I'm glad this post resurfaced - for some reason I couldn't find it. I wanted to share my own experience with my dd, who sounds very much like your dd. She was a VERY reserved child - didn't talk to anyone, took forever to warm up even to familiar people (like grandmas), did not interact with other children at all, and suffers from severe seperation anxiety. So the preschool question was a biggie. At that time, our only real activity was library hour, which she loved, but which really gave her no social outlet.Â
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For my dd, we really had to get everything right for preschool to work - the right environment, the right time of day, the right activities, and especially the right teacher. I looked at nearly a dozen schools before I found a play-based co-op. It was absolutely the right place for my sweet, quiet child.  The teacher was so understanding, so intuitive, so caring! She was amazing.
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Like another poster, I also attended with my dd for about 2 months before we were at the "drop-off-and-leave" stage. For 3 weeks, I stayed full time. Then the next few times, I had to leave to "take a phone call outside" for 5-10 minutes. Then I had to return something to the library (20 min). Then I had a quick errand to run (30 min) - you get the picture. It was a very gentle seperation, and the teacher was 100% available to my dd while I was gone (there were also an assistant and a parent helper).
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Some things that helped:
1 - Being in the room allowed me to facilitate my dd's exploration of the available materials. I'm sure she would have found them all eventually, but there were a lot of really fun activities tucked into the shelves that dd loved, and others overlooked. Most of the kids liked the play kitchen area or the blocks. DD gravitated toward puzzles and games. On her own, she may not have had the confidence to grab a puzzle and spread out on the floor. And she couldn't tell the teacher what she wanted to do, due to anxiety and selective mutism (poor kid). The cool thing was, once she had found something she wanted to do, there was ALWAYS another child who wanted to do it with her.Â
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2 - Being in the room for a few weeks also allowed me to help dd with all the transitions. Transitions are so hard for anxious kids, but once they know the drill, the routine can be very comforting. Staying until your dd is comfortable with the day's routine can make a lot of the anxiety go away.
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3 - I had to be a parent helper in the class about once a month. That time showed me which kids my dd gravitated to, and it helped me come up with conversation topics about school once I was no longer in the classroom.Â
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4 - The school had a great outdoor play policy - at the end of every day (only 2 days/week for 3yos), the kids played outside for about 15 minutes before pick-up time. But parents were encouraged to let the kids stay a little longer and play. Many parents would stay an extra 15-30 minutes for the "easy play date". The kids loved it, and it gave the parents time to get to know one another. It was also a great time to talk to the teacher if I had any questions or concerns. Imagine - a conference twice a week if I wanted/needed it!
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5 - The outdoor play time also gave me a chance to set up one-on-one playdates. Once dd was more comfortable with 2-3 of the kids, it was much easier to engage her at drop-off.Â
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I'll admit, dd didn't race to the door when it was time to leave for school. But she also never cried at drop-off, and she genuinely enjoyed her time at school that year. At the end of the day (well, 2 1/2 hours), she BEGGED to stay longer. It was a fun place to be.
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But the big payoff came NEXT year, when dd suddenly blossomed into Miss Social Butterfly, with confidence and assurance I was sure she would never have. Her ability to make friends astounds me to this day (1st grade now). She is still the same reserved child, she still takes forever to warm up - BUT she makes friends easily, and I have seen her manage conflict beautifully. I'm also seeing the selective mutism fade away, partly due to some of the coping strategies that dd's preschool teacher worked on (and the kindy teacher continued with). I attribute dd's social growth almost completely to our fantastic preschool co-op, and especially the teacher who loved my dd enough to let her grow at her own pace. I hope you find something like this for your child too!