I just realized that I didn't offer any particulars for my own child in my post.

DD (now 11) is taking honors geometry, which is (I guess) considered the "10th grade" course in the 'regular' progression. Now, she's an 8th grader, so that means she's 2 yrs ahead, but that's artificial as well since it doesn't account for her chronological age. She should (chronologically) be in 5th grade, maybe 6th. So I guess that means she's four grades above her chronological placement in mathematics. But this, too, is somewhat artificial since the school has set the pace for her for the last three years, and there is NO doubt that it's slower than ideal for her personally. She worked through Prentice-Hall's math series starting with course 1 when she was eight, and has since done Course 2, Pre-algebra, and Algebra 1.

I definitely do not think of her as being particularly mathy-- she has a leaning toward applied mathematics but really doesn't care much for theoretical math for its own sake. She was not a kid that seemed to figured out a lot of things early and on-her-own. At least not obviously so. She just seemed to only need one repetition to learn almost anything. Long-division excepted. She was definitely able to handle simple algebraic manipulations and symbolic thinking well before age 5, however. She worked through Singapore's curriculum (supplemented with the CWP workbooks, which she loved) levels 1-4 in about two years at ages four(ish) to six.

In contrast, her rate of acquiring literacy was a lot faster-- she went from phonetically controlled readers and easy readers at age 4, to reading Harry Potter on the sly under the covers with a flashlight about 8 months later, and reading college level materials less than six months after THAT. She has never been challenged in terms of literacy by anything that school/curriculum has thrown at her. She read her first Shakespeare play at age seven.

She is EG/PG.

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Schrödinger's cat walks into a bar. And doesn't.