Here's an article that's relevant to this conversation: https://www.stanforddaily.com/2019/02/21/students-educators-discuss-challenges-in-transitioning-to-stanford-from-under-resourced-schools/ It's about Stanford undergraduates who were admitted from what they now call "under-resourced schools" who arrive unprepared for the academics and can't continue in their intended fields. When I was in college, this sort of thing was swept under the rug. Students would breezily say they arrived intending to be premed or study engineering, but fell in love with some other humanities field instead. Now students are angry. Though weirdly, they direct their anger at Stanford, rather than at their high schools that provided poor preparation: Despite this support, some students said they also felt unprepared for the rigor of Stanford classes, compared to students who had experience in college-level subjects during high school. Students specifically criticized courses such as the introductory chemistry series. “It just seemed like everyone else around me but me had some kind of rigorous curriculum that helped them, that gave them an advantage when taking the class,” Adebagbo said. To these students, the professors also appeared to be gearing their classes more toward students who did have some background in the subject. “I felt like my professors automatically assumed that their students had a sufficient background to at least understand the concepts that they were presenting in the class,” Cusic said.

Are you talking about college or private high schools? (Did you find this at Stanford?)

One unit.

I studied the material covered in Intro C&P when I was in high school. I took the Intermediate NT class last summer and it was challenging, but it definitely boosted my confidence and added to my problem solving toolbox.

Another vote for following the student's interest. There aren't any lock-step prerequisites in history classes. It's not like you can't learn about WWII until you've already studied Renaissance, thought it might help. But advanced learning comes from a deep understanding of history generally: moving to primary sources, getting beyond more superficial cause/effect, moving beyond hagiographies of historical figures to a more nuanced biography.

"Never attribute to malice that which is adequately explained by stupidity"

What accrediting agency do you need approval from?

Wow, WendyRoo that's very impressive! I agree those are very good skills to learn, and at such a young age, he'll be reaping the benefits when he reaches high school. Regarding mishaps, adults aren't immune to those. Once I ordered a year's worth of science supplies in August, and and stashed them all into a closet. Turns out, one of those items was a freshwater living Elodea plant. By the time I pulled it out, months later, it had turned into some dead brown mush!

This is the number 1 reason I homeschool. My weakness is teaching writing. I wasn't worried about their math skills, but worried that I was causing them anxiety over their writing, so I outsourced that at around middle school. Locally I have seen families who pull their sons out of regular school to homeschool, but leave their girls enrolled. The difference is boys are more likely to complain and make a fuss if they aren't challenged. Many (not all) girls are more eager to please even if they aren't adequately challenged. As long as they receive praise for sitting quietly at their desks and solving their multiplication problems, then they keep on in school.

My dd's both used the MCT curriculum from elementary to middle school. The Level 1 curriculum doesn't have a lot going on, but it was elementary level after all. We spent most of our time working through the practice books, 4-level analysis of 2 sentences per day. That practice I think really sealed their understanding of grammar and usage for years to come. I'm also a huge fan of Caesar's English for vocabulary. Just an amazing beautiful way to learn vocabulary. Unfortunately we were not fans of WWW...why did he change up what was such a lovely approach to vocab? Also, the more advanced grammar books did not dove tail with the practice, so it was hard to really be fluent with some of the more advanced grammar concepts, but it all seemed so advanced anyway, I didn't care. Finally I agree with others that the high school level writing curriculum just wasn't enough for me; by middle school I was outsourcing writing instruction anyway since I'm so bad at it myself. Since dd won an essay contest and has been writing essays successfully for various things, and her verbal SATs are strong, I can recommend MCT.

We would spend 1-3 days each on the end of chapter Review Problems and Challenge Problems.

I have digital access to the NY Times and received the print copy on Sundays. Also the local daily paper.

What turned you off from an academic career?

This was pretty much me just now:

Googling now, lol! Sincerely, though, that's such an accomplishment. Gold medal, wow.

@square_25: Also, you might enjoy this documentary about Maryam Mirzakhani, Secrets of the Surface. You might want to google around and see if there are any online screenings. (I'm kicking myself now for not telling about the one I attended. I'm eager to hear your take on her story, particularly her early years, leading up to the IMO.

WHO ARE YOU? (lol!) Seriously though, did you represent the US? Were you the gal they featured in the documentary Hard Problems?

I'm not sure how much a vet tech needs to know, but unit cancellation may be very important in her office. I know in pediatrics, dosing is often done in mg/kg, that is mg of some drug per kilogram weight of the child. I imagine with dogs coming in so man different sizes, they also dose this way. A quick check of a vet dosing guide found this for example: https://www.merckvetmanual.com/pharmacology/antifungal-agents/imidazoles#v3337140 You might ask what the dose would be for a 20 pound dog or a 3 pound chicken.

I haven't seen this mentioned here, but one big problem I have with FB is the recursive nature of the posts. Sometimes I come late to an interesting topic, and I see there are already 30 posts, with replies within other replies, sub-posts within posts. Some are long and informative, some short like "following!" and "me too". Sometimes if it's a post longer than 5 lines, you need to click again to reveal the whole thing. I know it seems weird to write when all I'm doing is waving a cursor around, but it gets exhausting. One thing that drew me to these boards is the linear nature of the threads. If I'm late the conversation, it's a matter of simply reading: start to finish. (like with this thread!) If this applies to you, may I suggest google groups or groups.io?

I second the Atlantic Monthly. Similar to New Yorker, but the essays are much shorter!

How much precalculus is needed for successful enrollment in a calculus course? If a student had a so-so precalculus course and might want to review this summer, what would be good preparation? What are the key topics that need to be mastered?

Thanks for writing this. Can you provide some examples in the AoPS textbooks (not the BA level) where they do an inadequate job of explaining difficult concepts?

Thank you for raising this issue. I remember having a discussion about the lies we sometimes tell our children with Bernie Nebel and users of BFSU. For example, we often tell our students the lie that electrons rotate around the nucleus like planets in a solar system. Then one day, it's like Santa Claus, and now electrons occupy a probability distribution. I felt uncomfortable telling my students the lie of electron orbits versus orbitals, but some argued that orbitals are just too much for younger students. (I still don't really get it.) Do you have other examples of lies, in math or other subjects?

Wow, I have no words for this, and after all the extra help you provided. Is this common? It also reminds me of teaching my kids python in middle school. They would type in their code, would not bother to even run it once, and then announce to me that they were done and it works perfectly. 🤔

This resonated with me. I refuse to use the phrase "cross multiply" because I think that's an unnecessary level of abstraction, even with my students in calculus. I will always, always say, "we multiple both sides by 3" or something similar. It harkens back to first principles: do the same thing to both sides and equality still holds. When dividing fractions, I like to tell younger students, "Remember, our new definition of division is to multiply by the reciprocal." Or I'll ask them "What is our new definition of division?" I want students to be clear on what has been proved and what has been defined. Great topic!