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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:

    Quote
    Two circles are externally tangent at point P. Segment \overline{CPD} is parallel to common external tangent \overline{AB}. [I've omitted a diagram: as you'd expect, A and C are on one circle, B and D on the other, with C and D on opposite sides of their respective circles.] Prove that the distance between the midpoints of \overline{AB} and \overline{CD} is AB/2

    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.


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    Wow-- THANK you for the very thorough review. Tremendous insights into this.


    Schrödinger's cat walks into a bar. And doesn't.
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    Got it! smile (At least I've convinced myself with a picture.)
    Geometry was my weak point in competitions since we didn't do it much in school. I once successfully solved a competition problem using coordinates, and formed the false hope, despite warnings to the contrary, that this was the way to go. The warnings were right. Maybe I need to take this course.

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    Just some key points, many details omitted, and hopefully my picture didn't fool me. No peeking til you've tried it.


    M:=midpt of CD
    N:=midpt of AB
    perp bisector of AB meets CD at midpt of P and M
    |NM|=|NP|=|NA|=|NB|

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    Originally Posted by 22B
    Got it! smile (At least I've convinced myself with a picture.)
    Geometry was my weak point in competitions since we didn't do it much in school. I once successfully solved a competition problem using coordinates, and formed the false hope, despite warnings to the contrary, that this was the way to go. The warnings were right. Maybe I need to take this course.
    I never did either competitions or (much) geometry at school, and I learned a lot from this course :-) Since DS's school maths teacher was sometimes letting him do these problems at school, I undertook to produce and send in a set of model answers each week, so that when DS was stuck the teacher didn't have to solve the problems in his head to help DS while also dealing with the rest of the class doing something completely different. It was more of an undertaking than I thought when I made it! (And it's both encouraging and probably good for school-home relations that the one time I had to confess I hadn't solved one of the problems yet, DS's teacher promptly sent me a solution!)

    ETA yup, your solution is consistent with DS's (though my guess from the wording is that the method was not identical - there are several ways to approach this I think).

    Last edited by ColinsMum; 12/15/13 01:33 PM. Reason: add note on 22B's solution

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    Yes, great review! DD has done some Alcumus and work with some of the AoPS books but it does make me wonder whether DD should ever take this course because I am not very mathy at all and it has been sooooo long since I had geometry. So it would take a significant amount of effort for me to even try to 'unstick' her, assuming I could even figure it out. Does AoPS have tutors available, or people you can ask if you get stuck with a problem and don't have a helpful parent or friend around? Otherwise I am not sure how DD would be able to deal with this course, as she is quite mathy but does get very frustrated when stuck, and I am of very little use despite my most earnest efforts. frown

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    Originally Posted by Dbat
    Yes, great review! DD has done some Alcumus and work with some of the AoPS books but it does make me wonder whether DD should ever take this course because I am not very mathy at all and it has been sooooo long since I had geometry. So it would take a significant amount of effort for me to even try to 'unstick' her, assuming I could even figure it out. Does AoPS have tutors available, or people you can ask if you get stuck with a problem and don't have a helpful parent or friend around? Otherwise I am not sure how DD would be able to deal with this course, as she is quite mathy but does get very frustrated when stuck, and I am of very little use despite my most earnest efforts. frown
    Oh, parental unsticking is definitely optional, and not necessarily even a good thing. Arguably, it's better for them not to do every question. But DS's frustration tolerance, while excellent for his age, wasn't really up for that, and it was natural for me to help.

    There are hints available for the questions. The instructor and TAs watched the forum so students ask there, and there's a mechanism for doing so completely anonymously if they like. Also, I didn't mention that the students arranged to meet "in the classroom" to work on any leftover problems just before each deadline - again, in the middle of the night for us though!

    What I'd say is that a student does have to be able to ask coherently for help - I don't know what happens if someone struggles silently, but I suspect they just drop out - and may need to be able to tolerate a delay before they get help (eta but not a longer delay than someone in a b&m school might have if they get stuck on a homework question). I'm sure you could help with those skills even if you did get stuck on the maths, and modelling a good reaction to being stuck might in itself be useful!

    You can get a full refund several weeks into the course - up to the start of the third class iirr - so it's possible to try a course and bail if it's not going to b work.


    Last edited by ColinsMum; 12/15/13 11:43 PM.

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    We have integrated maths here and I think geometry is the discipline that gets least attention. It is also the only one I didn't at least do to first year at university so I wouldn't be a lot of help. It looks quite scary!

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    Thanks for the details, ColinsMum! I couldn't quite tell how it would from the course descriptions I saw, and the help that is available sounds like it is set up well. And I often get chances to model not being able to get an answer to something!! although DD often moves on to something else before I am done showing her how to persevere, so I continue to work on that wink

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    If you could get a kid to actively participate in the school and the community it would help them a lot I bet.

    I have been looking at Introduction and intermediate to counting and probability for my ds 10. He is pretty stretched right now but maybe for some summer work. It is pretty cool stuff that could get a kid hooked if they hang in there but might be too much review.

    We tried some ALEKS stuff and thought it was horrible. How did your son like it?

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