We haven't finished, but are still right on pace to finish it in 8-9 months. Jump in difficulty is hard to assess - that's such an individual thing. We have found it not as hard as PreAlegbra, but harder than Intro to Algebra. It's a different kind of work, as it gets into proofs by induction, etc, which are commonly found in precalculus texts.

I don't know that we're opposite - I suspect your multivariate class was taught the wrong way, if it involved any memorization at all. It was the first one that I took that required no memorization of any sort.

In many AP courses, that may be true, but a good calculus course is not run this way. Mine was theory, theory, and a bit of application. Not a whole lot of memorization. Calculus III was the first course I had where I truly fell in love with math as art. I really wish people would stop trying to turn math into arithmetic!

I find those to be mutually exclusive outcomes. It's a curriculum built around deep conceptual understanding. There are no gimmicks allowed. If ever you feel AoPS is teaching tricks, you really need to either find additional support or a new curriculum. This would be a perfect example of why it's not the best for every situation.

Great questions, and lots of useful background! Each student faces different challenges in AoPS, but in general, the Intro to Algebra book is easier than the Pre-Algebra - if, and ONLY if the student has done the Pre-Algebra text first. That is because the Pre-Algebra book is so strong. Doing it as a review is an extra big plus. AoPS works best for students with good working memory, so if that is a concern, you might need more time to complete the book. AoPS themselves split the course in two, which should provide insight into its breadth. Having access to a tutor or mentor is very important with AoPS. However, your own efforts and perseverance will go a long way in support. You can do well with a co-learning style. Courses like video text or khan definitely won't match up, but a classic beginning & intermediate algebra textbook would make a good fallback.

Depending on whether you wanted "started" or "formal": We started with theory of arithmetic at 6 with younger DS, and that is absolutely a branch of algebra. Formal AoPS algebra was two years later. ETA: echoing what others said, for any child below 10 doing algebra, PLEASE - I implore you - PLEASE do not put them on Saxon! It really is robbing the brightest mathematical minds of the theory which makes the mathematics beautiful. If you do choose to use it, then PLEASE follow it up with a more sound program like AoPS. Two years of quality algebra will not slow their progress down.

That's pretty much how we see it, too. DS doesn't really use Cogito, but it is there. Maybe younger DS will, though. We'll have him try out next year, just in case. Unfortunately, that doesn't work here. To be fair, we aren't on either coast, so there are no "local" options. There is a Duke TIP equivalent (and, honestly, their summer courses are better), but requires a perfect score.

Just curious (if you don't mind my asking)... We met with the staff, as well, and that was the only meaningful conversation we have had. Have you actually found benefit from SET, beyond the medal and magazines? Not really meaning to knock it - it is a study, after all, and not a secret society or anything - it just seems to me that it's easy to get one's hopes up that kids will have better access to educational opportunities due to the SET label.

Would definitely be interested. We would like an honors-type section with high content, but "normal" honors rigor/difficulty. We loved the MIT course, but 0 to MIT is a bit of a large jump. Something just shy of AP with labs, and we'd be all over it.

Honestly, even AOPS Pre-Algebra provides a lot of prep for the SAT. You should be well covered, but it may be worthwhile to get some practice exams just to see where strengths / weaknesses lay. SET, by the way, has proven little more than a curiosity for DS. The free magazines are nice (you can also pay for them), but that's all that we have seen come from it. There are some possibilities for future networking, so there's that.

Honestly, McMurray Fay is recent and quite good - one of the best I've seen. Mind you, my sample set for chemistry is considerably smaller than for physics or math...

I still have a 1st edition S&Z (can hold both books in one hand!) and a 2nd Halladay Resnick, because they don't have any of this junk.

Well, physics has changed, but the introductory texts are mostly derived from the same origins. Sears & Zemansky is still holding on from the 1940s!

They offer guided sections and even tutoring throughout, for a reasonable fee.

This makes sense. Wheelock was better for writing. We had DS translate passages all through each program, but that was clearly Wheelock's strength.

DS started with Oxford in 5th (self study), moved to Wheelock for 6th and 7th (completed it), then finished Oxford in 7th-8th. He then started Cambridge, and is finishing that up in PS (9th) this year. He could probably sit for the AP now, but isn't in a rush. Though I've heard good things about many other programs, Wheelock was very good for him. Oxford - the weakest of the three, but still fine. Cambridge has the most complete program, and it's not that pricey. If we were to start over, we'd have started with Cambridge, then moved to Wheelock. Regardless, I can honestly say any of those would be ok for a 6th grader. Basis (the public charter) uses Wheelock starting in 5th, and it's the least accessible of the three.

Texas Tech University runs a K-12 program for distance education. It's all accredited, but nothing advanced. It's a pretty good deal for kids who travel a lot (sports, drama, etc), as well as for highly accelerated kids. They don't check prerequisites - you just pay for the courses you want. If you have an accelerated middle school student, a basic high school course can be just about perfect for them. They arrange all curriculum and grading - including worksheets and additional depth, but it's more-or-less self-study or parent-led.

We're doing geography through TTUISD. It hasn't been that bad - actually rather good for DS, and it grants documented/accredited HS credit.

We used Deutsche Welle online - it's free, and is stuffed with activities, progress tests, etc, and will take you as far as level C2. We paired it with Deutsche Aktuell and a local native speaker for extra practice. After a year of that, DS joined a local B&M HS at second-year, but is clearly operating at third or even fourth year proficiency compared to other students.

That's so obvious that I'm embarrassed not to have thought of it. We always have done this, just in case we needed to account for public school expectations.

I'm not at all familiar with the requirements there, but I'll try to chip in. Those topics can go very deep. Since they must be used as examples of applications of algebra, I assume that it is a fairly cursory overview. If so, you can probably get supplementation from the most basic stats text you can find, or even a schaum's outline. If you look for an AP stats or business stats text, seek out one which spoon-feeds material, because you'll need those very basic introductions to each topic.

It just occurred to me to add something. My younger brother and I wrote a program for our local EAA (experimental aircraft assoc) chapter when we were in high school. The program would allow the user to input desired flight / propulsion characteristics, and it would design an optimal airfoil for the builder to use. The work was based on his readings of Ernst Mach and my work on current mathematical models for the airfoils. It was a fun project, and a big hit with the EAA community. My older brother even used it to design and build custom model airplanes (like the big ones you can find at a hobby store).

Flight is a standard topic in almost every physics course. You could spend a little extra time focusing on some concepts, but creating a course devoted to the physics of flight would require stronger math and a solid background in mechanics up front. The history, as you mentioned, is easier to pull together. For additional depth added to an existing curriculum, look for labs on balloon flight (the latex variety), airfoils, and propellers. Those three will provide lots of insight.

I have the same question. Are you looking for leadership experience (eg scouting), or formal PM training? If the latter, I suggest some project experience prior to trying a PMP program. Relative importance will feel all out of whack, otherwise.

If it helps, the actual definition of a limit is online at http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfLimit.aspx It requires a bit of rigor, but it's actually a bit of a "squishy" thing, once you understand it. By the way, three things every good calculus student should know by heart: the definition of a limit, the fundamental theorem of calculus, and the mean value theorem...