A 7 on the AIME will be very helpful in college admissions for all demographics other than Asian boys. I’ve mentioned this before, and take it for what it’s worth, but I’ve been told by someone involved in coaching at the highest levels (think MOP and IMO coach, e.g.) for over twenty years that USAMO qualification for a girl is practically auto admit anywhere. (USAMO normally requires at least around a 10 or 11 on the AIME.). There are probably only 40 or 50 or so girls who qualify USAMO in the entire college applicant pool in a given year (obviously could be a few more or less - don’t hold me to exact numbers!).
Don’t shoot the messenger, just telling you what I know. There is a paper somewhere by Andreescu that discusses female participation in USAMO, MOP, IMO, etc. I’ll try to see if I can find it…
Obviously, don’t do math competitions just for college admissions purposes. Kids who do well do well because they enjoy it. I don’t think college admissions would be a very sufficient lure anyway to really get someone who didn’t enjoy them to USAMO level, so it’s a bit of a moot point.
One thing to keep in mind is that if you wind up in your first year of college in, say, Math 55 at Harvard or Math 216-218 at Princeton, many if not most of your classmates will have been competitors at high levels in the contests.
USACO (comp sci olympiad) training pages…http://www.usaco.org/index.php They are in the middle of upgrading their site, so things might be a little clunky. S1 had a bunch of books on algorithms, theoretical CS and combinatorics, but they are not popping up in my Amazon order history. Can ask him about them, but they were more upper UG/graduate-level and assumed a lot of background. Sorry I can’t be more helpful on this – S taught himself programming and DH and I just watched!
Is USAMTS (USA Mathematical Talent Search) still around? That was a four-round event with take-home problem sets. All proofs. It gets scored and your score places you in award bands, but was fairly low key. S found it challenging in a good way, as it reinforced what he learned at the summer math camp (which was was less competitive in those days and more about playing with concepts).
One can get into outstanding math programs without lots of math competition hardware. What’s more important is the underlying knowledge.
^ I also don’t know how much you need to know for CS at high school level. They have to pass the weed out courses to move forward in CS in college. Again this is just a story, my son never did any CS coding or competitions at high school, and he recently received his 4th Stanford degree in MS-CS with GPA of a 3.97 (he missed a course with an A-.) He also has a BS in math and a MBA. The MS-CS and MBA were done full time while he was a full time at Google. He is by no means advanced at high school. Now he is a product manager at Google.
Only on these forums do people say that US students who take calculus as high school juniors are not advanced, when that is actually two years advanced of the normal sequence.
For physics she might enjoy watching Walter Lewin’s MIT lectures on physics.They are on youtube. He’s quite entertaining. There’s a lot of stuff at the MIT Open Courseware site as well. I know my son did some of their computer science stuff on his own.
My kid actually mostly taught himself computer programming with some guidance from DH when he was in elementary school. His first textbook was “Visual Basic for Dummies”. I am sure there are much better resources out there now, but we could find very little at the time. He learned Java in a week at summer camp in middle school.
@ewho, at S1’s HS, students were required to get through two full years of programming. Freshman year was Foundations, which covers what used to be CS AB (College Board dropped AB a while back) and a number of additional topics, and Algorithms and Data Structures soph year (post-AP level). This was part of the preparation for research & engineering projects across subject areas and for senior research projects.
Formal education wasn’t a big part of his knowledge base. S started out playing the Logical Journey of the Zoombinis when he was really young, learned html to launch a Pokemon website, started programming games on his TI-84 instead of paying attention in reading class ;), and learned Visual Basic and Java for middle school science fairs. He read a lot of books on combinatorics and complexity theory for fun. I had no idea what he was talking about, but I had the Amazon account to feed his interest.
USACO was a way to get complex, interesting problems. Hackathons and other non-academic programming competitions were not yet a thing. Mathmom’s S is a year or two ahead of my S, and self-learning was pretty much the only way to go for a young person with a keen interest. (Accelerated math options were a few years ahead of the curve compared to CS.)
My former DIL planned to major in physics, got to university and took a CS course freshman year and fell in love. Majored in math and CS. Won a big programming award in her country in her last year of college. Is now also a happy member of the Google tribe.
About girls and the value of math contests, here’s a nice 2004 interview I came across with Melanie Wood, now a math prof at Wisconsin. She was the first girl to represent the USA in IMO competition as well as only one of two to have ever won the Putnam (top 5) when she was in college at Duke (she turned down Harvard and Stanford).
Turn out she was also a cheerleader, actress, and newspaper editor in high school. She sounds pretty cool.
Also, FWIW, here is the Andreescu piece I referenced above somewhere. On re-skimming it, I think it is a little gobbledy-gooky, but perhaps some might find it useful. It’s also referenced and briefly discussed in the NYT article linked above.
I think the article that SatchelSF linked is actually very valuable. I read it when it first came out. It was in Monthly Notices of the American Mathematical Society. It is not a totally trivial read, but it’s perfectly understandable.
If you want to cut to the chase, look at Table 6 which compares the percentage of girls among the participants in the IMO from various countries. In particular, check out East Germany vs. West Germany, pre-reunification; Japan vs. South Korea; and the Czech Republic vs. Slovakia, after they split up. The differences look to me like very strong evidence of a cultural influence on the participation of girls at IMO level.
^ You’re right @QuantMech. I had read the article a few year ago, and now rereading it a little closer after your comments, I can see a lot of interesting points there. I especially think that the section on “Social Stigma” on p.1256 really captures what we’ve seen, and accounts for the lion’s share of the reason that math education is so poor in the United States, and Andreescu’s recognition that girls are more susceptible to social pressure than boys is spot on imo.
Nevertheless, things have improved substantially in the decade since the paper was written. I don’t really think that anyone seriously believes that girls cannot do math at the highest level anymore (p.1258, first recommendation). There have been too many super talented girls that all the competitors see. Of course, as the authors imply, whether we are ever going to see proportional representation is really something a study like this cannot answer (see beginning of “Discussion” on p.1256-57) and truly we shouldn’t care about it anyway. We should encourage each student to realize his or her potential, and let the chips fall where they may at the end regarding what the final ratios between girls and boys winds up being. That there is unidentified talent out there is obvious.
Also, in terms of improvement in math resources and education, the growth of the internet over the last 10 years, and the availability of quality online options (together with the growth of IRL math circles, math camps, competition programs, etc.) has greatly increased opportunity. Teacher quality in our experience still remains abysmal at the elementary level and even higher levels, but to some extent it is totally unrealistic to expect that very gifted math kids are ever going to find adequate instruction. Even on CC, one can see the undercurrent of suspicion that kids who are getting to calculus in 7th (or even 6th!) grade are being “pushed” by their parents. Believe me, no doubt some are, but without the innate ability and desire, very few can succeed and in my limited experience most of these kids are advancing on their own (certainly the case, at least initially for our own, who after discovering that the school program - www.ixl.com - that was offered in 2nd grade could be “hacked” to get to higher levels started waking up in the middle of the night unbeknownst to us, sneaking over to the computer, and doing problems; by late in the first semester they had already completed more than 8000, reaching in many topics up to the Algebra 2 and even precalculus levels). Other countries can do a much better job with teaching, because ability identification and tracking from an early age are not taboo, as they are here. Fortunately, online resources have stepped in to fill the void for these kids.
Andreescu’s recommendations 4 and 5 on p.1258 are also very on target.
I agree with letting her progress at her natural ability.
Do you live near any universities where she could DE when she is older? Our ds fell in love with physics in 8th grade and graduated from high school with 5 of his in-major physics core classes completed (and iirc, a math minor completed or close to it if not.) He was able to pursue grad physics classes as an UG.
When he was your dd’s age he loved the Great Courses physics lectures. I think we own just about every physics and astronomy course they produced before he turned 18. Off the top of my head I also remember him enjoying Kip Thorne’s black holes and time warp book.
He is on his way to grad school for theoretical physics. He is super excited to finally be exactly where he wants to be!
Thanks everybody! You’ve been an absolute treasure trove of information. Thank you for all the book, course and video recommendations! I have never heard of any of these physics or computer science resources so they’re much appreciated. I have some research to do but based on what I’ve seen so far, some of these recommendations are perfect for her studying these topics.
Thanks also for the Andreescu article and the links. The table is very telling. I expect in the USA even boys may sometimes feel socially pressured to not pursue math although that is definitely changing as “nerds” have become socially cool. For girls, that social pressure has always been greatly magnified and while it’s been lessening of late, I expect there are still many girls discouraged from pursuing math as well as other areas such as computer science, electrical engineering. physics and even chess. I’d also not heard of Melanie Wood but I agree that she does sound cool as well as extremely talented.
There is a university close by though they prioritize their own students over high schoolers so some of the courses offered might be difficult to get into. There is also a community college close by. I’ll have to discuss dual enrollment with the guidance counselor/administrator at her school. I didn’t know such a possibility existed until posters on this forum mentioned it!
I absolutely agree that it should be my daughter who chooses the pace of her math courses and her other studies. She’s the leader in this endeavor. For her, it’s far more important to stick with her cohort than care about what effect there might be on her high school gpa. It wasn’t until the counselor mentioned her concerns that I even considered the possibility that the path my daughter has been forging could have repercussions.
That’s why I turned to this forum. I have to say I’ve been so impressed with the advice and information posters on this forum have provided. Certain comments and stories seem to mirror my own experience and your ability to relate to my situation has been invaluable. The posters on here should probably write a book containing advice about getting children through their school years and beyond which I expect would be filled with far more useful advice than the books written by so-called experts on the subject!
I have a similar child. my advice is to let her take math at her desired pace, don’t put artificial roadblocks like GPA bumps and even college credit in her way. You mentioned access to Stanford’s online math classes, that will keep her busy and learning for some years. If she runs out of math before graduating, she can do research with some college professor at the end of her courses to further increase her skill level. By that time, issues such as credit for Calculus will be distant history. And lastly, have her apply to universities (not colleges) so she can take graduate level math as a freshman!
Thanks! I agree with your advice. Currently, she is taking precalculus and really enjoying it. I didn’t want her to overload herself so although she wanted to take honors physics, I talked her out of taking it this year somewhat to her regret. Partly, I talked her out of it because the seventh grade science teacher is great and he teaches biology - a subject she really didn’t like up until this year so I was hoping that with a great teacher that would change. It has as she now enjoys biology though she isn’t passionate about it like she is with math. The other two middle school students in her precalculus class are very much enjoying honors physics and now she wishes she could have taken the course with them. She now wants to take honors physics next year even though she will likely be the only middle schooler in the class. She will also probably not get a GPA bump for that course but if she wants to take it next year, I won’t stand in her way. Thanks once again for your advice!