Suki Wessling, a local writer who is home-schooling her kids, recently wrote an article about distance-learning oppoturnites for gifted kids: Boutique distance learning offers variety for gifted kids – National gifted children | Examiner.com. We have not used any of the “boutique” services she mentioned, nor, for that matter the large services like Johns Hopkins University’s Center for Talented Youth or Stanford’s Education Program for Gifted Youth.

There are several reasons we’ve been reluctant to use many on-line courses:

- Many are quite expensive. EPGY courses are around $500 to $750, plus $50 registration and shipping fees, JHU-CTY courses are $500–$1280. I’d want to know that the course would be a very good fit and of higher quality than a corresponding community college class (about $300) before committing to an online course.
- Too much screen time. My son already spends more time in front of a screen than is healthy (as do I, so I can’t chide him too much). At least with community college classes he gets the exercise of bicycling to the class (in fact, this provides so much exercise that it counts as his PE class: about 4 hours a week).
- Difficulty in finding courses that fit his educational needs and interests. There are undoubtedly a number of courses that would be an excellent fit for him, but it is very difficult to distinguish them from other courses that have similar descriptions but would be at the wrong pace, wrong level, or have too much busy work.

So far we have only used one on-line course provider: Art of Problem Solving. A year ago, I posted about our experience with with their precalculus course: Good online math classes. My son did their calculus class this year with the same instructor, and we had similarly good results. The AoPS calculus classes are not cheap ($500 with books), but they were an excellent fit for my son. If I could be assured of as good a fit in other online courses, I would be more willing to use online providers.

This year my son has been keeping time logs for his consultant teacher in the home-school umbrella. For the AoPS calculus class that just ended, he did almost all the weekly and challenge problems, but not quite all. We added up the total hours (class and homework) for February and March, and got 56 hours—just under 7 hours a week. His total workload for all courses (including the cycling that counts as PE) averaged 40.75 hours a week in February, which I regard as about the right amount of time for a high school student to be spending on school. It is certainly much larger than the 2–3 hours a day that some home schoolers regard as adequate. The main advantage for us of home schooling is not a reduction in workload, but a spending the time on appropriate work, rather than busy work or dead time.

I think that the calculus class was a good deal higher workload than the Precalculus class last year, but we did not keep time logs then, so I may be mistaken. My son did not take any of their lower-level classes, so I can’t comment on the workload of any of them (though we did use the intro algebra and intro geometry books some earlier, and were happy with them, which is why I was willing to give AoPS online courses a chance).

My understanding is that by the end of the AoPS calculus course well over half the students had dropped, possibly because they could not keep up with the pace or the workload. You only get your money refunded if you drop in the first 3 weeks, so a lot of families ended up wasting the tuition money. I’m afraid of a similar thing happening if we pick an online course that is not a good fit for our son.

He will probably do one AP practice test before taking the AP Calculus BC test next month, but that should only take about 3.5 hours. The AP test should be a good review of the essential material of the course, but so far as I can tell, the AoPS Calculus class covers more material in greater depth than the usual AP calculus BC course or the usual first-year college calculus class. It is definitely a calculus-for-mathematicians course, with a lot of emphasis on problem solving and rigorous foundations (like using Darboux integrals, a somewhat cleaner equivalent to Riemann integrals). Some of the differential and integral equations they had in the last challenge set seemed difficult even for me (though I must admit that ODE was never my favorite subject, and it has been over 30 years since I last did any differential equation other than a trivial exponential decay).

The AoPS courses also cover complex numbers fairly well, something that is not always done in other precalculus and calculus classes. Another gifted high school student I know has taken calculus through multi-variable calculus at the local community college. I was amazed to find out that he’d had almost nothing about complex numbers: not even such fundamental things as Euler’s formula: . This lack came to light during physics class, when I was deriving acceleration for something moving in a circle by taking the second derivative of with respect to t. It is so much easier to work with exponential functions than trig functions that it didn’t occur to me that the community college calculus classes would not have covered it.