@Mom2aphysicsgeek Oh my gosh, you’ve described my younger sister. She is also accelerated in math, a lot her own doing. (We’re a homeschooling family, K-12). When she started math, our family was going through a move and my mom didn’t have time to get a textbook for her to start work in. So, my mom would write out problem sets in notebooks and give them to my little sister. She would work though them and return promptly - and ask for more. My mom was surprised that she kept wanting more math, but she gave it to her because it made her happy and kept her busy. My mom is very good at math, and there was definitely a rhyme and reason to the way she taught her - it wasn’t random. My sister would just master the concepts quickly, so my mom would teach her something new to keep her challenged, so she wouldn’t get “bored to tears” as she (and you!) put it. In doing so, she covered at 3 years of math in my sisters first year of school. After that she put her in regular textbooks, just a few above her grade level by age. By the time she was 9 and I was 13, she and I were essentially doing the same math, and she was doing better than me. :"> So, my mom merged her in with me when I started algebra, and she was with me in the math sequence from that point on. She finished pre-calc by the time she was 13, and then we had to fight the community college tooth and nail for months to get her in. In the meantime, she took the SAT and got a 730 on math and did Calc I essentially on her own, and passed the CLEP exam with a perfect score. (I took Calc I at the community college, since I was 17 so it wasn’t an issue.) Finally, they let her in, after a long appeal process and whatnot, and she took Calc II with me during my senior year and is currently taking Calc III. The thing is, she’s going to have to go to the state university for more math classes since she’s exhausted what the community college can offer her, and while they were happy to admit her after one look at her scores and classes, it’s becoming a struggle since she’s at the bottom of the barrel for registration since she’s a dual enrollment student. So she doesn’t know if she can get into Diff Eqs and other classes for next semester… She plans to take other classes as well to round herself out - gen eds, language classes, etc. And she is not a total math nerd - she does a lot of activities, like choir, chess, Civil Air Patrol, and more.
Anyways, it was definitely a case of her not being pushed, as it was her pulling ahead and my mom placing her appropriately. She doesn’t really care about physics, but she loves math. She plans to be a math major and dreams of being a Rhodes Scholar… who knows, but she could probably do it if she tries hard enough, she’s very bright. I took physiology during high school, at the regular pace, and sweated blood to get through with a low A. She’s doing it in one semester, double the pace, and acing everything. She doesn’t like it, but she can understand it and connect all of it… it just didn’t compute with me, I’m not a biologically minded person. But I like physics more than she does, so I reckon that compensates a little…