There's plenty of time for "horizontal" later, though you may need to eventually abandon Connections Academy to get what you need. There's foreign languages, various math options, science as far and as deep as you like, and history/geography/social studies is endless. You don't need to be constrained by the academics that the curriculum designers decided were important and practical to teach.
But early in elem, it really is about acquiring a set of information, learning strategy, and discipline and love for learning. Going fast now does not equate to early college.
The psychiatrist probably hasn't read studies and data on acceleration.
YES. Which goes right alone with my post above. I feel that Connections was 90% positive for my DD when she was 6-8 yo and in elementary. In middle school, more like 60-70% positive. Since? More like "least worst," and let's not talk about that...
As long as you understand that you may be closing doors into B&M options... and leaving "homeschool" as your fallback position, then all is (probably) well.
RE: the psychiatrist... wow-- bias, much??
I'd consider that reason enough to ditch that psychiatrist, honestly-- how helpful can such a person be for PG children if s/he doesn't even understand THAT much?
