Our year went the other way. Mine is happier to not learn anything in school. He's gotten in trouble a couple of times for cutting up with the other kids rather than paying attention. It does really starkly show that getting a good education in through school is going to be tricky. The teacher said my son is advanced, but that he is not bored by work below his level, which is very true. I'm right there with you being overly nervous about kindergarten.
I thought that by teaching handwriting and following instructions and reading directions I was taking away the hinderances to getting an appropriate good education. Now I have learned through trial and error that my child is super slow, too slow to keep up with the class doing kindergarten work at a school's pace. It's scaring me that "how can he get a good education now?" They used the word Piaget's and I'm thinking the asynchronisity is not as smooth and polished as it appears, as we've worked for. Really, nothing's wrong. But we're getting the nerves now who didn't get it at the beginning of the school year.