I am profoundly grateful that American universities were not even discussed until my son was half way through his Junior year when he brought it up that February. He made the decision to go for it 2 months later in April, which left him exactly one shot at the SAT and 6 weeks to prep if he wanted to apply early decision, because NZ doesn't offer it very frequently. He had always planned to go to University of Auckland, and in NZ students who pass the national exams have automatic entrance, so there was no reason to try to outcompete others for any slots. We just did our own homeschooling thing. Those who have been on the board for a few years may remember the crazy effort I had to make that summer to organize all his independent readings and interests into courses that the universities could understand. We were basically unschoolers with no tests, schedules, or detailed plans, so it was quite a thing to sort it out for an American transcript and course descriptions. But the wonderful wonderful ramification of this, is that my ds was never in the competition for entrance to the elites. He never did *anything* with that goal in mind until the SAT that May. I cannot imagine how I would have felt all those years in middle and high school trying to chase a goal that is only a lottery. Trying to see inside the minds of the admissions people and try to align my ds's courses and ECs to my impression of someone else's expectations. Just Yuck! Perhaps the admissions folk could tell that he had never been chasing the goal. Everything he did, he did for his own improvement and desires.

Thanks for this.

deleted I'm not sure what would have happened had he not had a strong family to be there for him. He is now one of the top students, but he needed support to get him through the initial hurdle to reach his full potential.

I think the problem with the Ivy's and other elite universities is when a student thinks 'if I just get in, I'll have my ticket in life.' They are after the prestige, not the education. There is no way around it, there is a high when you get in -- we definitely felt it. Like you have been *chosen*. But at MIT, you better be willing to work and work hard. My son is currently so overwhelmed with work that he is going to have to drop a class. He did 85 hour per week for the last 3 weeks in a row. By dropping the class, he should drop to 65 hours. This is 65-85 hours of difficult proofs, machine learning configurations, presentations, papers, complex topics, etc. I'm sure you could go to MIT and take easier classes and do easier research than my son, but he really wants to take advantage of what is on offer. There is a driving desire to learn. I think a parent should really know their own kid before encouraging elite universities. My ds has known kids who have found the 'drinking from the fire hose' to be overwhelming, and have taken a year off. The experience has been the worst in their life, but they feel the need to finish because of the perceived bump to their future life options. But I worry that it will crush their spirit, and change them as a person for the rest of their lives. I think you need to find just-the-right-fit in the university you attend to ensure optimal outcomes. Not too hard so as to break a kid; not too easy which leads to arrogance and laziness. Tricky business.

It was a very difficult and miserable decision to turn down the top scholarship to xxx, and choose to take a massive financial hit for him to go to MIT. deleted But he *really* wanted the big pond. He was *Done* with being a big fish. In some small way I think he wanted to no longer be at the top, he wanted his ideas to be challenged by his peers. I think he wanted to fight for recognition not slide into it.

This is fair. My son is doing great research, but his direct supervisor is a post-doc not a professor. He talks to the postdoc most days, but to the prof only once a week. I think that you get more individualized attention at 1) a university where you stand out at way above the crowd, or 2) a small university/teaching college.

Yup. Most of those kids are his friends. At this point, MIT is attracting a huge amount of the math talent in America. Not all of it, of course. But there is critical mass in the dorms. My son told me that in his half of his floor at MIT (20 kids), they had enough IMO medalists to be a top 5 country. The conversations that happen in the commons room are pretty mathy, to say the least. These kids choose to take classes together, and then do the psets together. The professors are able to make the psets hard enough that this group of kids have to work together for 7ish hours each week to get them solved before they write them up independently. Those are some hard problems! But the benefit of the group work at his level is enormous. Once again, I loop back to personal development - social, emotional, intellectual, etc.

My son went to be challenged. deleted I do not regret all the money we have spent. The longer he is there, the less I regret it. But if you choose to attend a top school, be careful you are not a bottom student, because that is incredibly detrimental to the psyche. My dh was bottom 5% at Duke, and he carried that around with him for 20 years. Lots to think about, Good Luck to you. Ruth in NZ

The stuff I have in my head is so different than what a silo-ed teacher has in her/his head. They teach 1 grade, and in high school 1 subject. I've taught every subject in every grade. My content knowledge about the progression is enormous, but I think undervalued. I considered doing my second career in learning theory, but decided that I could not make an impact given my background and limited time (I'll be 55 when I come out), so have decided instead to go into environmental geology, and remediate soil and rivers. If I could clean up just one river, I would feel like my retraining had meaning. I think that Not_a_Number is in a different situation because honestly her contest math career and gender make her an anomaly. I think she will be taken very seriously, as she is close to one of a kind in North America.

If it is anything like NZ, geometry is pretty light. There are some algebraic geometry problems but only at the highest level so most kids don't get to that. The problem with integrate math is that you spend a lot of time reviewing each year, so you don't get as far as in the American system. The positive side is that there is 1) a lot of review which is good for many kids, and 2) the opportunity for kids to be late bloomers and not really get algebra until age 15.

Definitely done that! But we seem to do it a lot.....

I will add, that there are *very* few people who teach a single student for 12 years. What you are learning from teaching your daughter is special and unusual. Don't underestimate the ramifications of what you learn. Sure she is just one kid, but that is called a case study. You don't need to do a double blind study to learn in any field. Deep study of a single case study leads to new knowledge in a different way. Different not lesser.

I've been paying attention! I think you need to start taking some detailed notes and keeping some of your kids' and tutor kids' work examples. You have asked me before about what xxx looked like that I noticed in a student or my younger boy, and I couldn't remember the details. Start thinking more about the ramifications of what you are learning to helping a wider audience once you figure it all out. I think you have a real chance to make a difference in the field of gifted math education. Most people of your mathematical level and intelligence are off doing math research, as you know. That means that the people doing research on gifted math teaching methods are just education researchers, and they don't get it like you do.

Well you can either influence many people to a small extent, or very few in a profound way. Most people respect the first more, unfortunately. I have found that I am dismissed if I say I am a tutor and people change the subject. But if I say that I work with at-risk youth, people become very interested, ask lots of questions, and respect me more. It is all about how you sell it. So he is my elevator pitch for you: I am researching the best methods to teach mathematics to gifted and profoundly gifted youth. I'm comparing the effectiveness of different methods across 3 different domains - high impact daily teaching, one-on-one weekly teaching, and online classroom teaching. I am interdisciplinary, merging learning theory with Information processing theory. I am also interested in self-regulated learning. I expect the research gathering stage to take about a decade, and I am still considering how to best to communicate my findings to make the biggest impact. 🙂

You have every reason to be proud. As I'm sure you can imagine, ds's first term at MIT was quite a complex and somewhat overwhelming endeavor -- going to a foreign country and being one of only 2 homeschoolers there that year. There was a LOT to adapt to. He didn't realize that the entire USA IMO team and a good chunk of the camp were attending MIT that year. There was a lot of jostling for position in a somewhat hierarchical situation, and ds had to somehow feel that his under-performance at the IMO was not representative of his capability. There was a lot of trama associated with the last IMO -- he jokes about PTSD, but he still struggles to take exams in a large room with lots of other people because of his experience in his senior year IMO. It was just that bad. He put way way too much pressure on himself, and cracked. So to find out to his surprise that he is actually a good mathematician when compared to all these kids that he kind of idolized was a good feeling for him. Sorry, if you thought I was dismissing you. Not at all. You are my hero!

Fair.

No, I think that kids with tutors and mentors that can direct their studies for IMO success would be far superior to what my son did to prepare. We couldn't find anyone to help, and I certainly couldn't, so he prepared as best as he could on his own. However, the self-teaching aspect of his approach was/is hugely important to his current success. He learned not only how to nut it out without help, he learned to struggle and not fear it. The day that an IMO perfect scorer knocked on my son's door to get help with his homework was a special day indeed. It showed him that his knowledge was different from someone who could well on the IMO, but it was not lesser. Basically, he couldn't do IMO problems in the time frame allotted, but if the questions were harder than IMO questions (questions that could take all day to solve), he was better than the other IMO kids.

Just an FYI, Carnegie Mellon required that ds submit a complete reading list of every book he had read in high school. This was separate to my course descriptions.

I do think he did Olympiad problems and I know he enjoyed them, but I think he spent more time working on textbooks like baby Rudin. I know that he took at Grad class in combinatorics at MIT that had 5 prereqs that he didn't officially have, but yet somehow he had studied the content in high school. I just don't remember the resources he used as he often used online content. So he improved his knowledge of combinatorics but I'm not sure he did that through Olympiad problems until the last year. I'm glad you liked the problem! However, my point was that he solved that with only Introductory AoPS text knowledge. He could do it because of the deep problem solving he developed by how he used the books. I think that a LOT of kids that use AoPS don't use it to its full potential, especially kids taking the classes which go pretty fast and have way fewer problems. The kids also often get hints or work together, which undermines the development of their problem solving. So to answer the OP's question, AoPS is only as deep as how you use it.

He was not really into competing. His math competitions were just an offshoot of his love for math. In addition, there were no other opportunities to be with mathy kids unless he did them. But it was *how* he used AoPS that was effective. Because he went so slowly and independently in the introductory series, and did every single problem without hints, he developed deep problem solving beyond just the content of the books. To give you a feel for how far AoPS got him, he solved this problem for his first camp selection problems, having only gotten through the 4 introductory AoPS books, and got full points for his proof. At this time, he was *completely* self taught. He had refused all help/teaching in math since he was 7.5 and had not started the AoPS classes at that point. So the only knowledge he had when he solved this problem was what was in those books, and this level problem was clearly not. Those books taught him deep problem solving because he used them to their fullest. In a sequence of positive integers, an inversion is a pair of positions such that the element in the position to the left is greater than the element in the position to the right. For instance the sequence 2,5,3,1,3 has five inversions, between the first and fourth positions, the second and all later positions, and between the third and fourth positions. What is the largest possible number of inversions in a sequence of positive integers whose sum is 2014?

Honestly, I'm not sure. Not many. He didn't study for the the first 2 IMOs. He had no teacher, tutor, coach, or math circle throughout middle and highschool. What he did do was Every. Single. Problem. in. All. the. Textbooks -- on his own without any hints. That is what I mean by using the program to its fullest.

My ds went from the AoPS sequence directly into independently studying Analysis with baby Rudin. So I don't know that you actually need anything deeper than AoPS if you are using it to its full potential. To use AoPS well you need to develop deep problem solving by doing the hardest problems without getting hints. This takes quite some time.

I used Mathematics: a Human Endeavor with my younger boy. We did it concurrently with Life of Fred. LoF is not exactly a survey text, LOL, but LoF does get kids thinking about math being used in life. The applied nature of their Biology, Physics, and Economics preA books complemented the more math-as=beautiful approach of MaHE.

I absolutely incorporated STEM into his English classes. This is an x-post I wrote yesterday on the high school board x-post As for English, if you are in charge of content, then focus on what will be useful to him. My older boy is a STEM kid and for English, we focused on him being able to write about science for a lay audience. So we studied and mimicked Scientific American agenda articles and their short summaries of current research, and studied and mimicked the Economist informational style article in the science and tech section. We practiced oral presentations of his science fair research, and how to answer questions from a lay audience. For research skills, we worked on understanding the bias of different actors in issues like GE crops. For GE, we studied the different language and arguments for Monsanto, activists, Ecological Society of America, and the EU government. We worked to understand how language can be used to influence people. Point is, do something that he values and will be of value to him. If he doesn't want to do literature and poetry, then don't. It is not required to make an effective English class.

Keep in mind that kids pick up speed. My so at the beginning of 8th grade, could not write The Cat in the Hat, because he could not spell the words, or understand where to put a period. He had deep ideas, but could not organize them into writing. We spent the next 5 years, working hard to remediate this, and his speed of learning picked up over the teen years. You can get it done in the time you have if you make a plan and he agrees to it. As for English, if you are in charge of content, then focus on what will be useful to him. My older boy is a STEM kid and for English, we focused on him being able to write about science for a lay audience. So we studied and mimicked Scientific American agenda articles and their short summaries of current research, and studied and mimicked the Economist informational style article in the science and tech section. We practiced oral presentations of his science fair research, and how to answer questions from a lay audience. For research skills, we worked on understanding the bias of different actors in issues like GE crops. We studied the different language and arguments for Monsanto, activists, Ecological Society of America, and the EU government. We worked to understand how language can be used to influence people. Point is, do something that he values and will be of value to him. If he doesn't want to do literature and poetry, then don't. It is not required to make an effective English class.