> I'm sure you put in a lot of hard work to become Valedictorian!

Sadly, no. I hate to sound like one of those 'gifted' people, but a lot of it just came naturally. I never learned how to study; university was a rude awakening, though I still didn't really learn until after graduating there when I started self-studying things.

> Realistically, people like you and I who had a stable upbringing probably would be successful in any reasonable system.

Exactly. I'm thinking now to all my classmates and what they did after. The ones who didn't struggle in school (not necessarily excelled, but they didn't struggle), were all those who had stable households. As far as I'm aware, minus a few who got into opioids (rural America!), most are doing well for themselves. It really does impact a lot.

> I personally attended a poor middle school and didn't learn algebra until 9th grade, but still managed to end up as a mathematics postdoc at a very nice place.

Awesome! Mathematics is what I've started self-studying (I did physics, now dong a physics/applied mathematics masters), and it's super interesting. Just proving stuff is so much fun.

> I cannot wrap my brain around the reluctance to make changes to the system in the face of statistics like the one I mentioned elsewhere and have observed with my own eyes (that is, there are very, very few African American PhDs in mathematics).

Exactly! Part of me thinks it's because it forces us to look behind the curtain, so to speak. If we look at why, we realize it's because of the socioeconomic factors, and then we have to look at what caused that, etc.

> although you can teach college without knowing any formal pedagogical methods,

Sadly, I sometimes wonder the validity of education research. Formal pedagogical methods certainly helped me (I did a MAT while teaching, and there was a noticeable difference), but I really didn't become a decent (wouldn't say I'm good yet) teacher until I had a coworker who really was great and took and interest in explaining things and working with me. It really changed my whole outlook on teaching.

> And I've come to the conclusion that backing away from homogenized curricula most hurts 1) bad teachers and 2) textbook companies.

Absolutely. I'm a huge proponent of public schools, but part of me has really wanted to start a charter school. There would be one major requirement when hiring: the teachers have studied the subject. So your math teachers all have math degrees, English teachers have literature degrees, etc. I think this would really work for lower levels, as you get teachers who are interested in it (instead of being taught math by a teacher who isn't a 'math person', which rubs off on the kids), but because they also understand it at a deeper level and can hopefully find new approaches to it. No textbooks, either. Hopefully it'd be small enough that they wouldn't be needed. Also, at least at a younger level, no homework and let the kids actually be kids and play. I'd argue at least an hour or more recess a day, and a long lunch.

I'd certainly be interested to hear some of your ideas for moving away from the homogenized curricula, and will be looking into those two you mentioned. Thank you!