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DS10 finished this course today, so I thought I'd report on what it was like, for those who might consider it or another AoPS course.

Short version: very valuable, much harder than I expected.

I had thought I was playing safe and giving him a gentle introduction to AoPS by picking this course - he's done a fair amount of geometry in other settings over the years, including ALEKS high school geometry back in Feb'12. Not a bit of it, and thank goodness I didn't encourage him into anything harder!

The course (their details here) ran over 24 weeks. Each week there was a "homework" exercise sheet of roughly 10 questions, usually 8 short-answer and marked automatically and immediately, and two proofs that were marked by humans. The marking was picky, in a good way - DS didn't often lose marks, but often had it pointed out to him where he could have proved something more elegantly or explained himself more clearly. I mostly agreed with the markers, but not absolutely always :-) DS took a completist attitude and insisted on doing every question - it might have been better to be prepared to give up sometimes, but that wasn't going to happen. I unstuck him when he needed it, and I scribed for him sometimes. Proofs were written in LaTeX and always had to be accompanied by a diagram, which DS produced in Geogebra - he is now reasonably competent in LaTeX and very proud of being "the Geogebra wizard", far more familiar with it than I am. (Geogebra was a big help and he often used it even for the short answer questions - obviously this means he had help that he wouldn't have in competition, but I felt it was good for him to use it. The answers typically involved surds and so couldn't just be read off, but there was a fair bit of "hmm, geogebra says that angle is equal to that one, can I prove it?"!) Most weeks there were one or two questions that gave him serious trouble. Every few weeks there'd be one that gave me some trouble too! Here's the very last question of the course for anyone who'd like to try their hand - it's a nice example, requiring only very elementary techniques, but nevertheless reasonably challenging:


Each week except the last few, there was also an assignment of Alcumus topics to do; this tended to be light relief for DS who was already well advanced in the Alcumus geometry before the course started (another reason I hadn't expected it to be hard). There was usually a chapter of the textbook to read, on which I have to admit DS skimped.

There was an online class which DS couldn't attend in real time because it was in the middle of our night, but transcripts were posted, showing both the instructor's words and those of the students' that had been posted (it's all text based; students ask and answer questions, the instructor decides which student typing goes into the class transcript, and there are also TAs who can have side conversations with students who need it). He enjoyed reading the transcripts and would, I'm sure, have loved being able to attend class. One good thing about the format is that there's very little in the way of clues to student age.

There was also a class forum, for which I had high hopes, but it was so quiet that DS was too shy to post there except for one exchange early on. The instructor posted extra questions each week to the forum, but hardly any of them attracted responses - maybe other students also found themselves fully occupied by the homework. The occasional student question to the forum was promptly and helpfully answered.

Given that really the only aspect of the course DS used was the homework problems, and given that I could have set and marked these myself with some help from the book and competition papers, one way to look at this would be as a very expensive way to have someone else do for him what I could have done myself! But he would never have kept up the pace without the external pacing the course provided, and it was very helpful to have the proof pickiness come from someone else - it happened more than once that I criticised a proof, he decided to leave it as it was, and then the marker criticised the same thing :-)

He had a bit of a love-hate relationship with this course, and now that it's over, he definitely does not want to do another course immediately, and tbh I concur. Overall, it probably took him 5-7 hours/week, which is about what they estimate; it's just that I had assumed that would be an overestimate for him, and it wasn't. Given a 12 hour school day (including travelling) and two instruments to practise, that meant it was really a substantial chunk of his free time. On the other hand if he were being homeschooled, I have no doubt we'd be hooked. As it is, I think we'd need to be looking at a shorter course that ran mostly in school holidays. I have my eye on Intermediate Number Theory, possibly in the summer... but we'll see. For the next few months, I think just Alcumus will be fine.