I'm going to be a bit of a devil's advocate here. I think that you need to be more pro-active in assessing the teaching style before you have your kid in there. You are shopping for a school for more than one child. I would ask the potential teacher how they work with advanced kids and kids who are struggling. I would acknowledge that kindergarten classes tend to have a large range of ability and readiness to be in a classroom. You can describe the type of reading/math that your first child is doing and ask how that child would fit in the teacher's current class. You may be pleasantly surprised to hear that they meet kids at whatever reading level they are at or you may have someone who starts telling you that they start at the beginning to make sure that there are no "gaps." We've had both styles of K teachers at the same school. Embrace the former and run like h*ll from the latter. Remember, a couple months of sheer boredom can seem like a lifetime to your kindergartener (which often translates to misery for you too BTW).
Unfortunately, we got one of those teachers who is afraid of gaps with my youngest (DS7). He started kindergarten so eager to go to big kid school. His beginning of the year assessments showed that he was reading at a beginning of first grade level and he got a perfect score on the math assessment. Despite numerous talks with a very kind but cautious teacher, he got no differentiation. I asked numerous times, why did he have to go over things where he had already demonstrated proficiency on their own assessments. I kept getting the "no gaps" line. As I posted here last year, he was miserable by Christmas and didn't understand why he had to go back to school after Christmas break because he wasn't learning anything.
