OMG I am so dealing with this with my Intro C&P student right now. It's pulling teeth just to get him to step back and understand big picture the problem we are trying to solve. We solve 3 mutually exclusive cases, and then he wants to multiply them! Why ? I'm still trying to figure out what questions to ask him to get him to see the answer.

One more point is that NaN's sees a wide variety of students in her AoPS classes. I'm guessing many are plopped into those classes because they've proven themselves to be good math students in their BM schools, which is a low bar...equivalent to being good at pattern matching. These students arrive in NaN's class ready to deploy pattern-matching once again and fail. I'm guessing homeschooling parents take a more thoughtful approach to selecting AoPS, as evidenced by all the threads on this board titled "Is AoPS right for my student?"

Having written the above post, I can see what you mean by memorizing formulas. I have a student who for every single problem wants to throw at it, even when it's wildly inappropriate.

I believe you, but I find it hard to believe. I mean, isn't it just a matter of creating different outfits of shirts and pants? Once you start making outfits, doesn't the multiplication principle become obvious?

I think part of the misunderstanding here is the assumption that a student who has not taken Intro C&P knows absolutely zero counting and zero probability. Same with NT. IIRC, the AoPS Intro Algebra have brief introductions (1 chapter each?) on those topics, and if a student has already been doing math contests, they probably have had some exposure to both topics before being introduced formally in the actual classes. I know this is the case with my kids. I was teaching them basic C&P in the context of prepping for various math contests before they actually cracked the book for formal study.

I get this sentiment, and I am sympathetic to the cause of students advocating for themselves. But ultimately I think this is unfair to the OP. Students in regular school are often guided by experienced college counselors who attend meetups with college recruiters and have a solid understanding of the landscape of higher education. If a parent is unfamiliar with how college admissions works in the US, it is well worth their time to understand what it's all about. It's an endeavor that is fraught with high costs, poor outcomes, and dissatisfied students. It's never a bad idea to become informed about things like a school's reputation, and strengths and weaknesses of college rankings, selectivity, school culture and everything else. Educating yourself is not the same thing as making decisions for the student.

You'll find out 2 weeks after her birthday.

I might separate math instruction from problems with documentation and careless errors. If she otherwise understands the math, I would continue to make forward progress, while still working on techniques to avoid careless errors. I view these as very separate skills, plus I think it might be demoralizing to repeat material, and also make her more likely to make careless errors?

This was before covid, but my dd spent a lot of time attending adult type in person meetings and then scheduling informational interviews with all kinds of people. (She's still doing this this summer.) Anything from attending Commonwealth Club talks to anything else she can find. Then introducing herself and scheduling a coffee or lunch. It was kind of a bridge to adulthood for her.

Wow, I mean wow. This sounds really cool. I would encourage her to double down on this. Find out how she can pursue this. Are there opportunities to share and display this? Can she schedule an informational interview with people who this for a living? (Maybe someone at Pixar?)

I'm sorry I don't, but I have called the National Merit organization directly in the past and found them to be very helpful.

If your student wants to practice the PSAT, then he should take the PSAT, not the PSAT10. Taking the actual PSAT will let him know if he's in the ballpark for qualifying for National Merit in your area (it varies by state). Taking a different exam will not. From PrepScholar: "The content and format of the PSAT 10 is identical to that of the PSAT/NMSQT and very similar to that of the SAT. The only major difference is that the PSAT 10 is shorter than the SAT is, and its questions do not get as difficult since they're designed for students at the sophomore level." Skip the PSAT10. You are correct regarding asking schools for permission to test. States and schools vary in their rules for allowing students to test. Here's some more information about testing sites and some tips (look at post #2). When the school year starts up again, I'd try calling because they may not have updated their website and a school's policy can change at any time. Don't rely on the College Board list, I think it's fairly useless. Finally if National Merit is a goal, then there are alternative ways to qualify.

I think you are off to a great start. And it's a good idea to get an early start. My DH and I edited and re-edited our counselor letter so many times, when it was finally submitted my DH said, "I need a new hobby."

The advantage of homeschooling is you can write your counselor letter so that it complements rather than repeats what is contained in other documents. So if your robotics champion student will be writing extensively in her essay about her experience on the robotics team, you can use the counselor letter to write about some other aspect of her personal qualities.

But you're a published author already aren't you?! Who am I to criticize your writing?

Okay, so this isn't going to be constructive at all, and I apologize in advance, but... I found this blog post to be... um... useless? Again, I'll admit I don't read well on screen. But you lead with an anecdote about your dd. I stop at the word "subitize" because I don't know what that means, and I've never heard anyone use it before. So then I wonder is that some kind of education jargon, and I start to question the content. I found paragraph 2 difficult to read. Can you use Latex with Wordpress? I think you delimit it with $latex x^2 $. I skip three paragraphs down you describe how difficult it is for students to understand "counting on" but that was not my experience with my own daughters. Continuing to skim, I see you prefer option (b), so I look back to read what option (b). (I don't bother to read option (a) because you aren't advocating for it.) Then you say you don't like either option (a) or (b) so now I'm a little irritated that you made me read about option (b) for nothing. Then you put the words "mental model" in a pretty blue/green bold, but then you don't define it. So now I feel like I've read a blog post with zero ROI. (This also tells you more about me than it does about your writing, lol.)

No, no, no, it doesn't. I was just worried you were starting go down that route. I think my bias comes from not reading well on screen. If it's a short article, nicely formatted, with gobs of white space them I'm good. If it's more like a novel then I give up very quickly. I supposed i'm also irritated because Garlikov has some excellent ideas but he had the gall to make me work to find them.

Also, I want you to avoid that trip to crazy town that is Garlikov's website, with its preambles and citations and left-margin-to-right-margin formatting. (It's not a good look.) Busy parents don't care about that stuff. He should delete everything and start with part 4) Representation of Groups, halfway through the second paragraph with "We have these 3 different color poker chips." Then he should delete part 5 and everything that follows it. While he's at it, he should insert some more white space into part 4. His power point is actually quite nice this way. I just don't want you to get too caught up in why we should do something. Show us what you do, and write a little bit about how it's been helpful in your experience. We can take it from there.

Okay, then let me describe you this way: "A gold medal IMO winner who also has experience teaching young children over average ability AND poorly prepared Stanford undergraduates AND is currently teaching her own 2 daughters." I think you are truly unique in this respect, and as Cal Newport says, you are the best person to write this book.

Honestly I don't need any theory. If a gold medal IMO winner says, "This is how I teach math," then I'm listening.

Yes, this is very helpful. I was inspired by this thread to return to the fairly unreadable Garlikov (?) blog post...and try again to reread it. And, since I mainly use a Chromebook, I went to the trouble to get some sort of powerpoint extension so I could view his A/V powerpoint. (Did he create this before youtube was invented.) And...genius. The blog post is terrific. (Too bad all the good stuff is buried in the middle of a bunch of useless boring stuff, so you really have to search for it. But the powerpoint is terrific. It could have been a video, but as a ppt, it was nice to be able to step through each slide. It all reminds me of what I did with the algorithms in Singapore Math, but his approach is slower and gentler. For me it's like I didn't even both introducing place value until we studied the major algorithms. Garlov (??) didn't extend it to long division, but that's and easy enough extension. I think the big loss is his powerpoint isn't really accessible. Is the author still alive?

Yes! I found this too! It was annoying. I hope they fix it.

My course descriptions and transcript were organized by subject, with the most recent/most advanced coursework first. I saved my documents as PDFs before uploading in order to ensure the formatting is retained. Don't worry; you'll be able to preview your upload and change it if you don't like it. I found all the fields in the Common App to be very friendly this way. You can change and delete and re-upload any number of times until you hit the final SUBMIT button. You can print a hard copy of the entire application, all fields completed if you are like me and prefer to edit on paper rather than on screen. And even the final submit requires multiple, multiple steps, so you really can't accidentally submit.

Yes, please!