I'm not sure about the problems in the book vs the challenge problems in the courses, but my son had done C&P, NT, Alg I and Alg II before geometry and it was very challenging and a completely different level than the other courses.
Responses to the challenge problems were not sentences but multiple paragraphs with embedded diagrams, etc. and often took many hours to work out. Courses are different now with fewer of the hard challenge problems, but they are still challenging.
I would think your DS should be ready for a lot of writing down answers before thinking about the geometry course.
This again reinforces the "AoPS Intro Geometry is hard" message. So does this
http://www.artofproblemsolving.com/School/courseinfo.php?course_id=intro:geometry&
"This is the most challenging of our Introduction series of classes. We recommend that students complete our Algebra 2 course, or are able to pass the Algebra 2 post-test, prior to taking Introduction to Geometry."
And here
http://www.artofproblemsolving.com/School/recommendations.php"Students who have completed Algebra 1 in school or our Algebra 1 course are ready for our Introduction to Counting & Probability, Introduction to Number Theory, Algebra 2 and Introduction to Geometry courses. We recommend starting with the Counting & Probability and Number Theory courses. Of these four, Introduction to Geometry is the most advanced."
Whereas
"Those students who have completed a rigorous Prealgebra program, such as our Prealgebra 1 and Prealgebra 2 courses, are ready for our Introduction to Counting & Probability and Introduction to Number Theory courses, although most students take these courses after finishing Algebra 1."
So Intros C&P and NT are pegged as being much easier, only needing (solid) Prealgebra as a prerequisite. I was mistaken to think that Algebra 1 was absolutely needed first. So it really is fine for DS to start these right now.
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Anyway, the typical US math sequence has students doing Algebra 1 one year and Geometry the next. I don't see why the AoPS timeline would be that different. The Intros to Alg(Alg1&Alg2), C&P, NT books should keep DS8 busy for a year or so. Maybe after that, will the mathematical experience, and the passage of time, he'll be fine with AoPS Intro Geometry.
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And he probably will just naturally get better at writing carefully etc, given a little practice and time. I like how many problems with DS solve themselves if I can manage to be a little patient :-)
It's is common for advanced kids to have writing as a relative weakness compared to other academics, and we can try to find ways for them to move forward with learning without imposing unreasonable writing expectations. But at this age, DS8 should be able to write things out more, and it's really a case where he couldn't be bothered or doesn't see the point, rather than that he can't do it (or try to do it and gradually get better). Some parental pressure is called for at this point.
