I recently had my son enter Kimdergaryen he is a young Kindergartener but was very advanced. I worried also when I saw them going over letters with my child who could do all of that at 18 mo and at 2 was reading. I pushed the school to test him because I wanted to know if I was dealing with a high learner or a gifted child. In my case the school luckily decided to try him in 1rst grade. However his new teacher was very reluctant to accept him. My mother in laws both teachers told me we were wrong to accelerate him. When the district psychologist finally tested him he hit the ceilings on every subtest and came in at 160+ IQ. That made the psychologist really take notice of his unique learning style and get a team of people helping him as well as helping his teacher see we weren't just pushy parents. He was not yet doing double digit math (he had never been taught) and is reading at a high level not quite Harry Potter. So bottom line it is not normal for a child at that age to be doing what yours is doing. If your child had a learning disability you wouldn't stop until you got intervention. I feel these gifted kids are the same they need intervention and as parents understanding as to what you are dealing with. So push for the test they can't say no. However the first thing they said to me after testing my son was public school may not be the right fit long term. Looking creatively at options is important.