a theory by Stokes and Osnes (1989). I have not read the article, but it reportedly suggests using 1. peer models, 2. video modeling, and 3. training in self-monitoring to promote generalization. I will read this article next if I can find it.
Finally, this point goes into every lecture, consultation, or blog post about social skills training I do. Remember that kids typically learn very few social skills from adults. Most social skill learning and practice happens with other kids. At the very least, your child's social skill intervention should have as a goal to get your kid around other kids as much as humanly possible. This is different from inclusion that suggests if ASD kids are around "normal" kids, they will learn to be "normal". This is actually not true, and has never been true, and has lead to a lot of hardship for "not-normal" kids like those on the Spectrum. Your child's social skills training program should teach them how to benefit from the interactions with and feedback from their peers, and then get them to be in the place where they can learn and practice. Even social skills groups are generally a poor substitute for the kind of learning kids can do effectively playing with their peers at recess.