We are trying to debate acceleration of subjects vs depth in various subjects. But this is most glaring for us in math. For example for any level in math there is in order of depth:
1. School math
2. Basic level math core age from books
3. EPGY/Khan academy level math
4. AOPS level math
5. etc etc
How have you traded off on mastery of depth vs advancing in grade levels?
The short answer is mastery of depth over advancing in grade levels to the extent possible. The higher level your student attains the more obviously beneficial this approach will prove to be.
However, practically speaking, you have an additional obstacle due to the low level of your "School math". One possible solution is to disregard school math and proceed independently to ensure depth. If in fact your school math is so extremely low level, there is little benefit/meaning in advancing in grade levels unless you supplement with depth simultaneously.
In our case, school math is higher level than EPGY and significantly higher level than Khan Aacdemy. I am judging EPGY based on what I have seen of CTY(similar curriculum) and the fact that our district stopped allowing its use a few years ago as an alternative curriculum for certain accelerated (beyond regular GT) students who needed an online course. It appears not to have kept up with advances over the last decade so that there are holes in areas such as word problems, problem solving and written explanations compared to what our GT students are supposed to master. Khan Academy is very basic coverage meant for the "Everyman" rather than GT students. It is great for basic practice, remediation and an additional source of quick topic coverage.
If your child is to keep pace with high achieving students nationally, you need to go beyond Khan Academy level math. AOPS is an obvious choice for Pre-Algebra and beyond. I am not familiar with Beast Academy but presumes it has depth due to the source. Glenn Ellison (an MIT Economics professor who coached mathcounts) also has a book aimed at middle school competition level math and another one aimed at elementary kids. DS used the middle school one the summer after 4th grade (after completing school GT Pre-Algebra) and learned some new topics. I considered the elementary one for DD and he kindly PM me to offer a few chapters via email after we exchanged posts on this forum.
Sometimes you do need to double back, particularly for higher level math courses. The AOPS courses are invaluable for the proof writing and challenge problems. If you can't takes the courses, the books will provide some challenge although not as much as the actual courses.
