I don't know if my son would have evened out by third grade if I had left him in our public school. When my son was almost through with kindergarten he had made what would normally be a passing score (but not the required 90% because of his handwriting) on an end of first grade test to see if he could skip first grade since he was already reading and comprehending at a 5th grade level, but the kindergarten teacher was recommending holding him back in a transitional first grade (year in between kindergarten and first grade) so that he could work on fine motor skills without OT even though he has a disability that affects fine motor skills. The principal, a relative of mine, arranged for me to talk to a first grade teacher at the school who was the mother of two gifted boys and was working toward a master's in special ed where she learned even more about gifted education. She looked at samples of my son's work. She had already heard about him. She told me that she thought he was probably highly gifted. Her advice was that I should put him in private school or homeschool him. I told her that I couldn't afford private school and didn't think I could homeschool my son. She gave me some teaching materials and made sure I understood that I would have to homeschool my son and that I should absolutely not under any circumstances let him go to that school.
She was right. We did homeschool. He did not even out.
Our wonderful small town school with the amazing football team that our relatives just love because their kids who are very good in football are treated like royalty, would not have been a good school for my son. The school has a bullying problem. Their ACT scores are below state average. Yet the relatives still believe it is a great school and don't want to hear otherwise. My son's piano teacher recently took her child out of this amazingly wonderful school because the focus is definitely not on academics and her smart kid did not fit in. People in our small town were giving her a hard time about it.
I had to learn to trust my gut feeling on what was best for my child. That was hard to do. Educational experts with years of experience were telling me very different things. I am grateful for message boards like this one because they often gave me better advice than the experts, but then I guess they are the real experts.
My son is now 14 and 2E with some sensory issues or overexcitabilities and dyspraxia and he is going through some difficult and distracting, painful physical issues now that make it impossible for him to enjoy most activities with kids his age, but he is still smarter than I am and he learns more quickly than I ever did if given the opportunity to learn the way he learns best.