Gifted Issues Discussion homepage Forums Recommended Resources AoPS Intro to Geometry course review

Firstly, kudos to ColinsMum for talking the plunge with AoPS and then doing us the service of putting together a detailed and positive review.

I have been wondering what to do with DD after the SG primary series peters out and also dread pushing ahead without a coherent plan/syllabus. AoPS seems like a good way to build on the foundation that DD already has from SG primary maths and it appears to present its material in a very coherent and incremental way.

I had DD take the 'pretest' and she went through it like a dose of salts with one transcription error from the test paper to her 'work paper' causing an incorrect answer.

I will be signing up my DD for a pre algebra I class in February.

What I meant was that I never saw anyone disclose age; DS didn't come under any pressure to do so, and I don't see that he would have done, even if he'd been more active. When I first heard about AoPS I assumed (as apparently many people do) that there'd be audio or video participation involved, and that, obviously, would reveal age clues. A typing interface does not in the same way. At the start of the class, I mailed the instructor about a couple of things, and mentioned DS's age in an "I hope this won't show but just in case it does" way, and got the response that I shouldn't worry provided he was up for it and "we have lots of younger students". I didn't clarify whether this meant "younger than your DS" or "younger than average to be learning the material" - I suspect the latter, but I saw everything that DS saw about the other students and I couldn't tell which ones might be his age or younger. Yours might not have come across this so much, being homeschooled, but DS finds it a bit tedious being known for being good at maths at school (though he sort of enjoys it too) so it was very welcome that he felt safe from that in AoPS. [Well, in practice, he was invisible so of course he was safe; but he also didn't see anything to suggest that he'd have attracted that kind of attention if he'd been more visible.]


Don't know so much about difficulty (though see the comments upthread quoted from WTM). I think the "x < y means course x contains material that is prerequisite for course y" partial order contains these and their consequences:

Forall n. Algebra n < Algebra n+1

Forall X. Introductory X < Intermediate X

(better put those in ;-)

I think probably

Forall X. Algebra 1 < Introductory X

for being able to handle basic algebra including quadratics, at least (this was certainly assumed in the geometry course).

Their material suggests:

Forall X. Algebra 3 < Intermediate X

but it's not clear to me whether this is really a question of prerequisites, or more a "mathematical sophistication required" thing. We have the Intermediate Algebra book which goes with their Algebra 3; I had in mind to ask on their classes forum whether there were specific chapters to revise, before signing DS up for Intermediate Number Theory (if he does want to do that later).

I have read that all three intros are incomparable wrt prerequisites, but geometry is harder than the others. I'm less sure that I've seen it from them in writing, but I think the same is true of Int C&P and Int NT. I'm less sure about the AMC8 courses; clearly they're at introductory level of difficulty, and I think they neither have nor are prerequisites within your course list. What I'm not sure of is whether there'd be anything to be gained from them if one already had a good understanding of the introductory courses' material.

The AMC8 ones, and Intro to Number Theory, have the advantage of being shorter than the other reasonable possibilities for a course to do before Intro to Geometry - that's probably an advantage for a toe-dipping! I think if I were you, I'd probably decide which AMC8 one would be more your DS's level, and offer him the choice of that or Intro NT.

I don't have experience, but I suspect that depends more on the individual's characteristics such as processing speed than on age, really. DS is a relatively slow processor, I think - I predict that would be his lowest WISC index by a fair way, if we had him tested - and I think I am too. I see (some, but reassuringly not all, even of the best) colleagues well able to learn in real time from seminars, something I still can't generally do! (I can get the gist, of course, from a competently given one, but if I want to fully grok what's going on I have to think about it alone later. It's rare that I can ask a penetrating question at the end of the seminar.) That said, pretty sure I personally would find a class in which there was a written record of everything the teacher said in front of me at all times much easier than an ordinary spoken one!

Thanks for clarifying that. So you can give full details of age, background, etc to AoPS "staff" to get the best feedback on course suitability, but you can be totally (age, background,name)-anonymous to the other AoPS "customers".

Thanks for analysing the courses. I've now had a good explore of the AoPS website. We are looking for a "toe-dipping" course, just to see if AoPS will work out yet for DS8. (I'm concerned he'll find the format unappealing at his age, or that he won't be able to keep up with the non-mathematical aspects of it.) It's a good idea to look at the shorter (and cheaper) courses, and for the lower level courses that means:

Introduction to Counting & Probability $265 ($307 with books) 12 lessons of 90 minutes each.
Introduction to Number Theory $265 ($312 with books) 12 lessons of 90 minutes each.
MATHCOUNTS/AMC 8 Basics $245 12 lessons of 90 minutes each.
Advanced MATHCOUNTS/AMC 8 $245 12 lessons of 90 minutes each.

It seems that MATHCOUNTS/AMC 8 Basics only needs Prealgebra, while Intros to C&P and NT need about the first half of Algebra 1, so that suggests AMC 8 Basics as a course to start with. I realize the AMC 8 courses could be redundant if you do all the "Intro" courses, but on the other hand if it falls through (if DS8 doesn't take to AoPS at the time) there's not much lost and he doesn't need to "repeat" some course to cover "irredundant" material. It would just be (difficult, compared to K12Inc) problem solving, which is what he needs.

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DS8 just finished the K12Inc Prealgebra, and found it very easy. The problem is that these courses are designed to only require a rudimentary "mastery" of the material. He could probably get through a few more of these "rudimentary" types of K12Inc courses pretty easily, but I'm worried about how that would turn out. (It's not just K12Inc. The problem is with any course aimed at typical students.) I'm torn as to how to proceed. I'm seriously thinking of not getting the next K12Inc course (Alg1) until August, and instead working through Alcumus for a while, then taking an AoPS course and generally trying to "toughen" DS8 up a bit, and also get a much broader coverage of maths topics than just what's in the standard Alg1/Geom/Alg2/TrigPrecalc/Calc path. On the other hand Alg1/Geom/Alg2/TrigPrecalc/Calc is just basic stuff a mathy person should learn before going to more advanced stuff, so why delay, why not just keep going through these courses as soon as one is ready? (DS8 is in a virtual school and can do courses at his pace. I'm trying to optimize the pace.) It's quite a dilemma. Thoughts, anyone?

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My thought would be that exposure to finding problems hard is important, far more important than getting through any particular material, so yes, I'd notionally put that in first and then see what else there was space for. Depending on personality and what you use for that and maybe other stuff too, you might find your DS is happy to spend all the time that seems reasonable to spend on maths on the hard problem stuff, or you might find that his tolerance for that is initially limited and it's good to have some more routine stuff in the mix too.

Do you have complete flexibility about when to start classes, and can you let them go to the backburner for a bit without penalty if you like? E.g., suppose your DS started a K12Inc course now and then hadn't finished it when the AoPS AMC8 course starts in March, could he temporarily drop the K12Inc work for the duration of the AoPS course, if it wasn't convenient to keep both up? If so, I don't see a downside to starting all the hares running and just playing it by ear. If, on the other hand, once you start the next K12Inc course you need to keep at it consistently, then I'd be inclined to agree that taking a break to work on Alcumus and AMC8 stuff now might well be sensible.

The thing I find helpful to remember is "he has time". If you take a decision that turns out not to be absolutely optimal - e.g., he does something he turns out not really to be ready for, so that he forgets it and needs to do it again later - no big deal.

I think the appropriate place to start with AoPS depends on interests and mathiness of the kid and whether the kid hates or feels challenged by exposure to material he/she cannot master.

My DS did some online math courses at 8 hated them. Hated the material. Hated the math. Hated the repetition. At 9, he tried AoPS Algebra I. This was a while ago and it's much different now, but it was a sink-or-swim situation (no help from parents, pretty much mastering typing and LaTeX at the same time and no prior exposure to hard problems). It was a bit brutal, but he loved it and it restored his love of math. He subsequently took all the intro and some non-intro AoPS courses and he agrees with Colinsmum that geometry was the toughest of the intro courses (AoPS founder also says this).

If you are considering toe-dipping, I'd recommend starting with pre-algebra. If he's already had pre-algebra *and* has mad and well-developed deep problem solving skills, I'd consider algebra but AoPS pre-algebra will not be the same as a standard pre-algebra course. Perhaps the pre-algebra 2, rather than the first one if you wish, but it would be kinder to start developing perseverance with harder problems with material he has some familarity with rather than also learning a new subject. And this is really, really different than typical math.

The AMC/Mathcounts problems are easier since they all require speed so the problems can't be that deep. There are tricks learned and initial problem solving skills, but a big difference between those skills and challenge level geometry problems which DS would work on for an hour sometimes.

I don't think of doing C&P and NT as delaying, but rather enriching the typical and somewhat limited typical school sequence. Since the courses are not full year for any of them, the kid ends up further accelerated anyway. So DS did algebra I, algebra II, geometry, C&P, NT, pre-calc in far less time than alg I, II, geo would be in a regular sequence, but he much learned more math.

Some kids don't like the format. Some kids don't like math problems they can't solve. Some kids get frustrated with the difficulty. But some kids eat this stuff up and if you have such a kid, AoPS is simply fabulous.

Now that you say this, I wonder why I didn't also suggest considering it :-) DS had in principle done the geometry material a long time before he did AoPS geometry, after all, and still got challenged. One thing to note is the "full refund before third class" policy and the fact that there are Prealgebra classes starting in February. So if you're not sure whether Prealgebra will be right or will be too much repetition and AMC8 would be better, you could sign him up for a prealgebra course and bail if it does turn out to be too easy, with time to enroll in the AMC8 course instead in that case. If the geometry course is typical, you'll see three sets of challenge problems in the prealgebra course before you reach the point of commitment, which should be enough to make a good judgement of whether it's suitable.

How is your DS finding Intermediate Number Theory, solaris? In particular, how long is he needing to spend each week, roughly, and is he doing all the questions? The further the geometry course recedes into the distance, the more tempting it looks to have DS do that course in the summer... but I don't want to overload him.

I'm not Solaris, but DS experience with the classes was similar to your son's in terms of geometry. Hard but rewarding. Number theory (both versions) was not nearly in the same league. NT was easy, fun, and not much work.

Thanks both! So, different experiences there from the sound of it. Interesting... Solaris, I wonder, could you maybe share (by pm if you prefer) just one of the questions that were hard on that first sheet, to help me get an idea of what we're talking about?

ETA DS was also unwilling to use the forum, and come to that, so are my own students, so I'm no help.

Lots of great comments. I'll get back to the rest, but I was curious about this.


This makes me like AoPS even more. But it makes me wonder, how exactly are their classes structured. Do they lecture about some theory, with adequate proofs/explanations? Or do they lead you to "discover" things via a sequence of problems/exercises/questions? Or a combination of these? Or what?

For comparison, the K12Inc Prealgebra course simply stated formulas (after adequately defining n!)
P(n,r)=n!/(n-r)!
C(n,r)=n!/[(n-r)!r!]
without any explanation of why LHS=RHS. (Usually they give some kind of explanation for things, but not this time.) Then they have some "worked examples" which are easily skipped past, then a routine quiz.

How does AoPS take a student who hadn't seen n! before, and lead them to know these formulas and understand why they are true? And what other activities surround the learning of that particular piece of maths? (Or substitute any other piece of maths for the purposes of this discussion.)

How does AoPS work?