Is the problem here that these "equalities" are not actually equal to each other? Is it bad mathematical notation? It's a little hard for me to understand how students might not understand multiplication, but I suppose it is because mental math is not taught much in the US.

In AoPS Intermediate Algebra we were getting quite sick and tired of polynomials. I distinctly remember one day ME: "Ah! Finally we're done with our 3 chapters of polynomials!" <turns page> "Chapter 9: Factoring Multivariable Polynomials" Oy!

Professor >>> Class!

Another vote for introductory counting and probability (if she hasn't taken it yet), intro to number theory, and/or intro to programming in python. All are offered at AoPS, or the math classes you can do self-study with the textbooks.

It is funny to say you are happy to know you have ADD, but just having a diagnosis can be such a relief! He sounds like a great person, and I hope he gets the accommodations he needs to succeed.

We have a few AoPS Academies opening locally. Do you know how the experience of those students will differ from students taking online classes?

I was hooked after reading this post: https://mathwithbaddrawings.com/2015/05/20/us-vs-uk-mathematical-terminology/ "You know who uses scientific notation? Scientists, that's who."

Squeaky wheels are annoying, but they are the ones who get results. I suspect the lady doesn't feel as "harassed" as your dd thinks she does. Another way to look at it is if you paid a feel to apply to the college, you are paying for some minimal level of service: to acknowledge with accuracy when your application is complete.

This year $90/hour, and I only teach AoPS and prep for math contests. Last year I was busier so I was charging $120/hour. But those kids returned to school. (The downside of being expensive is private school starts to sound more affordable 😉.)

(Take that, Saskatchewan!)

(Fun times reliving my glory days...) Yes, I kept all my math exams and many of my notes: The AMCs were a big deal at my high school. (They were called the AHSME back then.)

...and the hilarity that was my academic life continued into my senior year:

I'm a fan.

Okay, so what does precalc actually mean? We didn't have that class at my high school. Our math sequence was: 9th: geometry 10th: functions + analytic geometry 11th: advanced algebra and trig 12th: calculus It looks we covered complex numbers in 11th grade and vectors in 10th grade. And for fun, here's some samples of my work. (Yes, that is purple mimeograph ink!)

I also did not have my kids take AoPS online classes, except for the extra test prep classes for AMC and MathCounts. We spent one day on each chapter section, and then 2-3 days each on end of chapter Review and Challenge Problems. We also school year round, so we had extra time to make up for our snail's pace. In the time I've been tutoring, I have had several students who are taking the AoPS online classes, helping them with their homework and reteaching material they should be learning in class. I wonder if the students aren't supposed to also be doing the exercises in the book in addition to the online homework? Because I think my kids did many more practice problems from the book than the online homework which only has 10-12 problems per week. I spent a few days working through my AoPS online precalc student's homework. I needed to return to the textbook and review a few problems before I could solve his homework.

Do you have any inkling of the demographics of your students? Are many of them radically accelerated in math? Are they taking precalc for the first time, or again after having studied it at BM school? Are many of them homeschoolers?

I'm really surprised here. I mean, in my own high school, I remember on the first day we were told "A vector is a quantity with magnitude and direction." I suppose I wasn't the only one because I was pleased to see this in a popular movie: Interestingly I just took on a new student who is doing the AoPS online precalculus course. I've been working on his homework on complex numbers and those last 2 were challenging! I can't image students who made it that far in the course are struggling with vectors.

Ahem? Some sort of gardening course?

Gosh, sorry, I forgot the link: https://www.latimes.com/opinion/story/2019-11-21/math-anxiety-elementary-teacher

This is a really good question. On the one hand, a stellar student in a sea mediocrity is more likely to be noticed by their professors, perhaps receiving invitations to work on research projects, etc. If your student is not one to be influenced by peers, this may be a good option. A stellar student who is at the bottom of her class may have more difficulty standing out and have greater stress if she is prone to comparing herself to others. But peer groups are also important. Outstanding peers can be inspiring, and they often graduate into positions of importance and accomplishment. Your student may rise to a higher level of achievement by following their example. If your student's peers are mostly rich kids whose parents bought their way in but are otherwise not qualified, that can give your own student a skewed view of the academic world. It's a tough decision and highly personal, and perhaps also dependent on career goals.

This article advocates for releasing elementary teachers from teaching math altogether, and bring in math specialists instead. This idea that elementary math teachers are math-phobic is a big reason I decided to homeschool.

Does NZ give some sort of allowances for students with learning differences, like dysgraphia, with extra time, or other accommodations? There is much discussion locally about accommodations in US universities for students with disabilities, even those that are learning differences. I'm on the fence about it. I hate to see an LD holding back a student who could otherwise do the work. But then I wonder what is the point of college anyway if not to give the best learners an opportunity to move to higher learning? Do we grant accommodations to athletes who are too short for basketball?

I put it altogether: academics + ECs +essays together determine whether a school is a safety. Even at a school like CMU, it depends on the department. The CS department is way more competitive than the liberal arts school. But really it's about your best guess for your own students probability of admission. Some schools have an automatic admission for a certain minimum test score. If you exceed that, then it's a safety. Some have admit rates that are so high, and with a test score IQ range that's so low, that you can generally be assured of being admitted. If your student wants to attend a college when they graduate, then it's a good idea to apply to a couple of safeties. Even if you don't, plenty of schools have rolling admissions and you could still attend. The definition of a safety depends on the student as much as the school or it's department.

Wow, that is an impressive exam. I would love to see American students take this exam for college admissions. It's so much more interesting and way more challenging than anything you'd see in the States.

@lewelma Could you provide some more background on this exam you linked to in the first post? Is it for all 10th graders? What score is required to advance to 11th grade? What is a median score? Is this exam score used for college admissions? Is the Level 2 exam more challenging?