This discussion was created from comments split from: How to skip Geometry?.
My parents want me to do the AoPS course for geometry, but I would rather get the book as I am much more of an independent learner. How do the books compare to the online classes?
@FunintheSun1211 - The AoPS book on Geometry is fantastic - easily the best geometry book I have seen (at the basic level). If you diligently work through the problems, and consult the solutions manual only after struggling on your own, you will have a very strong foundation in geometry.
However, you will be missing out on some important aspects if you don’t do the actual course. The most important of these, in my opinion, will be the feedback on the written proofs (or solutions) that you need to write each week for the course. You will also miss out on the interchanges and back-and-forth on the dedicated discussion forum (for the class), as well as the ability to ask questions (and see others’ questions) in the weekly class sections. The level of ability on the AoPS forums and classes simply cannot be replicated in a boarding school class, and so the discussion will be tailored to that level of student. Don’t be surprised if you encounter 9 and 10 year olds on there who are already more accomplished than 99% of high schools students.
Last, you will miss out on the ability to ask questions of a world-class mathematician (if you take the 3/26 section taught by Blumberg). You can’t find that level of ability in high school teachers.
If you do go the books-only route, you can still register on AoPS forum and participate in general discussions. In addition, I believe that even with a free registration, you can participate in Alcumus, the online adaptive learning tool that AoPS uses. Setting it to geometry only will take you from basic problems of the type you will encounter in most honors geometry courses right up (almost) to difficult Olympiad-level problems, although none requires the proof writing that you would get with actual participation in the course.
I looked into it a few years ago and I think I concluded that the AoPS course will satisfy the UC requirement that an actual course be taken. A letter grade can be requested, in addition to the detailed course-end progress report that is provided. If the University of California is a possibility in your future, i would definitely confirm this.
Whichever you choose (books only, or actual course), know that mathematics is probably the easiest subject to learn on your own, so long as you have the innate talent and the interest to sustain the effort required. It is not unusual any longer for highly talented kids to run through the standard elementary and high school curricula in a few years, with a level of mastery that few kids will ever get in brick and mortar institutions. In many ways, this is a silly article, but it hints at what is going on these days, and is fairly accurate insofar as it goes: https://www.theatlantic.com/magazine/archive/2016/03/the-math-revolution/426855/
Good luck!
@FunintheSun1211 If you’re a good independent learner in math, the book should be sufficient. I’d get the book first and see if you can do the problems. With mostly proof-based problems, you either can do them or you can’t (assuming you’re good with logic). With almost any math problem, there’re usually multiple ways to solve the same problem. Even if you didn’t solve it in the most elegant way, it’d still be a better learning experience if you did it on your own. In terms of boarding school classes in this area, probably only Exeter offers comparable or better training (with Dr. Zuming Feng, who’s been the coach of US Math Olympiad team for years).
Agree about Exeter. But do keep in mind that there are a number of world class high school mathematicians there, and the presence of those truly extraordinary kids will suck up a huge portion of the the oxygen. Most courses and teachers at Exeter in math are only so-so, unless of course you are a member of the cohort of the 10 student prodigies or so who enter every year. YMMV of course.
Threads like this one make me so sad.
I’m not sure why, @bjkmom. I think you are a math teacher yourself. Surely, you have faced the difficulty in trying to tailor your classes to satisfy wildly opposite priorities and ranges of ability. I’m sure there are terrific teachers out there for many students, but the incredibly poor results of formal US math education speak for themselves.
We faced the issue of poor teachers and an incoherent curriculum ourselves in a very highly rated public elementary school district. Our response was simply to have our child in effect “opt out” of the entire curriculum from about 2nd grade until around the high school precalculus level, and judging from the results we have observed from friends’ children who stayed, it was the best decision we could have made!
Obviously, independent study, math circles, enrichment activities and competition math are not the answer for everyone. But again, looking at the standard curriculum and the unevenness of teaching ability, I find it difficult to endorse the “standard” approach for anyone. Earlier grouping by ability might alleviate some of the problems, but schools have been going in the opposite direction for some time. Admittedly, I am just generalizing from our own experiences (including my own, 30+ years ago), and making some inferences based on publicly available testing materials and results.
What saddens you?
Quick question: Approximately how long would this course take if I work like one hour a day, at a reasonable speed.
On time commitment for AoPS, I’d say it really depends on your innate talent and how rigorous you want to be in learning the material. I’ll just hazard a very rough guess based on my experience working with some gifted and motivated math kids in 6th, 7th and 8th grades: total of about 10 hours per week on average - 1.5 class time; 4.0 reading text and doing all review problems and half the challenge problems and reviewing solutions; 1.5 homework problems; 1.0 Alcumus; 1.0 proof writing (often takes a while because you will be drawing diagrams and scanning them and also, hopefully, learning LaTeX if you don’t know it already); and 1.0 goofing off in the forums/problem of the week. Some weeks might be a little tougher, and you could do all the challenge problems if you like for a little more time. The course gets a bit easier for older kids when it gets into an introductory treatment of trigonometry and analytic geometry, since most kids will have seen this already.
Geometry is super cool, and totally fun. After this course you can wow your friends with an off the cuff derivation of Heron’s formula. And if you like it you could always take the olympiad level geometry course afterwards and see if you can’t somehow work that into an elective at your school. Good luck!
PS - As you might have seen, you can sign up for the course, and drop it for a full refund anytime prior to the 3rd class, so you can see if you like the format.
AoPS is generally tailored more to competition math IMO, which some find really interesting, and some don’t.
Also, @SatchelSF Geometry = 
^AoPS is geared to competition math only in the sense that competition math = problem solving.
The online course is good for keeping on track and for getting feedback on proofs. Some of the online proofs can be quite difficult, not the type of problem to start an hour before it’s due as it may take some sleeping-on, but juicy and fun.
A bit of advice: do the book section first before the weekly online homework (ideally, do the book section prior to the class on that topic).
If the school placement test is expected to include two-column proofs, note that the two-column form is not covered in AoPS, which eschews them for the much cooler paragraph proofs. It shouldn’t be hard to look up some resources on two column proofs and will be well worth the effort for test purposes even though they will feel pedantic in comparison to AoPS.
All in all, AoPS Geometry is fantastic. It’s great for the student who likes puzzles. I wish I had learned that way back in high school - it might have turned me into a math major.
AoPS’s online practice program, Alcumus, is free to sign up, for those who would like to try it out.
DS has taken almost all of the AoPS series, including Geometry, and has really enjoyed each class. Geometry was a difficult class and he worked through every problem in the book and afterwards he did the online course for the feedback on the problems that @SatchelSF mentioned. AoPS was a great resource!!
The thing about AoPS is that it depends on the kid and the goals. Had DD taken an AoPS class or worked through the books, she would have been nothing but a pile of mush on the floor within 10 minutes. For DS who hadn’t been challenged for years in math and finally found AoPS prealgebra in 4th or 5th grade, the online class was amazing. It was challenging, fun, involved a community of like minded people to share origami designs with or play online chess with or giggle over really hard or really silly word problems. If you don’t particularly love math and mathematical thinking and need to do AoPS just to cover ground…I just don’t know how that would go.
It is hard and you are really pushed to think and think hard. To cover ground it may be better to have something with more of a “here is what it is, here is how to apply it methodology.”
I could be wrong - my sample size consists of my 2 kids and some homeschooler friends.