Do you have tips on how to manage this for precalculus/algebra 2 / statistics / other upper level classes? especially at the AP or IB level? honestly it feels like those courses rely on so many different prior knowledge standards that were never really mastered in the first place so cognitive overload's practically a guarantee.

Yes, and as obvious as this may seem, many students are pushed into such courses, whether for status, or to help them get into selective universities. You have to know basic arithmetic and algebra, and unfortunately, an alarming number of students have not mastered such skills. And I don't mean being able to "explain" to show "understanding". I mean being able to use the various algorithms and procedures. I've had students in algebra who didn't know how to do column multiplication and used some inefficient method with numbers all over the place, taking forever to do the multiplication and getting a wrong answer. And no, calculators are not the answer!

yeah it's hard because administrators expect you to follow an AP/IB curriculum (like you said, funding and school rankings definitely cause kids to be pushed into the wrong courses). and there's some kids who can handle it mixed in with some who can't

Do you have tips on how to manage this for precalculus/algebra 2 / statistics / other upper level classes? especially at the AP or IB level? honestly it feels like those courses rely on so many different prior knowledge standards that were never really mastered in the first place so cognitive overload's practically a guarantee.

The fundamentals of algebra need to be mastered, and many students entering Alg 2, pre-calc, etc are lacking these skills. I discuss the prerequisites from K-8 in my book "Traditional Math". https://www.amazon.com/Traditional-Math-effective-strategy-teachers/dp/1915261546

so would you recommend not teaching at the AP or IB level until fundamentals are mastered?

Yes, and as obvious as this may seem, many students are pushed into such courses, whether for status, or to help them get into selective universities. You have to know basic arithmetic and algebra, and unfortunately, an alarming number of students have not mastered such skills. And I don't mean being able to "explain" to show "understanding". I mean being able to use the various algorithms and procedures. I've had students in algebra who didn't know how to do column multiplication and used some inefficient method with numbers all over the place, taking forever to do the multiplication and getting a wrong answer. And no, calculators are not the answer!

yeah it's hard because administrators expect you to follow an AP/IB curriculum (like you said, funding and school rankings definitely cause kids to be pushed into the wrong courses). and there's some kids who can handle it mixed in with some who can't