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Part of PDD/SPD/A Little Bit Autistic, what have you, is a deficit in socialization. In my view, what to do about social impairment draws on medical science, treatment philosophy, but also norms, in the general sense. From a normative perspective, I'm of the mindset that it's okay to not be social. If Brad likes solitude, then I don't want to project my preconceived notion of happiness (having a lot of friends) on him. Also, if Brad is quirky, I have no interest in de-quirkifying him. Normal is overrated.
That having been said, I want Brad to be happy, and if Brad wants friends but doesn't know how to make friends, then I want him to have the facility to make friends and if school can further that goal, then I welcome the help. My goal then for Brad is the facility to make friends.
So that's a high level description of our goals, from a parenting perspective.
As for interventions, at school Brad's speech language pathologist joins Brad in class (including on the playground) and focuses on social pragmatics. In english, this means she facilitates play, including greetings, turn taking, sharing, and the like. Sample progress note, from his SLP:
Bradley did a GREAT job today on the playground! I was on the playground and I didn't even have a chance to go up to him to ask him if he wants to play hide-and-seek or tag. He came right up to me and said, "I want to play tag!". There were already two boys playing tag, so I told him to join them, and he just ran right up and joined in the game. He played for a few minutes and only needed a couple of prompts from me to keep going. Then, the boys started playing with a kickball, so I prompted him to keep after the ball in the group. The group then went over to play basketball and he needed prompts to keep up with the ball (someone throws the ball and all the kids run after it -- he just needed prompts to be more assertive and stay with the ball). He was actively engaged in games all of recess and feeling connected with the other kids. When you play tag at home, try having him chase you, and then teach him to run up to you and say in a nice loud voice, "Now you chase me!". After playing tag for a few minutes where he was chasing other kids, he wanted someone to chase him, and we practiced going up to a friend and saying, "Chase me!".And this:
When I was in class today, I sat with Bradley and made bat, cat, and pumpkins with him out of play dough. We used the language for rolling, pulling, pushing down, etc. Then, I prompted him to show friends what he made, which he did when I prompted him to do so. I prompted him to use a louder voice when talking to friends. He also told his friend that he liked his cowboy costume!To me, this seems like a nice, safe way to introduce Brad to social situations. I don't see any downside.
That having been said, there are a two social interventions which I disapprove of for Brad, from a normative perspective, and my disapproval is actually in Brad's IEP: (1) no "look me in the eye"; and (2) no social scripting.
Regarding "look me in the eye", at issue I believe is working memory. If you asked me to do long division in my head, either I wouldn't be able to do it, or I'd have to close my eyes or look away while I think about it. This is a normal response. For children who have a weak working memory, a lot of ordinary interactions tax them from a sensory perspective like long division taxes me. That's the way I see it. Also, I've read enough first hand accounts of autistic adults who recall being forced to look so-and-so in the eye, and it's a source of anxiety and instills a sense of failure. When Brad was two and a half, the specialty provider who came to administer Floortime starting doing the face touch, where the therapist gently touched Brad's face under the chin when he wouldn't make eye contact. I told her to stop.
As for social scripting, I just don't like it, and I don't think it's necessary for Brad. Social scripting refers to teaching a child to say, for example, "do you want to hold my hand and walk with me?" the idea being that typical children know to do this naturally and atypical children need to be taught. My thought is that holding another child's hand should come from a place of joy and affection, and not from a place of "if I do X, I'll get external reward Y." But, again, this is normative, in part, so I say live and let live. If another parent prefers that their child learn social scripts, that's fine. For me, I don't want that for Brad. As for prevalence, I don't know about other school districts, but I know that a few children in my district are taught social scripts (and it shows).

